middle school mathematics skills wkbk with answers

Unit 1: Decimals

Lesson 1: Adding Decimals

Lesson 2: Subtracting Decimals

Lesson 3: Multiplying Decimals

Lesson 4: Dividing Decimals

Math Reference for Middle Grades

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Unit �: Decimals—Lesson �, Practice �

CD Exercises Unit 1: Decimals

Lesson 1, Practice 1: Adding Decimals

Example:Findthesumof7.2and4.1.

Step 1:Writeinverticalform,and 7.2 lineupthedecimalpoints. +4.1 Step 2:Bringdownthedecimalpoint. .

Step 3:Add. 7.2 +4.1 11.3

Hints:Ifyoudonothavethesamenumberofdigitstotherightofthedecimalpoint,usezerosasplaceholders.Ifacolumnofnumbersaddsuptomorethannine,carrythetensplacenumbertothenextcolumn.

Write each problem in a vertical format, and find the sum.

1. 8.4+2.5= 2. 9.0+2.3=

3. 1.2+5.1= 4. 4.4+3.2=

5. 13.08+9.1= 6. 2.1+3.8=

7. 5.1+9.2= 8. 3.8+4.7=



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Lesson 1, Practice 2: Adding Decimals

Write each problem in a vertical format, and find the sum.

1. 1.5+6.5= 2. 7.0+3.11=

3. 10.8+7.2= 4. 3.34+2.17=

5. 75.6+3.9= 6. 56.1+83.2=

7. 2.5+6.5= 8. 3.8+5.7=

9. 132.6+45.11= 10. 489.35+24.06=

Unit �: Decimals—Lesson �, Practice �




Answer Keys: Adding Decimals

Lesson 1, Practice 1 1. 10.9 2. 11.3 3. 6.3 4. 7.6 5. 22.18 6. 5.9 7. 14.3 8. 8.5

Lesson 1, Practice 2 1. 8.0 2. 10.11 3. 18.0 4. 5.51 5. 79.5 6. 139.3 7. 9.0 8. 9.5 9. 177.7110. 513.41

Unit �: Decimals—Lesson �, Answer Keys



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Unit �: Decimals—Lesson 2, Practice �


Lesson 2, Practice 1: Subtracting Decimals

Example:Findthedifferenceof29.5and11.7.

Step 1:Writeinverticalform,and 29.5 lineupthedecimalpoints. –11.7 Step 2:Bringdownthedecimalpoint. .

815

Step 3:Subtract.Regroup,orborrow, 29.5 fromthenextcolumnifneeded. –11.7 17.8

Hints:Ifyoudonothavethesamenumberofdigitstotherightofthedecimalpoint,usezerosasplaceholders.

Write each problem in a vertical format, and find the difference.

1. 7.5–3.4= 2. 6.6–5.3=

3. 8.5–8.1= 4. 4.5–2.3=

5. 8.5–7.3= 6. 76.1–2.2=

7. 6.42–2.15= 8. 19.6–3.5=


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Lesson 2, Practice 2: Subtracting Decimals

Write each problem in a vertical format, and find the difference.

1. 5.75–2.39= 2. 61.9–28.7=

3. 15.2–8.7= 4. 69.24–53.97=

5. 78.23–60.97= 6. 5.664–4.793=

7. 53.876–32.774= 8. 11,008.7–10,997.3=

9. 29.8–6.43= 10. 103.27–20.4=

Unit �: Decimals—Lesson 2, Practice 2




Answer Keys: Subtracting Decimals

Lesson 2, Practice 1 1. 4.1 2. 1.3 3. 0.4 4. 2.2 5. 1.2 6. 73.9 7. 4.27 8. 16.1

Lesson 2, Practice 2 1. 3.36 2. 33.2 3. 6.5 4. 15.27 5. 17.26 6. 0.871 7. 21.102 8. 11.4 9. 23.3710. 82.87

Unit �: Decimals—Lesson 2, Answer Keys



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Lesson 3, Practice 1: Multiplying Decimals

Example:Findtheproductof3.0253and79.6.

Step 1:Writeinverticalform. 3.0253 x79.6 Step 2:Multiply. 3.0253 x79.6 181518 272277 211771 24081388

Step 3:Counthowmanydigitsthere 3.0253 aretotherightofthedecimal x79.6 pointinthenumbers.Thisishow240.81388 manydecimalplacesshouldbe intheanswer.

Hints:Ifyoudonothavethesamenumberofdigitstotherightofthedecimalpoint,usezerosasplaceholders.

Write each problem in a vertical format, and find the product.

1. 2.7x3.3= 2. 6.6x1.9=

3. 4.5x3.7= 4. 1.5x2.6=

5. 3.9x4.3= 6. 4.9x8.2=

7. 5.15x2.3= 8. 45.6x5.2=



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Lesson 3, Practice 2: Multiplying Decimals

Write each problem in a vertical format, and find the product.

1. 1.93x48.2= 2. 6.25x4.9=

3. 167.2x1.5= 4. 42.8x31.7=

5. 1.75x6.5= 6.16.7x1.75=

7. 56.4x5.25= 8.9.38x2.13=

9. 0.831x6.2= 10. 11.05x2.195=





Answer Keys: Multiplying Decimals

Lesson 3, Practice 1 1. 8.91 2. 12.54 3. 16.65 4. 3.90 5. 16.77 6. 40.18 7. 11.845 8. 237.12

Lesson 3, Practice 2 1. 93.026 2. 30.625 3. 250.80 4. 1,356.76 5. 11.375 6. 29.225 7. 296.100 8. 19.9794 9. 5.152210. 24.25475




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Lesson 4, Practice 1: Dividing Decimals

Example:Findthequotientof11.797and2.35.

Step 1:Writetheproblemusinglong 5.02 divisionsymbol. 2.35.11.79.70 1175 Step 2:Makethedivisorawholenumber 470 bymovingthedecimaltotheright.470 0 Step 3:Movethedecimalinthedividendthe samenumberofplacesasyoudidin thedivisor.Alsoplaceadecimalinthe samepositionupontheanswerline.Divide. Hints:Ifyoudonothavethesamenumberofdigitstotherightofthedecimalpoint,use

zerosasplaceholders.

Write each problem in a long division format, and find the quotient.

1. 53.167÷7.9= 2. 8.194÷1.7=

3. 9.0÷1.5= 4. 27.5÷4.4=

5. 45.355÷4.7= 6. 61.138÷7.7=

7. 425.248÷9.7= 8. 185.888÷7.4=



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Lesson 4, Practice 2: Dividing Decimals

Write each problem in a long division format, and find the quotient.

1. 300.39÷9.5= 2. 235.69÷9.8=

3. 133.653÷6.9= 4. 394.165÷15.5=

5. 27.39÷4.15= 6.13.5377÷3.97=

7. 203.812÷81.2= 8.17.622÷2.67=

9. 0.0413÷0.1= 10. 0.5238÷0.6=





Answer Keys: Dividing Decimals

Lesson 4, Practice 1 1. 6.73 2. 4.82 3. 6 4. 6.25 5. 9.65 6. 7.94 7. 43.84 8. 25.12

Lesson 4, Practice 2 1. 31.62 2. 24.05 3. 19.37 4. 25.43 5. 6.60 6. 3.41 7. 2.51 8. 6.609. 0.41310. 0.873


Unit 2: Pre-Algebra

Lesson 5: Factors and Greatest Common Factor

Lesson 6: Prime Factorization

Lesson 7: Multiples and Least Common Multiple

Lesson 8: Exponents and Properties of Exponents

Lesson 9: Order of Operations

Lesson 10: Square Roots and Approximating Square Roots

Lesson 11: Scientifi c Notation

Lesson 12: Variables and Evaluating Expressions

Lesson 13: Simplifying Expressions



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Unit 2: Pre-Algebra—Lesson 5, Practice �

CD Exercises Unit 2: Pre-Algebra

Lesson 5, Practice 1: Factors and Greatest Common Factor

Example:FindtheGreatestCommonFactorof18and27.

Factors of 18: 1,2,3,6,9,18 Factors of 27:1,3,9,27

9istheGCFof18and27. True or False?

1. 4isafactorof20 2. 6isafactorof20






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Lesson 5, Practice 2: Factors and Greatest Common Factor

Find the GCF of each pair of numbers

1. 14and49 2.15and75

3. 30and45 4. 18and24

5. 27and90 6.27and84

7. 90and84 8.2,940and3,150

9. 2and12 10. 3and27

Unit 2: Pre-Algebra—Lesson 5, Practice 2



3 CD Exercises Unit 2: Pre-Algebra

Answer Keys: Factors and Greatest Common Factor

Lesson 5, Practice 1 1. T 2. F 3. T 4. F 5. F 6. T 7. T 8.F

Lesson 5, Practice 2 1. 7 2. 15 3. 15 4. 6 5. 9 6. 3 7. 6 8. 2109. 210. 3

Unit 2: Pre-Algebra—Lesson 5, Answer Keys



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Lesson 6, Practice 1: Prime Factorization

Prime numbers are numbers that can be divided by only 1 and the number itself. A factor is a number multiplied by another number to get a product. The prime factors of a number are the prime numbers that, when multiplied together, equal that number.

Example: Find the Prime Factorization of 24.

Step 1: Set up a factor tree.

Step 2: Factor the number until there are only prime factors left. 2 x 2 x 2 x 3 is the Prime Factorization of 24. Find the prime factorization of each number below

1. 62 2. 61

3. 66 4. 83

5. 65 6. 92

7. 200 8. 39

24

Tree level 1: 2 x 12

Tree level 2: 2 x 2 x 6

Tree level 3: 2 x 2 x 2 x 3



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Lesson 6, Practice 2: Prime Factorization

Find the Prime Factorization of each number below

1. 30 2. 420

3. 1,280 4. 36

5. 24 6. 27

7. 48 8. 50

9. 12 10. 15





Answer Keys: Prime Factorization

Lesson 6, Practice 1 1. 2 x 31 2. 61 3. 2 x 3 x 11 4. 83 5. 5 x 13 6. 2 x 2 x 23 7. 2 x 2 x 2 x 5 x 5 8. 3 x 13

Lesson 6, Practice 2 1. 2 x 3 x 5 2. 2 x 2 x 3 x 5 x 7 3. 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 4. 2 x 2 x 3 x 3 5. 2 x 2 x 2 x 3 6. 3 x 3 x 3 7. 2 x 2 x 2 x 2 x 3 8. 2 x 5 x 5 9. 2 x 2 x 310. 3 x 5




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Lesson 7, Practice 1: Multiples and Least Common Multiple

Example:Findthemultiplesof4.

First five multiples of 4: 4,8,12,16,20 Find the first five multiples of each number below

1. 5 2. 10

3. 7 4. 12

5. 15 6. 18

7. 24 8. 6



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Lesson 7, Practice 2: Multiples and Least Common Multiple

Theleastcommonmultiple(LCM)ofasetofnumbersisthesmallestnumberthatisamultipleofallthenumbersintheset.

Example: Multiples of 4:4,8,12,16,20 Multiples of 12:12,24,36,48,60

TheLCMof4and12is12.

Find the LCM of each set of numbers below.

1. 12and15 2. 18and24

3. 9and10 4. 14and42

5. 18and30 6. 8,9,and12

7. 4and5 8. 7and5

9. 2and8 10. 3and6





Answer Keys: Multiples and Least Common Multiple

Lesson 7, Practice 1 1. 5,10,15,20,25 2. 10,20,30,40,50 3. 7,14,21,28,35 4. 12,24,36,48,60 5. 15,30,45,60,75 6. 18,36,54,72,90 7. 24,48,72,96,120 8.6,12,18,24,30

Lesson 7, Practice 2 1. 60 2. 72 3. 90 4. 42 5. 90 6. 72 7. 20 8. 359. 810. 6




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Lesson 8, Practice 1: Exponents and Properties of Exponents

Exponents are used to show repeated multiplication of a number called the base.

Example: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 28

2 is the base, and 8 is the exponent.

Write each number using exponents.

1. 5 x 5 x 5 x 5 2. 8 x 8 x 8 x 8

3. 7 x 7 x 7 4. 4 x 4

5. 10 x 10 x 10 x 10 x 10 6. 12 x 12 x 12

7. 11 x 11 x 11 8. 14 x 14 x 14 x 14

9. 6 x 6 x 6 x 6 x 6 x 6 10. 50 x 50



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Lesson 8, Practice 2: Exponents and Properties of Exponents

Here are some properties of exponents to remember.

A number raised to the zero power equals 1. 50 = 1

Anumberraisedtothefirstpowerequalsthatnumber. 71 = 7

When numbers with the same base are multiplied, add the exponents. 45 x 42 = 45 + 2 = 47

When an exponent is outside the parentheses, (32)4 = 32 x 4 = 38

multiply it by each exponent inside the parentheses. (83 x 82)4 = 812 x 88 = 820

Use properties of exponents to simplify

1. 30 2. 91

3. 102 x 106 4. 62 x 65

5. (2 + 3)2 6. (46)3

7. (83 x 86)2 8. (25)2

9. (34)2 10. 32 x 34





Answer Keys: Exponents and Properties of Exponents

Lesson 8, Practice 1 1. 54

2. 84

3. 73

4. 42

5. 105

6. 123

7. 113

8. 144

9. 66

10. 502

Lesson 8, Practice 2 1. 1 2. 9 3. 108

4. 67

5. 52

6. 418

7. 818

8. 210

9. 38

10. 36




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Lesson 9, Practice 1: Order of Operations

Remember to perform the operations in the correct order from left to right.

P: Parentheses E: Exponents MD: Multiplication/Division AS: Addition/Subtraction

Example: 2 + 3 x 4 = 2 + 12 = 14.

Evaluate using the order of operations.

1. 4 + 3 x 7 = 2. 25 – 8 + 4 =

3. 9 x 2 - 7 = 4. 12 – 6 ÷ 2 =

5. 16 + 10 x 2 = 6. 18 ÷ 6 + 4

7. 9 – 9 ÷ 9 = 8. 16 – 10 ÷ 2 =



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Lesson 9, Practice 2: Order of Operations

Use properties of exponents to simplify

1. (8 – 5) ÷ (6 – 2) = 2. (12 ÷ 4) + (15 ÷ 3) =

3. (16 ÷ 4) + (12 – 4) = 4. (8 + 2) x (12 – 6) =

5. (12 ÷ 2) – (4 x 1) = 6. (18 ÷ 3) – (12 ÷ 4) =

7. 22 x (4 – 2) = 8. 3 x (6 + 3) ÷ 32 – 1 =

9. 32 + (4 + 2) = 10. 2 x (7 + 8) =





Answer Keys: Order of Operations

Lesson 9, Practice 1 1. 25 2. 21 3. 11 4. 9 5. 36 6. 7 7. 8 8. 11

Lesson 9, Practice 2 1. 0.75 2. 8 3. 12 4. 60 5. 2 6. 3 7. 8 8. 2 9. 1510. 30




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CD Exercises Unit 2: Pre-Algebra—Lesson �0, Practice �


Lesson 10, Practice 1: Square Roots and Approximating Square Roots

Raising a number to the second power is called squaring that number.

Example: 32 = 3 x 3 = 9

The opposite of squaring a number is finding the square root.

Example: 25 = 5, because 5 x 5 = 25

Find the square root of each number.

1. 100 2. 4

3. 9 4. 16

5. 121 6. 49

7. 81 8. 36



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Lesson 10, Practice 2: Square Roots and ApproximatingSquare Roots

Find each square root using a calculator and round to the nearest hundredths place.

1. 10 2. 11

3. 54 4. 17

5. 400 6. 127

7. 75 8. 35

9. 18 10. 144

Unit 2: Pre-Algebra—Lesson �0, Practice 2




Answer Keys: Square Roots and Approximating SquareRoots

Lesson 10, Practice 1 1. 10 2. 2 3. 3 4. 4 5. 11 6. 7 7. 9 8. 6

Lesson 10, Practice 2 1. 3.16 2. 3.32 3. 7.35 4. 4.12 5. 20 6. 11.27 7. 8.66 8. 5.92 9. 4.2410. 12

Unit 2: Pre-Algebra—Lesson �0, Answer Keys



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Unit 2: Pre-Algebra—Lesson ��, Practice �


Lesson 11, Practice 1: Scientific Notation

Scientific notation is a way of writing very large or very small numbers.

Examples: 0.029 in standard form equals 2.9 x 10-2 in scientific notation.

672,480 in standard form equals 6.7248 x 105 in scientific notation.

Write each number in scientific notation.

1. 3,652.1 2. 1,975,842

3. 23.54 4. 0.214

5. 0.000987 6. 0.03004

7. 6,523.0012 8. 6.524



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Lesson 11, Practice 2: Scientific Notation

Write each number in standard form.

1. 2.5001 x 102 2. 1.0097 x 104

3. 6.54782 x 106 4. 2.006005 x 105

5. 5.55355 x 10-7 6. 4.97584102 x 10-8

7. 9.1624 x 10-11 8. 3.35795 x 10-9

9. 3.14 x 10-6 10. 1.42 x 103

Unit 2: Pre-Algebra—Lesson ��, Practice 2




Answer Keys: Scientific Notation

Lesson 11, Practice 1 1. 3.6521 x 103

2. 1.975842 x 106

3. 2.354 x 101

4. 2.14 x 10-1

5. 9.87 x 10-4

6. 3.004 x 10-2

7. 6.5230012 x 103

8. 6.524 x 100

Lesson 11, Practice 2 1. 250.01 2. 10,097 3. 6,547,820 4. 200,600.5 5. 0.000000555355 6. 0.0000000497584102 7. 0.000000000091624 8. 0.00000000335795 9. 0.0000031410. 1,420

Unit 2: Pre-Algebra—Lesson ��, Answer Keys



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Unit 2: Pre-Algebra—Lesson �2, Practice �


Lesson 12, Practice 1: Variables and Evaluating Expressions

To evaluate an expression with variables, substitute numbers for the variables and follow the order of operations to solve.

Example: 2x 3 – x 2 + y for x = -3 and y = 2

2(-3)3 – (-3)2 + 2 = 2(-27) – 9 + 2 = -54 – 9 + 2 = -61 Evaluate each expression for x = -3 and y = -7.

1. 3x 3 – 2x + 7y = 2. x ÷ 3 + 4y =

3. 3y 2 = 4. 2x – y =

5. xy = 6. 108 ÷ 9(x – y) =

7. 2x + (3y)2 – 7y + 12y 2 = 8. x 2y =



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Lesson 12, Practice 2: Variables and Evaluating Expressions

Evaluate each expression for x = 2 and y = 5.

1. 6x – 12 = 2. (x + y) ÷ x =

3. x – y = 4. 4x + 5 + y 2 =

5. 2xy = 6. 8y ÷ x =

7. 2x + 2y = 8. 4x =

9. 10x = 10. 10y =





Answer Keys: Variables and Evaluating Expressions

Lesson 12, Practice 1 1. -124 2. -29 3. 147 4. 1 5. 21 6. 3 7. 1,072 8. -63

Lesson 12, Practice 2 1. 0 2. 3.5 3. -3 4. 38 5. 20 6. 20 7. 14 8. 8 9. 2010. 50




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Unit 2: Pre-Algebra—Lesson �3, Practice �


Lesson 13, Practice 1: Simplifying Expressions

To simplify an expression, combine like terms.

Example: 12x 2y 3 + 5x 2y 2 + 7x 2y 2 – 3x 2y 3 (12x 2y 3 – 3x 2y 3) + (5x 2y 2 + 7x 2y 2) 12x 2y 2 + 9x 2y 3

Simplify each expression.

1. 2x + 3y – 2 + 3x + 6y + 7 2. 3b – (4b – 6b + 2) + b

3. 7a – 10a 4. 15b + 9 + 5b – 2

5. 5x 2 + 7x – 2x 2 – 10x + 5 6. -(5x + 7)

7. 2(6x – 5) – 3(5x + 4) 8. (3a + 9) + (7a – 2)



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Lesson 13, Practice 2: Simplifying Expressions

Simplify each expression.

1. 12x – (5x + 2) 2. c – 3c + 7c

3. 2(x + 3) – 3x + 4 4. 0.3x 2 + 1.5x + 0.2x 2 – 0.2x

5. 4x – (9x + 5) 6. 3x + 4x

7. 2x 2 + 3x – 4 – x 2 + x + 9 8. 10x 3 – 14x 2 + 3x – 4x 3 + 4x – 6

9. 3y + 3x + 2y 10. 2x + 3y + 4y





Answer Keys: Simplifying Expressions

Lesson 13, Practice 1 1. 5x + 9y + 5 2. 6b – 2 3. -3a 4. 20b + 7 5. 3x 2 – 3x + 5 6. -5x – 7 7. -3x – 22 8. 10a + 7

Lesson 13, Practice 2 1. 7x – 2 2. 5c 3. -x + 10 4. 0.5x 2 + 1.3x 5. -5x – 5 6. 7x 7. x 2 + 4x + 5 8. 6x 3 – 14x 2 + 7x – 6 9. 5y + 3x10. 2x + 7y


Unit 3: Fractions and Mixed Numbers Lesson 14: Equivalent Fractions

Lesson 15: Simplest Form

Lesson 16: Adding and Subtracting Fractions With Like Denominators

Lesson 17: Adding and Subtracting Mixed Numbers With Like Denominators and No Regrouping

Lesson 18: Adding and Subtracting Fractions With Unlike Denominators

Lesson 19: Adding and Subtracting Mixed Numbers With Unlike Denominators and No Regrouping

Lesson 20: Multiplying Fractions

Lesson 21: Dividing Fractions

Lesson 22: Improper Fractions and Mixed Numbers

Lesson 23: Adding Mixed Numbers With Regrouping

Lesson 24: Subtracting Mixed Numbers With Regrouping

Lesson 25: Multiplying Mixed Numbers

Lesson 26: Dividing Mixed Numbers



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Unit 3: Fractions and Mixed Numbers—Lesson �4, Practice �

CD Exercises Unit 3: Fractions and Mixed Numbers

Lesson 14, Practice 1: Equivalent Fractions

Equivalent fractions are different fractions that name the same amount.

Example: !s = @f & #h

Write two equivalent fractions for each of the given fractions.

1. sUa 2. #j

3. gO; 4. !f

5. !k 6. #f

7. ^k 8. !d



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Lesson 14, Practice 2: Equivalent Fractions

Write two equivalent fractions for each of the given fractions.

1. &k 2. !s%a

3. sU;W; 4. #g

5. #k 6. $g

7. $f$k 8. !j@s

9. !a)s 10. dYh





Answer Keys: Equivalent Fractions

Lesson 14, Practice 1Answers may vary. Examples are given.

1. aRs !d

2. !d%g !s@k

3. aQ;I; aWgU;

4. @k aRh

5. aWh sEf

6. ^k aOs

7. !a@h !s*f

8. @h #l

Lesson 14, Practice 2Answers may vary. Examples are given.

1. !a$h @s!f

2. #f)s $h%d

3. !g*; !f$;$;

4. aY; aOg

5. aYh sOf

6. aI; !a@g

7. @s@f !a!s

8. dYh aEk

9. @s)f #d)h

10. ! j@s aQ;Ik

Unit 3: Fractions and Mixed Numbers—Lesson �4, Answer Keys



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Lesson 15, Practice 1: Simplest Form

When a fraction is written in simplest form, the numerator and denominator have a Greatest Common Factor (GCF) of 1.

Example: aIs = aIs ÷ 4 = @d

Write each fraction in simplest form.

1. !s)f 2. aR;

3. @f 4. $h

5. $k 6. aW;

7. aI; 8. !s);

÷ 4



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Lesson 15, Practice 2: Simplest Form

Write each fraction in simplest form.

1. @k 2. aT;

3. aUs 4. ^l

5. aTg 6. #h

7. ^k 8. #f);

9. !s*f 10. aEg





Answer Keys: Simplest Form

Lesson 15, Practice 1

1. aTs

2. @g

3. !s

4. @d

5. !s

6. !g

7. $g

8. !s


1. !f

2. !s

3. aUs

4. @d

5. !d

6. !s

7. #f

8. #f

9. #f

10. !g




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Lesson 16, Practice 1: Adding and Subtracting FractionsWith Like Denominators

To add fractions with like denominators, add the numerators and write their sum over the de-nominator. Simplify if needed.

Example: #g + $g = &g = �@g

Find the sum. Write your answer in simplest form.

1. #j + @j = 2. aId + !a!d =

3. sIa + !s^a = 4. #k + !k =

5. %l + *l = 6. aUs + aTs =

7. !a%l + aUl = 8. %k + &k =



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Lesson 16, Practice 2: Adding and Subtracting FractionsWith Like Denominators

To subtract fractions with like denominators, subtract the numerators and write the difference over the denominator. Simplify if needed.

Example: ̂j – @j = $j

Find the difference. Write your answer in simplest form.

1. aO; – aE; = 2. $j – !j =

3. aIa – aEa = 4. !a@j – aUj =

5. &k – #k = 6. !a)d – aEd =

7. !s&a – !s#a = 8. aUs – aTs =

9. @h – !h = 10. %d – )d =





Answer Keys: Adding and Subtracting Fractions With LikeDenominators


1. %j

2. 1aYd

3. 1!j

4. !s

5. 1$l 6. 1

7. 1aEl

8. 1!s


1. #g

2. #j

3. aTa

4. aTj

5. !!s

6. aUd

7. sRa

8. !h

9. !h

10. 1@d




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Lesson 17, Practice 1: Adding and Subtracting Mixed Numbers With Like Denominators and No Regrouping

To add mixed numbers with like denominators, add the numerators of the fraction parts and write the sum over the denominator. Then, add the whole numbers. Simplify if needed.

Example: 1#g + 2!g = 3$g


1. 1!k + 3#k = 2. 4%j + 2!j =

3. 1#l + 1%l = 4. 2aRa + 3aYa =

5. 1aTs + 2aQs = 6. 1@g + 2!g =

7. 3!j + 2$j = 8. 5$l + 2!l =



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Lesson 17, Practice 2: Adding and Subtracting Mixed Numbers With Like Denominators and No Regrouping

To subtract mixed numbers with like denominators, subtract the numerators of the fraction parts and write the difference over the denominator. Then, subtract the whole numbers. Simplify if needed.

Example: 7aO; – 5aR; = 2aT; = 2!s


1. 2#f – 1!f = 2. 3@d – 2!d =

3. 6$g – 3!g = 4. 6%l – 2$l =

5. 3^j – 1$j = 6. 4&k – 2%k =

7. 5@d – 2!d = 8. 4#f – 3!f =

9. 5%h – 2#h = 10. 9!s – 7!s =





Answer Keys: Adding and Subtracting Mixed Numbers With Like Denominators and No Regrouping


1. 4!s 2. 6̂j 3. �*l

4. 5!a)a 5. 3!s 6. 3#g 7. 5%j 8. 7%l


1. 1!s 2. 1 !d 3. 3#g 4. 4!l 5. 2@j 6. � !f 7. 3!d 8. 1!s 9. 3!d10. 2




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Lesson 18, Practice 1: Adding and Subtracting FractionsWith Unlike Denominators

To add fractions with unlike denominators, find equivalent fractions with common denominators. Then, add the fractions, and simplify if needed.

Example:!s + #k =$k +#k = &k


1. @d + aIg= 2. !s + !a*k=

3. aTs + @s#f = 4. @d#h + !a!k=

5. @f@g + $l= 6. !d!; + aU;=

7. !s%k + $j= 8. !a#a + $g=



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Lesson 18, Practice 2: Adding and Subtracting FractionsWith Unlike Denominators

To subtract fractions with unlike denominators, find equivalent fractions with common denomina-tors. Then, subtract the fractions, and simplify if needed.

Example:#f – !d =aOs –aRs = aTs


1. %k – !f= 2. %h – !d =

3. !a&k – %l= 4. #g – sU; =

5. %k – aEh= 6. #f – aTs=

7. $g – aWg= 8. #g – sUg=

9. $g –aW; = 10. @d –aWg =





Answer Keys: Adding and Subtracting Fractions With Unlike Denominators


1. 1!g

2. 1!s

3. 1 #k

4. 1!f

5. !a$g

6.1aQg

7.1sEk

8.1%g$g


1. #k

2. !s

3. aUk

4. !f

5. aUh

6.!d

7. @d

8. sIg

9. #g

10. aIg




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Lesson 19, Practice 1: Adding and Subtracting Mixed Numbers With Unlike Denominators and No Regrouping

To add mixed numbers with unlike denominators, find equivalent fractions with common denominators for the fractions parts. Then, add the fractions and add the whole numbers. Simplify if needed.

Example:1&k + 2!a#h =1!a$h +2!a#h = 4!a!h


1. 3!d + 1$l= 2. 1aWk + 1%h=

3. 3aTf + 1@j = 4. 4aQ; + 1#g=

5. 1aTs + 1!s= 6. 1!k + 1aU;=

7. 1!d + 1#k= 8. 1aUs + 1@j=



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Lesson 19, Practice 2: Adding and Subtracting Mixed Numbers With Unlike Denominators and No Regrouping

To subtract mixed numbers with unlike denominators, find equivalent fractions with common denominators for the fraction parts. Then, subtract the fractions and subtract the whole numbers. Simplify if needed.

Example:5@d – 2!h =5$h –2!h = 3#h =3!s


1. 4#f – 2#k= 2. 5aU; – 3!g =

3. 3 Qq Et – 1$g= 4.6#j – 2aEf=

5. 4aIa – 3!s#s= 6. 1aO; – 1dU;=

7. 2%j – 1!h= 8. 4$g – 1@l=

9. 9!j –6!k = 10. 10@h –6!g =





Answer Keys: Adding and Subtracting Mixed Numbers With Unlike Denominators and No Regrouping


1. 4&l

2. 2 Qq Ui

3. 4aOf

4. 5aU;

5. 2!a!s

6. 2 Er Ep

7. 2 Qw Ur

8.3 Ui Er


1. 2#k

2. 2!s

3. 2aQg

4. 4aEf

5. �sEs

6.@d

7. 1@f#s

8. 3 Wr Yt

9. 3gQh

10. 4aWg




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Unit 3: Fractions and Mixed Numbers—Lesson 20, Practice �


Lesson 20, Practice 1: Multiplying Fractions

To multiply fractions, multiply the numerators and multiply the denominators. Simplify if needed.

Example: !g x #f = = sE;

Find the product. Write your answer in simplest form.

1. %l x *j = 2. ^j x !a)a =

3. #j x aOa = 4. *d x $j =

5. !a#g x %l = 6. aY; x aOd =

7. $l x aIg = 8. !j x #k =

1 x 35 x 4



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Lesson 20, Practice 2: Multiplying Fractions


1. aUg x aYa = 2. !s)a x #d%j =

3. !a%j x QjW = 4. $g!d x !a@j =

5. @s!j x #f*a = 6. !a*a x aTs =

7. @j x %k = 8. ^j x #j =

9. @f x aEg = 10. @d x @k =

Unit 3: Fractions and Mixed Numbers—Lesson 20, Practice 2




Answer Keys: Multiplying Fractions


1. $h)d

2. ^j)j

3. @j&j

4. 1!s!a

5. !s#j

6. @h&g

7. aEdWg

8. gEh


1. !g$g

2. aTaPa

3. 1aYaQl

4. $l(;@a

5. @d^h^l

6. !s%s

7. sTk

8. !f*l

9. aQ;

10. !h

Unit 3: Fractions and Mixed Numbers—Lesson 20, Answer Keys



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Unit 3: Fractions and Mixed Numbers—Lesson 2�, Practice �


Lesson 21, Practice 1: Dividing Fractions

To divide fractions, write the reciprocal of the second fraction. Then, multiply the fractions. Sim-plify if needed.

Example: !f ÷ #g = !f x %d = aTs

Find the quotient. Write your answer in simplest form.

1. !g ÷ @j = 2. #j ÷ $l =

3. @l ÷ %k = 4. &l ÷ !k =

5. !a@d ÷ $h = 6. !a!s ÷ aQd =

7. aWg ÷ !a!s = 8. aOg ÷ #f =



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Lesson 21, Practice 2: Dividing Fractions


1. #g ÷ $j = 2. !a@d ÷ !a$g =

3. ^j ÷ &l = 4. !a!g ÷ !a)a =

5. @f#a ÷ !a@g = 6. !s^; ÷ !a(g =

7. !a#g ÷ !a&k = 8. @j ÷ aEa =

9. #g ÷ aW; = 10. $g ÷ #g =

Unit 3: Fractions and Mixed Numbers—Lesson 2�, Practice 2




Answer Keys: Dividing Fractions


1. aU;

2. @s&k

3. !f^g

4. 6@l

5. 1aTd

6. 11!a!s

7. gIg

8. $g


1. 1sQ;

2. (l)a

3. 1fTl

4. !a@g!;

5. Qq Qy Tr

6. !a@l

7. &k*g

8. 1sQa

9. 3

10. 1!d

Unit 3: Fractions and Mixed Numbers—Lesson 2�, Answer Keys



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Lesson 22, Practice 1: Improper Fractions and Mixed Numbers

To rewrite an improper fraction as a mixed number, divide the numerator by the denominator. The number of times the denominator divides evenly into the numerator is the whole number of the mixed number. Write the remainder over the original denominator. This is the fractional part of the mixed number.

Example: &s = 7 ÷ 2 = 3 r 1 = 3!s

Rewrite each improper fraction as a mixed number. Write your answer in simplest form.

1. QfQ 2. &f

3. QgU 4. *d

5. #s!; 6. ElE

7. ^s%; 8. RkT



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Lesson 22, Practice 2: Improper Fractions and Mixed Numbers

To rewrite a mixed number as an improper fraction, multiply the denominator by the whole num-ber, and then add the numerator. Write this number as the numerator over the original denomi-nator.

Example: 9&k = (8 x 9) + 7 = 79 = JiL

Rewrite each mixed number as an improper fraction.

1. 3@g 2. 2#f

3. 1#f 4. 2@d

5. 1!s!; 6. 3@d

7. 3!f 8. 5%k

9. 2!s 10. 3!k





Answer Keys: Improper Fractions and Mixed Numbers


1. 2#f

2. 1#f

3. 3@g

4. 2@d

5. 1!s!;

6. 3@d

7. 3!f

8. 5%k


1. QgU

2. QfQ

3. &f

4. *d

5. #s!;

6. AeA

7. ArD

8. RkT

9. %s

10. SiG




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Lesson 23, Practice 1: Adding Mixed Numbers With Regrouping

Sometimes when you add, you end up with a mixed number that contains an improper fraction. Convert that improper fraction to a mixed number and add it to the whole number from your original answer. Simplify if needed.

Example: 1$g + 3aU; = 1aI; + 3aU; = 4 Qq Tp = 5aT; = 5!s


1. 5@d + 3$l = 2. 5@j + 2 Qq Pr =

3. 2 Qq Qw + 2!f = 4. 3aOg + 2#g =

5. 5 Qw Wq + 6@d = 6. 1$j + 1aYa =

7. 2$g + 2%l = 8. 3@d + 3aRa =



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Lesson 23, Practice 2: Adding Mixed Numbers With Regrouping


1. 2%h + 6dI; = 2. 5&k + 4 Qr Pi =

3. 9%l + 5 Wr Ut = 4. 5 Ey Ir + 1%k =

5. 2 Rr Pt + 4@g = 6. 3 Yu Rw + 5#k =

7. 1 Tt Pt + 5aUa = 8. 4 Qq Qy + 5&l =

9. 8aO; + 3aO; = 10. 8aO; + 2aQ; =





Answer Keys: Adding Mixed Numbers With Regrouping


1. 9!l

2. 8

3. 5!h

4. 6!g

5. 12sTa

6. 3jOj

7. 5!f^g

8. 7dQd


1. 9aQ;

2. 10aQs

3. 15fUg

4. 7dUs

5. 7 Qr Et

6. 9 Qu Ow

7. 7aYa

8. 10aYfUf

9. 12$g

10. 11




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Lesson 24, Practice 1: Subtracting Mixed Numbers With Regrouping

Sometimes when you are subtracting mixed numbers, the second fractional part is larger than the first fractional part. You need to regroup by borrowing 1 from the whole number and adding it to the smaller fractional part. Then, you can subtract. Simplify if needed.

Example: 3!f – 1!d = 3aEs – 1aRs = 2 Qq Tw – 1aRs = 1!a!s


1. 7!k – 2#f = 2. 6!l – 5!d =

3. 5aR; – 2$g = 4. 6!g – 5 Qw Rt =

5. 7sEk – 6!f = 6. 7!d – 4#d!h =

7. 3!f – 2!d = 8. 4!h – 3!g =



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Lesson 24, Practice 2: Subtracting Mixed Numbers With Regrouping


1. 5!k – 4@j = 2. 5#g – 3 Qq Qt =

3. 6#f – 5 Qw Up = 4. 7!s – 5 Qq Er =

5. 6dQh – 5!d = 6. 9sQa – 6@j =

7. 8!l – 6gOf = 8. 7!l – 3!k =

9. 9#l – 5%l = 10. 9!s – 4#f =





Answer Keys: Subtracting Mixed Numbers With Regrouping


1. 4#k

2. &l

3. 2#g

4. Qw Yt

5. ^j

6. 2 Qe Uy

7. Qq Qw

8. We Op


1. Rt Uy

2. 1 Qq Et

3. aO;

4. 1$j

5. We Ty

6. 2 Qw Yq

7. 1 Qq Ui

8. 3&j!s

9. 3&l

10. 4#f




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Lesson 25, Practice 1: Multiplying Mixed Numbers

To multiply mixed numbers, first convert the mixed numbers to improper fractions. Then, multiply the numerators and multiply the denominators. Simplify if needed.

Example: 1@g x 2#j =&g xQjU = 3@g


1. 1@d x 2$g= 2. 3$g x 2!l=

3. 1^j x 2&k = 4. 2!a#g x 1!a!s=

5. 3$g x 2*l= 6. 1aO; x 2&l =

7. 1!a!g x 2!a@h= 8. 1%l x 2aId=



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Lesson 25, Practice 2: Multiplying Mixed Numbers


1. 2$j x 3aUh= 2. 1aTa x 2!a&l =

3. 2@s!d x 3aIj= 4. 2!a@g x 3%l=

5. 2aUa x 3!g= 6. 1aIj x 2%h =

7. 3%j x 6aOd= 8. 1$j x 1aOa=

9. 4@k x3@l = 10. 7!h x4@g =





Answer Keys: Multiplying Mixed Numbers


1. 4@d

2. 8fQg

3. 5!g(h

4. 5aIkO;

5. 10$f$g

6. 5aTk

7. 4 We Ep

8.4 q Iq u


1. 8$g&h

2. 4aRl

3. 10dRlEa

4. 9$f#g

5. 8@g$g

6.4!h

7. 24^j

8. 2^j

9. 13 We Ty

10. 31aIg




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Lesson 26, Practice 1: Dividing Mixed Numbers

To divide mixed numbers, first convert them to improper fractions. Then, invert the second frac-tion and multiply. Simplify if needed.

Example:1!d ÷ 1@g =$d ÷&g =$d x%j = @s)a


1. 2#f ÷ 1%l= 2. 1#k ÷ 1$l=

3. 2^j ÷ 1@j = 4. 3!f ÷ 1!f=

5. 2!d ÷ 1!f= 6. 1aO; ÷ 1!j =

7. 2#f ÷ 1@d= 8. 1%j ÷ 1@d=



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Lesson 26, Practice 2: Dividing Mixed Numbers


1. 3!d ÷ 2@g= 2.4!j ÷ 2!k =

3. 6#f ÷ 1@d= 4.2!f ÷ 1!d=

5. 1%l ÷ 1!d= 6.2%h ÷ 1@d =

7. 4@d ÷ 1!g= 8.6!d ÷ 1@g=

9. 6aEa ÷3@h = 10. 5!h ÷4aTs =





Answer Keys: Dividing Mixed Numbers


1. 1$g#h

2. aO;Of

3. 2@l

4. 2#g

5. 1!a#g

6. 1%k#;

7. 1!s#;

8.1dQg


1. 1aUk

2. 1!a!a#l

3. 4sQ;

4. 1!a!h

5. 1!h

6.1aU;

7. 3*l

8. 4!s!a

9. 1aOaU;

10. 1gOd


Unit 4: Ratio, Proportion, and Percents

Lesson 27: Ratio and Proportion

Lesson 28: Solving Proportions

Lesson 29: Similar Figures and Scale Factor

Lesson 30: Fractions and Percents

Lesson 31: Decimals and Percents

Lesson 32: Using and Finding Percents

Lesson 33: Percent Increase and Decrease



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Unit 4: Ratio, Proportion, and Percents—Lesson 27, Practice �

CD Exercises Unit 4: Ratio, Proportion, and Percents

Lesson 27, Practice 1: Ratio and Proportion

Write a ratio of two numbers in the order they are given in the problem. Ratios can be written in

three different forms: 15 to 10, 15:10, or Qq Tp .

Example: There are 3 CDs, 4 marbles, 7 books, and 1 orange.

What is the proportion of books to marbles? 7:4

Write each ratio. Use the form 15:10.

1. CDs to marbles 2. marbles to oranges

3. books to CDs 4. CDs to oranges

5. marbles to books 6. books to oranges

7. CDs to total 8. marbles to total



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Lesson 27, Practice 2: Ratio and Proportion

Two ratios form a proportion if their cross products are equal.

Example: ̂l aIs 6 x 12 = 72 9 x 8 = 72 so ̂l = aIs

Write = or ≠ in the box to tell whether each pair of ratios form a proportion.

1. &a kRa 2. #f ^k

3. &f @d)g 4. @d !a^;

5. *d !f^s 6. aR; @a%;

7. $j #s%; 8. #s !a^;

9. !s #h); 10. #f @g

Unit 4: Ratio, Proportion, and Percents—Lesson 27, Practice 2




Answer Keys: Ratio and Proportion

Lesson 27, Practice 1 1. 3:4 2. 4:1 3. 7:3 4. 3:1 5. 4:7 6. 7:1 7. 3:15 8. 4:15

Lesson 27, Practice 2 1. ≠ 2. = 3.≠ 4. ≠ 5.≠ 6.≠ 7.≠ 8.≠ 9. = 10. ≠

Unit 4: Ratio, Proportion, and Percents—Lesson 27, Answer Keys



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CD Exercises Unit 4: Ratio, Proportion, and Percents—Lesson 28, Practice �


Lesson 28, Practice 1: Solving Proportions

You can solve a proportion by multiplying to find the cross products and dividing to find the un-known quantity.

Example: 15 x 3.30

= 120 3.30 • x = 3.30x 15 • 120 = 1,800

3.30x = 1,800 3.30 3.30

x = 545.45

Solve each proportion using cross products.

1. 1.2 12 2. 6 y 5

= x 8

= 24

3. 25 32 4. 6 7 20

= x 3

= x

5. 5 8 6. 13 m 50

= x 6

= 60

7. 9 8 8. 3 x w

= 3 4

= 21



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Lesson 28, Practice 2: Solving Proportions

Solve each proportion using cross products.

1. 8 60 2. 3.6 50 6

= x 30

= x

3. 1 120 4. 4 21 24

= x 3

= x

5. a 39 6. 3 b 13

= 60 6

= 7

7. 8 24 8. w 3 6

= y 9

= 8

9. x 5 10. y 3 3

= 10 2

= 4





Answer Keys: Solving Proportions

Lesson 28, Practice 1 1. x = 50 2. y = 18 3. x = 25.6 4. x = 3.5 5. x = 80 6. m = 130 7. w = 3.375 8. x = 15.75

Lesson 28, Practice 2 1. x = 45 2. x = 416.67 3. x = 2,880 4. x = 15.75 5. a = 8.45 6. b = 3.5 7. y = 18 8. w = 3.375 9. x = 1.510. y = 1.5




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Lesson 29, Practice 1: Similar Figures and Scale Factor

To find out if two figures are similar, set up ratios of the corresponding sides and find the cross products. If they are equal, the figures are similar. The scale factor is the ratio all the ratios re-duce to.

Example:

$k=@f, 4 x 4 = 16, 8 x 2 = 16, so the figures are similar.

The scale factor = !s.

Determine if the figures are similar. If they are, find the scale factor.

1. 2.

3. 4.

5. 6.

7. 8.

4 in.

8 in.

2 in.

4 in.

6 cm8 cm

10 cm

2 cm

5 cm

4 cm 6 cm8 cm

10 cm

12 cm16 cm

20 cm

3 in.

4 in.

5 in. 9 in.15 in.

12 in.

4 in. 4 in.

5 in.

12 in. 14 in.

20 in.

7 cm

10 cm

14 cm

20 cm

7 cm

10 cm

3.5 cm

5 cm

3 in.4 in. 15 in.

20 in.

3 in.4 in.

20 in.

26 in.



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Lesson 29, Practice 2: Similar Figures and Scale Factor

Determine if the figures are similar. If they are, find the scale factor.

1. Rectangles that are 6 x 9 inches 2. Rectangles that are 6 x 9 inches and 42 x 63 inches and 42 x 72 inches

3. Rectangles that are 2 x 3 inches 4. Rectangles that are 20 x 30 inches and 18 x 27 inches and 2 x 3 inches

5. Triangles that are 10 cm x 8 cm x 10 cm 6. Triangles that are 10 cm x 8 cm x 10 cm and 5 cm x 4 cm x 5 cm and 30 cm x 24 cm x 30 cm

7. Triangles that are 7 cm x 5 cm x 7 cm 8. Triangles that are 7 cm x 5 cm x 10 cm and 28 cm x 30 cm x 28 cm and 35 cm x 25 cm x 50 cm





Answer Keys: Similar Figures and Scale Factor


1. No

2. Yes, !s

3. Yes, !d

4. No

5. Yes, !s

6. Yes, @a

7. Yes, !g

8. No


1. Yes, !j

2. No

3. Yes, !l

4. Yes, QaP

5. Yes, @a

6. Yes, !d

7.No

8. Yes, !g




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Lesson 30, Practice 1: Fractions and Percents

To change a fraction to a percent, write it as a fraction with 100 as the denominator. Then, write the numerator with a percent sign.

Example: aW;P; = 20%

If the denominator is not 100, set up a proportion and find the value of x.

Example: aW; aW; = 100 10x = 2 • 100

10x ÷ 10 = 200 ÷ 10

x = 20

aW;P; = 20% Write each fraction as a percent.

1. !g 2. !f

3. !s 4. #f

5. !d 6. @d

7. $g 8. @g

x



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Lesson 30, Practice 2: Fractions and Percents

To write a percent as a fraction, write the number as a numerator over a denominator of 100. Then, simplify the fraction if needed.

Example: 55% = aT;T; = Qw Qp

Write each percent as a fraction.

1. 80% 2. 66%

3. 40% 4. 20%

5. 50% 6. 33%

7. 25% 8. 75%

9. 70% 10. 90%





Answer Keys: Fractions and Percents

Lesson 30, Practice 1 1. 20% 2. 25% 3. 50% 4. 75% 5. 33% 6. 66% 7. 80% 8. 40%


1. $g

2. Et Ep or also accept @d

3. @g

4. !g

5. !s

6. aE;E; or also accept !d

7. !f

8. #f

9. aU;

10. aO;




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Unit 4: Ratio, Proportion, and Percents—Lesson 3�, Practice �


Lesson 31, Practice 1: Decimals and Percents

To write a decimal as a percent, move the decimal point two places to the right, and add a per-cent sign.

Example: 0.5 = 50%

Write each decimal as a percent.

1. 1 2. 0.36

3. 0.275 4. 0.4

5. 0.05 6. 0.0125

7. 0.01 8. 0.47

9. 2.36 10. 0.008



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Lesson 31, Practice 2: Decimals and Percents

To write a percent as a decimal, move the decimal point two places to the left, and drop the per-cent sign. Be sure to put a zero in the ones place if there is not already a number there.

Example: 16% = 0.16

Write each percent as a decimal.

1. 0.2% 2. 70%

3. 33% 4. 6%

5. 36% 6. 68%

7. 37.5% 8. 63%

9. 188% 10. 5.2%

Unit 4: Ratio, Proportion, and Percents—Lesson 3�, Practice �




Answer Keys: Decimals and Percents

Lesson 31, Practice 1 1. 100% 2. 36% 3. 27.5% 4. 40% 5. 5% 6. 1.25% 7. 1% 8. 47% 9. 236%10. 0.8%

Lesson 31, Practice 2 1. 0.002 2. 0.7 3. 0.33 4. 0.06 5. 0.36 6. 0.68 7. 0.375 8. 0.63 9. 1.88 10. 0.052

Unit 4: Ratio, Proportion, and Percents—Lesson 3�, Answer Keys



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Lesson 32, Practice 1: Using and Finding Percents

To find the percent of a number, change the percent to a decimal, and then multiply.

Example: 25% of 60 = 0.25 • 60 = 15

Find the given percent of each number.

1. 53% of 225 2. 0.5% of 1,000

3. 28.75% of 375 4. 78.75% of 980

5. 350% of 250 6. 82% of 500

7. 25% of 300 8. 65% of 24,500

9. 2.3% of 82 10. 9% of 32



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Lesson 32, Practice 2: Using and Finding Percents

Sometimes, you need to know the percent of one number another number is. To find the percent, divide the second number by the first number. Then, change the decimal to a percent.

Example: What percent of 200 is 40? 40 ÷ 200 = 0.2 = 20%

Find what percent of a number the given number is in each question below.

1. What percent of 300 is 75? 2. What percent of 2,000 is 40?

3. What percent of 86 is 10.32? 4. What percent of 240 is 50?

5. What percent of 40 is 3? 6. What percent of 50 is 15?







Answer Keys: Using and Finding Percents

Lesson 32, Practice 1 1. 119.25 2. 5 3. 107.8125 4. 771.75 5. 875 6. 410 7. 75 8. 15,925 9. 1.88610. 2.88

Lesson 32, Practice 2 1. 25% 2. 2% 3. 12% 4. 20.83% 5. 7.5% 6. 30% 7. 11.1% 8. 16% 9. 50%10. 33.3%




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Lesson 33, Practice 1: Percent Increase and Decrease

To find the percent increase, subtract the original number from the higher number. Then, divide the difference by the original amount, and write as a percent.

Example: 112 to 150 150 – 112 = 38 38 ÷ 112 = 0.339

0.399 • 100 = 33.9%

Find each percent increase. Round to the nearest tenth of a percent, if needed.

1. 50 to 75 2. 32 to 60

3. 80 to 100 4. 45 to 90

5. 45 to 100 6. 106 to 110

7. 66 to 75 8. 95 to 100

9. 170 to 255 10. 8 to 19



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Lesson 33, Practice 2: Percent Increase and Decrease

To find the percent decrease, subtract to find the difference. Then, divide by the original amount, and write as a percent.

Example: 125 to 95 125 – 95 = 30 30 ÷ 125 = 0.24

0.24 x 100 = 24%

Find each percent decrease. Round to the nearest tenth of a percent, if needed.

1. 90 to 50 2. 225 to 190

3. 180 to 80 4. 72 to 65

5. 120 to 85 6. 46 to 25

7. 75 to 50 8. 84 to 60

9. 60 to 30 10. 100 to 75





Answer Keys: Percent Increase and Decrease

Lesson 33, Practice 1 1. 50% 2. 87.5% 3. 25% 4. 100% 5. 122.2% 6. 3.8% 7. 13.6% 8. 5.3% 9. 50%10. 137.5%

Lesson 33, Practice 2 1. 44.4% 2. 15.6% 3. 55.5% 4. 9.7% 5. 29.2% 6. 45.7% 7. 33.3% 8. 28.6%9. 50%10. 25%


Unit 5: Integers

Lesson 34: Adding Integers

Lesson 35: Subtracting Integers

Lesson 36: Multiplying and Dividing Integers

Lesson 37: Coordinate Graphs



Name: Date:

Unit 5: Integers—Lesson 34, Practice �

CD Exercises Unit 5: Integers

Lesson 34, Practice 1: Adding Integers

If both integers are positive, add as usual. The answer will be positive.

Example: 11 + 17 = 28

If both integers are negative, add as usual. The answer will be negative.

Example: -6 + (-7) = -13

If the integers have different signs, find the difference of the numbers, and give the answer the sign of the number with the greater absolute value.

Examples: 9 + (-5) = 9 – 5 = 4 (-13) + 6 = -7

Find the sum.

1. 8 + (-3) = 2. -18 + 8 =

3. 7 + (-8) = 4. -9 + 11 =

5. -13 + (-7) = 6. -7 + (-12) =

7. 19 + (-25) = 8. -12 + 21 =

9. 8 + 21 = 10. -32 + (-5) =



Name: Date:


Lesson 34, Practice 2: Adding Integers

Find the sum.

1. 6 + 9 = 2. -15 + 27 =

3. 9 + (-4) = 4. -8 + (-15) =

5. 12 + (-9) = 6. -20 + 7 =

7. -20 + (-15) = 8. -5 + 9 =

9. -1 + 5 = 10. 0 + (-4) =





Answer Keys: Adding Integers

Lesson 34, Practice 1 1. 5 2. -10 3. -1 4. 2 5. -20 6. -19 7. -6 8. 9 9. 2910. -37

Lesson 34, Practice 2 1. 15 2. 12 3. 5 4. -23 5. 3 6. -13 7. -35 8. 4 9. 410. -4

Unit 5: Integers—Lesson 34, Answer Keys



Name: Date:



Lesson 35, Practice 1: Subtracting Integers

Subtracting a negative number is the same as adding a positive number.

Examples: -1 – 5 = -1 + (-5) = -6 7 – (-3) = 7 + 3 = 10

Find the difference.

1. -5 – 6 = 2. 5 – (-6) =

3. -14 – 3 = 4. 14 – (-3) =

5. -10 – 7 = 6. 10 – (-7) =

7. -3 – 15 = 8. 3 – (-15) =



Name: Date:


Lesson 35, Practice 2: Subtracting Integers

Find the difference.

1. -9 – (-5) = 2. -9 – 5 =

3. -11 – 7 = 4. -11 – (-7) =

5. -6 – (-9) = 6. -6 – 9 =

7. -5 – 12 = 8. -5 – (-12) =

9. -8 – (-9) = 10. 1 – (-8) =





Answer Keys: Subtracting Integers

Lesson 35, Practice 1 1. -11 2. 11 3. -17 4. 17 5. -17 6. 17 7. -18 8. 18

Lesson 35, Practice 2 1. -4 2. -14 3. -18 4. -4 5. 3 6. -15 7. -17 8. 7 9. 110. 9




Name: Date:



Lesson 36, Practice 1: Multiplying and Dividing Integers

If the signs of the integers in a multiplication problem are the same, then the answer is positive.

Examples: 3 x 5 = 15 -2 x -9 = 18

If the signs of the integers in a multiplication problem are different, then the answer is negative.

Examples: -3 x 5 = -15 2 x -9 = -18

Find the product.

1. -9 x 52 = 2. 65 x 21 =

3. 7 x -18 = 4. -37 x 12 =

5. -25 x 6 = 6. -45 x -17 =

7. 31 x -8 = 8. 76 x -38 =

9. -28 x -7 = 10. -89 x -24 =



Name: Date:


Lesson 36, Practice 2: Multiplying and Dividing Integers

If the signs of the integers in a division problem are the same, then the answer is positive.

Examples: 20 ÷ 4 = 5 -32 ÷ -8 = 4

If the signs of the integers in a division problem are different, then the answer is negative.

Examples: 20 ÷ -4 = -5 -32 ÷ 8 = -4

Find the quotient. Round to the nearest hundredth if necessary.

1. -28 ÷ -7 = 2. -32 ÷ -4 =

3. 30 ÷ -6 = 4. -14 ÷ 2 =

5. -54 ÷ 9 = 6. -520 ÷ -84 =

7. -84 ÷ -12 = 8. 831 ÷ -18 =

9. 148 ÷ -4 = 10. -85 ÷ -5 =





Answer Keys: Multiplying and Dividing Integers

Lesson 36, Practice 1 1. -468 2. 1,365 3. -126 4. -444 5. -150 6. 765 7. -248 8. -2,888 9. 19610. 2,136

Lesson 36, Practice 2 1. 4 2. 8 3. -5 4. -7 5. -6 6. 6.19 7. 7 8. -46.17 9. -3710. 17




Name: Date:



Lesson 37, Practice 1: Coordinate Graphs

The first number in an ordered pair is the x-coordinate. The second number is the y-coordinate. To find a point, move right or left to the x-coordinate and up or down to the y-coordinate.

Example: B = (3, 2)

Write the ordered pairs that represent the location of the following points on the coordi-nate grid below.

1. A

2. B

3. C

4. D

5. E

6. F

7. G

8. H

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

109876543210

-1-2-3-4-5-6-7-8-9

-10

x-axis

y-axis

B

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

x-axis

y-axis

A

B

C

D

E

F

G

H



Name: Date:


Lesson 37, Practice 2: Coordinate Graphs

Plot the points with the given coordinates on the grid below.

1. K (-5, 7)

2. M (-8, -3)

3. O (9, 0)

4. I (8, 5)

5. P (0, -3)

6. N (1, -4)

7. L (8, 6)

8. J (-5, -9)

9. Q (-8, 5)

10. R (5, 5)


-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

x-axis

y-axis




Answer Keys: Coordinate Graphs

Lesson 37, Practice 1 1. (-4, 0) 2. (-7, 2) 3. (5, -1) 4. (-3, -6) 5. (0, 9) 6. (4, 6) 7. (3, -2) 8. (5, 7)



-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

x-axis

y-axis

K

M

O

I

P

N

L

J

Q R

Unit 6: Geometry and Measurement

Lesson 38: Perimeter

Lesson 39: Circumference

Lesson 40: Area of Rectangles and Parallelograms

Lesson 41: Area of Triangles

Lesson 42: Area of Trapezoids

Lesson 43: Area of Circles

Lesson 44: Surface Area of Rectangular and Triangular Prisms

Lesson 45: Surface Area of Cylinders

Lesson 46: Volume

Lesson 47: Pythagorean Theorem

Lesson 48: Angle Relationships and Intersecting Lines

Lesson 49: Angle Relationships and Parallel Lines



Name: Date:

Unit 6: Geometry and Measurement—Lesson 38, Practice �

CD Exercises Unit 6: Geometry and Measurement

Lesson 38, Practice 1: Perimeter

To find the perimeter of any polygon, add the lengths of all the sides.

Example: Perimeter = 35 + 35 + 56 = 126 cm

Find the perimeter.

1. P = 2. P =

3. P = 4.P =

5. P = 6. P =

7. P = 8. P =

35 cm35 cm

56 cm

36 in.

48 in.

60 in.36 in.

80 in.

50 cm

105 cm5 ft.

5 ft.

3 ft.

3 ft.

7 ft.

8 cm

12 cm

12 cm

12 cm

7 ft.

4 ft.

10 ft.

5 ft.8 in.

10 in.



Name: Date:


Lesson 38, Practice 2: Perimeter

Find the perimeter.

1. P = 2. P =

3. P = 4. P =

5. P = 6. P =

7. P = 8. P =


30 cm

24 cm25 cm

10 cm

20 ft.

25 ft.

30 ft.

25 cm 25 cm

10 cm

6 in.

8 in.

4 in.

10 in.

25 cm6 ft.

12 ft.

6 in.6 in.

10 in.10 in.

24 in.




Answer Keys: Perimeter

Lesson 38, Practice 1 1. 144 in. 2. 232 in. 3. 310 cm 4. 23 ft. 5. 40 cm 6. 48 cm 7. 26 ft. 8. 36 in.

Lesson 38, Practice 2 1. 59 cm 2. 75 ft. 3. 60 cm 4. 28 in. 5. 100 cm 6. 36 ft. 7. 56 in. 8. 150 cm

Unit 6: Geometry and Measurement—Lesson 38, Answer Keys



Name: Date:



Lesson 39, Practice 1: Circumference

The circumference is the distance around a circle. Find the circumference of a circle using this formula: C = 2πr.

r = radius (distance from the center of the circle to the edge of the circle) π is pronounced pi and is approximately equal to 3.14

Example: r = 4.75 in. C = 2 x 3.14 x 4.75 = 29.83 in.

If you are given the diameter (distance through the center of the circle from edge to edge), first divide the diameter by 2 to get the radius. Find each circumference. Use 3.14 for pi.

1. r = 15 m C = 2. d = 10 ft. C =

3. r = 10 in. C = 4. d = 3.5 cm C =

5. r = 6 in. C = 6. d = 15 cm C =

7. r = 4.5 ft. C = 8. d = 30 m C =

15 m 10 ft.

10 in.

6 in.

4.5 ft.

3.5 cm

15 cm

30 m



Name: Date:


Lesson 39, Practice 2: Circumference

Find each circumference. Use 3.14 for pi.

1. d = 25 m C = 2. r = 3 ft. C =

3. d = 10 cm C = 4. r = 5 in. C =

5. d = 2 cm C = 6. r = 9 in. C =

7. d = 8 ft. C = 8. r = 12 m C =


3 ft.25 m

5 in.10 cm

9 in.2 cm

12 m8 ft.




Answer Keys: Circumference

Lesson 39, Practice 1 1. 94.2 m 2. 31.4 ft. 3. 62.8 in. 4. 10.99 cm 5. 37.68 in. 6. 47.1 cm 7. 28.26 ft. 8. 94.2 m

Lesson 39, Practice 2 1. 78.5 m 2. 18.84 ft. 3. 31.4 cm 4. 31.4 in. 5. 6.28 cm 6. 56.52 in. 7. 25.12 ft. 8. 75.36 m




Name: Date:



Lesson 40, Practice 1: Area of Rectangles and Parallelograms

To find the area of a rectangle or parallelogram, use the formula: A = base x height.Area is written in square units, such as in.2 or cm 2.

Example:b = 36 cm, h = 80 cm A = 36 x 80 = 2,880 cm 2

Find the area of each figure.

1. A= 2. A=

3. A= 4. A=

5. A= 6. A=

7. A= 8. A=

80 cm

36 cm

50 cm

120 cm

50 in.

105 in.

6 in.

13 in.

3 ft.

5 ft.

5 ft.

15 ft.

2 cm

10 cm

8 in.

6 in.

3.5 m

20 m



Name: Date:


Lesson 40, Practice 2: Area of Rectangles and Parallelograms

Find the area of each figure.

1. A= 2. A=

3. A= 4. A=

5. A= 6. A=

7. A= 8.A=


5 in.

9 in.

3 cm

15 cm

10 in.

4 in.

2.5 m

15 m

7 in.

6 in.

3 cm

20 cm

4 ft.

10 ft.

2 cm

11 cm




Answer Keys: Area of Rectangles and Parallelograms

Lesson 40, Practice 1 1. 6,000 cm 2

2. 5,250 in.2

3. 78 in.2

4. 15 ft.2

5. 75 ft.2

6. 20 cm 2

7. 48 in.2

8. 70 m 2

Lesson 40, Practice 2 1. 45 in.2

2. 45 cm 2

3. 40 in.2

4. 37.5 m 2

5. 42 in.2

6. 60 cm 2

7. 40 ft.2

8. 22 cm 2




Name: Date:

Unit 6: Geometry and Measurement—Lesson 4�, Practice �


Lesson 41, Practice 1: Area of Triangles

To find the area of a triangle, use the formula: A = !s x base x height.Area is written in square units, such as in.2 or cm 2.

Example: b = 10 m, h = 4 m A = !s x 10 x 4 = 20 m 2

Find the area of each triangle.

1. A = 2. A =

3. A = 4. A =

5. A = 6. A =

7. A = 8. A =

10 m

4 m

5 in.

7 in.

9 in.

7 in.

3 cm

8 cm

9 m

24 m

8 in.

15 in.

8 in.

17 in.

11.4 m

9 m

9 m

15 m



Name: Date:


Lesson 41, Practice 2: Area of Triangles

Find the area of each triangle.

1. A = 2. A =

3. A = 4. A =

5. A = 6. A =

7. A = 8. A =

Unit 6: Geometry and Measurement—Lesson 4�, Practice �

3.6 cm

3 cm

6.7 cm

3 cm

9 in.

5 in. 4 m

5 m

4 m

8 m

10 m

56 m

48 cm

24 cm 48 cm

36 cm




Answer Keys: Area of Triangles

Lesson 41, Practice 1 1. 17.5 in.2

2. 31.5 in.2

3. 12 cm 2

4. 108 m 2

5. 60 in.2

6. 68 in.2

7. 51.3 m 2

8. 67.5 m 2

Lesson 41, Practice 2 1. 5.4 cm 2

2. 10.05 cm 2

3. 22.5 in.2

4. 10 m 2

5. 16 m 2

6. 280 m 2

7. 576 cm 2

8. 864 cm 2

Unit 6: Geometry and Measurement—Lesson 4�, Answer Keys



Name: Date:



Lesson 42, Practice 1: Area of Trapezoids

To find the area of a trapezoid, first add the lengths of the two bases, and then multiply by !s the

height. Use the formula: A = !sh (b1 + b

2). Area is written in square units, such as in.2 or cm 2.

Example: b1 = 15 cm, b

2 = 20 cm, h = 5 cm

A = !s x 5 x (15 + 20) = !s x 5 x 35 = 65 cm 2

Find the area of each trapezoid.

1. A = 2. A =

3. A = 4. A =

5. A = 6. A =

7. A = 8. A =

15 cm

20 cm

5 cm

6 in.

10 in.

15 in.5 in.

4 in.

2 in.

12 cm

3 cm

10 cm9 m 3 m2 m

7 in.

1 in.

2 in.

3 in.

8 in.

13 in.

1 m

12 m

9 m

10 m

5 m4 m



Name: Date:


Lesson 42, Practice 2: Area of Trapezoids

Find the area of each trapezoid.

1. A = 2. A =

3. A = 4. A =

5. A = 6. A =

7. A = 8. A =

Unit 6: Geometry and Measurement—Lesson 42, Practice 2

5 cm

6 cm

2 cm

3 cm

4 cm

8 cm

4 in.

12 in.

5 in.

13 m

11 m

9 m

7 m

10 m

6 m12 m

1 m

5 m

10 cm

12 cm

1 cm

6 cm

4 cm

2 cm




Answer Keys: Area of Trapezoids


2. 15 in.2

3. 75 cm 2

4. 22.5 m 2

5. 10.5 in.2

6. 31.5 in.2

7. 58.5 m 2

8. 45 m 2

Lesson 42, Practice 2 1. 11 cm 2

2. 28 cm 2

3. 40 in.2

4. 130 m 2

5. 65 m 2

6. 36 m 2

7. 65 cm 2

8. 18 cm 2




Name: Date:



Lesson 43, Practice 1: Area of Circles

To find the area of a circle, use the formula: A = πr 2. Square the radius, and then multiply by pi (3.14). If you are given the diameter, first divide the diameter by 2 to get the radius. Area is writ-ten in square units, such as in.2 or cm 2.

Example: r = 5 in. A = 3.14 x 52 = 3.14 x 25 = 78.5 in.2

Find the area of each circle. Use 3.14 for pi.

1. d = 10 in. A = 2. r = 5 ft. A =

3. r = 7 m A = 4. d = 30 cm A =

5. d = 5 in. A = 6. r = 2 ft. A =

7. r = 14 m A = 8. r = 3 cm A =

5 in.

10 in.

7 m

5 in.

30 cm

14 m

5 ft.

2 ft.

3 cm



Name: Date:


Lesson 43, Practice 2: Area of Circles

Find the area of each circle. Use 3.14 for pi.

1. d = 20 cm A = 2. d = 4 cm A =

3. r = 6 cm A = 4. d = 8 cm A =

5. d = 6 cm A = 6. d = 2 cm A =

7. d = 9 cm A = 8. r = 7 cm A =


6 cm

20 cm 4 cm

8 cm

6 cm 2 cm

9 cm 7 cm




Answer Keys: Area of Circles


2. 78.5 ft.2

3. 153.86 m 2

4. 706.5 cm 2

5. 19.625 in.2

6. 12.56 ft.2

7. 615.44 m 2

8. 28.26 cm 2

Lesson 43, Practice 2 1. 314 cm 2

2. 12.56 cm 2

3. 113.04 cm 2

4. 50.24 cm 2

5. 28.26 cm 2

6. 3.14 cm 2

7. 63.585 cm 2

8. 153.86 cm 2




Name: Date:



Lesson 44, Practice 1: Surface Area of Rectangular and Triangular Prisms

The surface area of a prism is the combined area of all the faces. A rectangular prism has six

rectangular faces. Remember, the area of a rectangle is base x height. A triangular prism has

three rectangular faces and two triangular bases. Remember, the area of a triangle is !sbase x

height. Find the area of all the faces, and then add them together to get the surface area. Look

carefully at the triangular bases. If the triangles are not equilateral, the area of each rectangular

face will have to be calculated separately and then added.

Example: SA = [2 x (15 x 2)] + [2 x (15 x 5)] + [2 x (2 x 5)] = (2 x 30) + (2 x 75) + (2 x 10) = 60 + 150 + 20 = 230 cm2

Find the surface area of each prism.

1. SA = 2. SA =

3. SA = 4. SA =

5. SA = 6. SA =

7. SA = 8. SA =

2 cm

5 cm

15 cm

6 in.

5.2 in.

20 in.

6 in.6 in.

2 ft.

4 ft.

5 ft.

3 m

3 m

5 m 5 in.

4.3 in.

10 in.

5 in.5 in.

10 in.

21 in.45 in.

15 in.

28 in.

34 in.

22 in.

10 m

5 m20 m 10 in.

8.7 in.

14 in.

10 in.

10 in.



Name: Date:


Lesson 44, Practice 2: Surface Area of Rectangular and Triangular Prisms

Find the surface area of each prism.

1. SA = 2. SA =

3. SA = 4. SA =

5. SA = 6. SA =

7. SA = 8. SA =


5 cm

1 cm6 cm

20 ft.

12 ft.25 ft.

19 ft.

2 cm

1 cm4 cm

10 m

12 m

15 m

22 m

3 cm

5 cm

7 cm

5 cm

4.3 cm

8 cm

5 cm5 cm

2 cm

1 cm 8 cm

6 cm

1.8 cm

9 cm

2.2 cm 5 cm




Answer Keys: Surface Area of Rectangular and Triangular Prisms


2. 76 ft.2

3. 78 m2

4. 171.5 in.2

5. 3,210 in.2

6. 2,114 in.2

7. 700 m2

8. 507 in.2

Lesson 44, Practice 2 1. 82 cm2

2. 1,323 ft.2

3. 28 cm2

4. 934 m2

5. 142 cm2

6. 141.5 cm2

7. 52 cm2

8. 129.6 cm2




Name: Date:



Lesson 45, Practice 1: Surface Area of Cylinders

To find the surface area of a cylinder, you find the area of the side of the cylinder and the area of the two bases. The bases are circles. The side is a rectangle whose height is the height of the cylinder and base is the circumference of the cylinder.

Example:r = 6 cm, h = 3 cm

Find circumference of base: C=2πr 2 x 3.14 x 6 = 37.68 Find area of rectangle: A=bxh 37.68 x 3 = 113.04 cm 2

Find area of two bases: A=2(πr 2) 2 x (3.14 x 62) = 226.08 Add the areas: 113.04 + 226.08 = 339.12 cm 2

Find the surface area of each cylinder. Use 3.14 for pi.

1. SA= 2. SA=

3. SA= 4.SA=

5. SA= 6.SA=

7. SA= 8. SA=

6 cm

3 cm

4 in.

6 in.

9 ft.

5 ft.

24 m

7 m

7 in.

8 in.

7 in.

9 in.

14 in.

3 in.

12 in.

4 in.

5 m

11 m



Name: Date:


Lesson 45, Practice 2: Surface Area of Cylinder

Find the surface area of each cylinder. Use 3.14 for pi.

1. SA= 2.SA=

3. SA= 4.SA=

5. SA= 6.SA=

7. SA= 8.SA=


11 cm

3 cm

6 ft.

8 ft.

2 cm

4 cm

18 m

3 m

2 cm

3 cm

12 cm

3 cm

4 cm

2 cm

2 in.

3 in.




Answer Keys: Surface Area of Cylinders


2. 791.28 ft.2

3. 1,431.84 m 2

4. 659.4 in.2

5. 1,205.76 in.2

6. 703.36 in.2

7. 502.4 m 2

8. 439.6 in.2

Lesson 45, Practice 2 1. 967.12 cm 2

2. 207.24 ft.2

3. 75.36 cm 2

4. 678.24 m 2

5. 62.8 cm 2

6. 339.12 cm 2

7. 150.72 cm 2

8. 94.2 in.2




Name: Date:



Lesson 46, Practice 1: Volume

To find the volume of a rectangular prism, multiply the length by the width by height. Use the formula: V = l x w x h. Volume is written in cubic units, such as in.3 or cm 3.

Example: V = 7 x 3 x 4 = 84 cm 3

Find the volume for each prism.

1. V = 2. V =

3. V = 4. V =

5. V = 6. V =

7. V = 8. V =

2 cm

1 cm 8 cm

3 in.

6 in.

8 in. 1 cm

6 cm

3 cm

4 cm

2 cm

7 cm

3 cm

4 cm

7 cm

2 in.

4 in.

5 in.

2 cm

4 cm

5 cm

4 in.

1 in.5 in. 7 cm

1 cm8 cm



Name: Date:


Lesson 46, Practice 2: Volume

To find the volume of a cylinder, find the area of one of the bases and multiply that area by the height. The base of a cylinder is a circle, so find the area of the base using B = πr 2. Then use that number to multiply by the height: V = B x h. Volume is written in cubic units, such as in.3 or cm 3.

Example: Find the area of the base: B = 3.14 x 22 = 12.56 Find the volume: V = 12.56 x 4 = 50.24 cm 3

Find the volume of each cylinder. Use 3.14 for pi.

1. V = 2. V =

3. V = 4. V =

5. V = 6. V =

7. V = 8. V =


2 cm

4 cm

11 cm

5 cm

22 cm

5 cm

8 in.

3 in.2 cm

10 cm

9 cm

3 cm

16 in.

11 in.

8 cm

12 cm

12 in.

7 in.




Answer Keys: Volume


2. 18 cm 3

3. 56 cm 3

4. 40 in.3

5. 16 cm 3

6. 40 cm 3

7. 20 in.3

8. 56 cm 3

Lesson 46, Practice 2 1. 1,899.7 cm 3

2. 1,899.7 cm 3

3. 602.88 in.3

4. 125.6 cm 3

5. 763.02 cm 3

6. 2,210.56 in.3

7. 3,165.12 in.3

8. 2,411.52 cm 3




Name: Date:



Lesson 47, Practice 1: Pythagorean Theorem

If you know the values for two sides of a right triangle, you can find the value for the third side using the Pythagorean Theorem: a 2 + b 2 = c 2. Substitute the length of the legs for a and b. Sub-stitute the length of the hypotenuse for c. Then solve the equation for the unknown value.

Example: 82 + 62 = c 2 64 + 36 = c 2 100 = c 2 100 = c 10 = c Solve the equations below to find the missing measurements in right triangles. Round to the nearest hundredth if needed.

1. 92 + b2 = 152 2. 102 + 72 = c2

3. a2 + 112 = 182 4. 42 + b2 = 112

5. 102 + b2 = 262 6. 42 + 92 = c2

7. a2 + 122 = 172 8. 802 + 602 = c2 _______

a = 8

b = 6

c = ?



Name: Date:


Lesson 47, Practice 2: Pythagorean Theorem

Write and solve the equation to find the missing measurements in the right triangles be-low using the Pythagorean Theorem. Round to the nearest hundredth if needed.

1. 2.

3. 4.

5. 6.

7. 8.


3 in.

4 in.

?

3 cm

5 cm

?

5.8 ft.7.9 ft.

?

1 cm

8 cm?

?6.1 in.

3.5 in.

5.2 m

1.1 m

?

8.6 cm3.5 cm

?

9.1 in. 12.9 in.

?




Answer Keys: Pythagorean Theorem

Lesson 47, Practice 1 1. b = 12 2. c = 12.21 3. a = 14.25 4. b = 10.25 5. b = 24 6. c = 9.85 7. a = 12.04 8. c = 100

Lesson 47, Practice 2 1. 32 + 42 = c 2 c = 5 in. 2. 32 + 52 = c 2 c = 5.83 cm 3. 5.82 + b 2 = 7.92 b = 5.36 ft. 4. a 2 + 12 = 82 a = 7.94 cm 5. a 2 + 3.52 = 6.12 a = 5 in. 6. 5.22 + 1.12 = c 2 c = 5.32 m 7. 3.52 + b 2 = 8.62 b = 7.86 cm 8. 9.12 + b 2 + 12.92 b = 9.14 in.




Name: Date:



Lesson 48, Practice 1: Angle Relationships and Intersecting Lines

Using what you know about the relationships of angles, if you are given one angle measurement, you can figure out the rest.

Example: If angle 1 = 130° angle, what is angle 2? angle 2 = 50° What are angle 3 and angle 4? angle 3 = 130° angle 4 = 50°

Find the measures of the angles in the pictures below.

angle 1 = 25°

1. angle 3

2. angle 2

3. angle 4

angle 2 = 60°

4. angle 1

5. angle 3

6. angle 4

angle 3 = 75°

7. angle 4

8. angle 1

9. angle 2

1

2 34

1

2

3

4

1

234

1

23

4



Name: Date:


Lesson 48, Practice 2: Angle Relationships and Intersecting Lines

Find the measures of the angles in the pictures below.

angle A = 120°

1. angle D

2. angle B

3. angle C

4. angle E

angle P = 35°

5. angle R

6. angle Q

7. angle T

8. angle S


A

B

CD

E

P

Q

RS

T




Answer Keys: Angle Relationships and Intersecting Lines

Lesson 48, Practice 1 1. 25° 2. 155° 3. 155° 4. 120° 5. 120° 6. 60° 7. 105° 8. 75° 9. 105°

Lesson 48, Practice 2 1. 90° 2. 60° 3. 30° 4. 60° 5. 35° 6. 145° 7. 90° 8. 55°




Name: Date:



Lesson 49, Practice 1: Angle Relationships and Parallel Lines

Using what you know about the relationships of angles, you can find the measures of the un-known angles.

Example: angle 1 = 30° angle 6 = 150° angle 2 = ? angle 2 = 150°

Find the measures of the angles in the picture below.

angle 1 = 60°

1. angle 2

2. angle 3

3. angle 4

4. angle 5

5. angle 6

6. angle 7

7. angle 8

8. True or False: angle 2 = angle 8



1 23

678

5

4

1 2

34

5 6

78



Name: Date:


Lesson 49, Practice 2: Angle Relationships and Parallel Lines

Find the measures of the angles in the picture below.

angle 2 = 110°

1. angle 1

2. angle 3

3. angle 4

4. angle 5

5. angle 6

6. angle 7

7. angle 8





1 2

34

5 6

78




Answer Keys: Angle Relationships and Parallel Lines

Lesson 49, Practice 1 1. 120° 2. 60° 3. 120° 4. 60° 5. 120° 6. 60° 7. 120° 8. True 9. True10. False

Lesson 49, Practice 2 1. 70° 2. 70° 3. 110° 4. 70° 5. 110° 6. 70° 7. 110° 8. True 9. False10. True


Unit 7: Probability and Statistics

Lesson 50: Measures of Central Tendency

Lesson 51: Possible Outcomes

Lesson 52: Simple Probability

Lesson 53: Independent and Dependent Events



Name: Date:

Unit 7: Probability and Statistics—Lesson 50, Practice �

CD Exercises Unit 7: Probablility and Statistics

Lesson 50, Practice 1: Measures of Central Tendency

The three measures of central tendency are mean, median, and mode. The mean is the average of the data set. The median is the middle number of the data set when the numbers are listed in order from least to greatest. The mode is the number that occurs most often in the data set.

Example: 4, 5, 5, 5, 7, 8, 9 mean = 4 + 5 + 5 + 5 + 7 + 8 + 9 = 43 ÷ 7 = 6.1 median = 5 mode = 5

Find the measures of central tendency for each of the given data sets. Round to the near-est hundredth if needed.

1, 5, 6, 7, 8, 9, 10, 10, 11, 12, 14, 15, 16, 18, 22, 28, 35

1. mean 2. median 3. mode

1, 4, 8, 9, 15, 20


23, 24, 26, 26, 29, 30, 30, 30, 35




Name: Date:


Lesson 50, Practice 2: Measures of Central Tendency

Find the measures of central tendency for each of the given data sets. First, put the sets in order from least to greatest.

34, 26, 24, 34, 24, 40, 24, 24, 26, 34

1.


250, 100, 70, 450, 70, 100, 70, 70, 70, 100, 100, 125, 125, 100, 70, 125, 250, 400, 450, 70, 125, 70, 250

5.


2, 1, 3, 2, 2

9.


Unit 7: Probablility and Statistics—Lesson 50, Practice �




Answer Keys: Measures of Central Tendency

Lesson 50, Practice 1 1. 13.35 2. 11 3. 10 4. 9.5 5. 8.5 6. no mode 7. 28.11 8. 29 9. 30

Lesson 50, Practice 2 1. 24, 24, 24, 24, 26, 26, 34, 34, 34, 40 2. 29 3. 26 4. 24 5. 70, 70, 70, 70, 70, 70, 70, 70, 100, 100, 100, 100, 100, 125, 125, 125, 125, 250, 250, 250, 400, 450, 450 6. 157 7. 100 8. 70 9. 1, 2, 2, 2, 310. 211. 212. 2

Unit 7: Probablility and Statistics—Lesson 50, Answer Keys



Name: Date:

Unit 7: Probability and Statistics—Lesson 5�, Practice �


Lesson 51, Practice 1: Possible Outcomes

To find the possible outcomes, multiply the number of options in one category by the number of options in the other category.

Example: Car make: Chevy, Ford, Dodge Doors: 2-Door, 4-Door Possible Outcomes = 3 x 2 = 6

Find the number of possible outcomes.

1. 2.

Breads: white, wheat Breakfast items: bacon, sausage, eggs,

Meats: ham, turkey, bologna pancakes

Drinks: orange juice, coffee, tea

3. 4.

Ice cream flavors: chocolate, Memory: 512 MB, 1 GB, 2GB

vanilla, swirl Computer types: Mac, PC

Containers: bowl, cone, waffle cone

5. 6.

Items: posters, books, teacher’s guide Classes: math, science, PE

Grades: Level 3, Level 4, Level 5, Times: 1st hour, 2nd hour, 3rd hour

Level 6

7. 8.

Vehicles: car, truck, van Sizes: small, medium, large, super-size

Colors: red, black, white, yellow, silver Soda flavors: cola, lemon-lime, orange,

root beer



Name: Date:


Lesson 51, Practice 2: Possible Outcomes

Find the possible outcomes.

1. 2.

Sizes: small, medium, large Mexican foods: taco, burrito, chalupa

Candy flavors: vanilla, caramel, Spiciness levels: mild, hot, fire

mocha, coffee

3. 4.

Computer colors: clear, black, blue, Items: poster, book

pink, green Subjects: math, science, history,

Drives available: CD, DVD English

5. 6.

Hair colors: brown, blonde, red Fuel types: unleaded, disel, E85

Eye colors: hazel, blue, brown, green Vehicles: car, truck, SUV

Wears glasses?: Yes, No Payment types: credit card, cash, check

7. 8.

House types: cottage, cabin, ranch Sports: baseball, football, hockey

Colors: red, grey, tan, green, white Cities: St. Louis, Chicago, New York,

Philadelphia, Pittsburgh, Los Angeles,

Washington, D.C.

Unit 7: Probablility and Statistics—Lesson 5�, Practice �




Answer Keys: Possible Outcomes

Lesson 51, Practice 1 1. 6 2. 12 3. 9 4. 6 5. 12 6. 9 7. 15 8. 16

Lesson 51, Practice 2 1. 12 2. 9 3. 10 4. 8 5. 24 6. 27 7. 15 8. 21

Unit 7: Probablility and Statistics—Lesson 5�, Answer Keys



Name: Date:



Lesson 52, Practice 1: Simple Probability

Probability is usually expressed as a ratio of the number of favorable outcomes to the number of possible outcomes.

Example: There is a game spinner with 12 equal sections marked 1 through 12.

The probability that the pointer will land on 6 is written as P(6) = aQs . Use the example of the spinner to answer the questions below. Simplify the fractions if needed.

1. P(2) 2. P(even)

3. P(>6) 4. P(<3)

5. P(7) 6. P(odd)

7. P(>9) 8. P(<7)



Name: Date:


Lesson 52, Practice 2: Simple Probablility

Use a standard deck of 52 cards to answer the questions below. Simplify the fractions if needed.

1. P(4) 2. P(red)

3. P(heart) 4. P(black King)

5. P(red Jack) 6. P(10)

7. P(Ace) 8. P(Queen of Hearts)

Unit 7: Probablility and Statistics—Lesson 52, Practice 2




Answer Keys: Simple Probablility


1. aQs

2. !s

3. !s

4. !h

5. aQs

6. !s

7. !f

8. !s


1. aQd

2. !s

3. !f

4. sQh

5. sQh

6. aQd

7. aQd

8. gQs




Name: Date:



Lesson 53, Practice 1: Independent and Dependent Events

To find the probability of independent events, find the probability of each event and then multiply.

Example: The letters PLAY are cut apart and placed in a bag. What is the probability that you draw an A, put it back, and then draw an L?

P(A then L) = !fx!f = !k

When finding the probability of a dependent event, you must take into consideration that another event has already taken place.

Example: 5 green balls and 4 red balls are placed in a bag. What is the probability that you draw 1 green ball, don’t replace it, and then draw a red ball?

P(G then R) = %lx$k = Wu Pw = aTk

The letters in the word STATISTICS have been cut apart and placed in a bag. Find the probability of the following events. Reduce fractions if needed.

1. Draw an A, put it back, and then draw an I

2. Draw S, don’t put it back, and then draw a consonant

3. Draw an I, replace it, and then draw a vowel

4. Draw a T, don’t replace it, and then draw an A

5. Draw an S, don’t replace it, and then draw an S

6. Draw a T, replace it, and then draw a T

7. Draw an I, replace it, and then draw an I

8. Draw an A, don’t replace it, and then draw a C



Name: Date:


Lesson 53, Practice 2: Independent and Dependent Events

Use a coin and a 20-side die to answer the following questions.

Heads up, and then roll a 9

1. Independent or Dependent? 2. P(heads, then 9)

Tails, flip again, and get tails

3. Independent or Dependent? 4. P(tails, then tails)

Tails, then roll even

5. Independent or Dependent? 6. P(tails, then even)

Use a bag with 7 blue marbles and 8 yellow marbles to answer the following questions.

Draw yellow, don’t replace it, and draw another yellow

7. Independent or Dependent? 8. P(yellow, then yellow)

Draw blue, replace it, and draw another blue

9. Independent or Dependent? 10. P(blue, then blue)

Unit 7: Probablility and Statistics—Lesson 53, Practice �




Answer Keys: Independent and Dependent Events


1. gQ;

2. !g

3. gE;

4. dQ;

5.aQg

6. q Op p

7. sQg

8. lQ;


1. independent

2. fQ; 3. independent

4. !f 5. independent

6. !f 7. dependent

8. aRg 9. independent

10. sRsOg




Name: Date:

Unit 8: Linear Equations—Lesson 54, Practice �

CD Exercises Unit 8: Linear Equations

Lesson 54, Practice 1: Solving One-Step Equations by Adding and Subtracting

Use inverse operations to find missing values in an equation. Addition and subtraction are in-verse operations.

Example:1+x=5 -1-1 x=4 Solve each addition equation.

1. 1+x=9 2. 1+x=-7

3. -2+x=0 4.-2+x=-7

5. 1+x=-6 6.9+x=4

7. -7+x=0 8. 6+x=6



Name: Date:


Lesson 54, Practice 2: Solving One-Step Equations by Adding and Subtracting

Use inverse operations to find missing values in an equation. Addition and subtraction are in-verse operations.

Example:x–11=-16 +11+11 x=-5

Solve each subtraction equation.

1. x–6=-2 2.x–(-5)=-4

3. x–5=-5 4.x–7=-3

5. x–(-5)=6 6.x–(-1)=1

7. x–6=-3 8.x–(-9)=17





Answer Keys: Solving One-Step Equations by Adding and Subtracting

Lesson 54, Practice 1 1. x=8 2. x=-8 3. x=2 4. x=-5 5.x=-7 6. x=-5 7. x=7 8. x=0

Lesson 54, Practice 2 1. x=4 2. x=-9 3. x=0 4. x=4 5. x=1 6. x=0 7. x=3 8. x=8

Unit 8: Linear Equations—Lesson 54, Answer Keys

Unit 8: Linear Equations

Lesson 54: Solving One-Step Equations by Adding and Subtracting

Lesson 55: Solving One-Step Equations by Multiplying and Dividing

Lesson 56: Solving Two-Step Equations

Lesson 57: Graphing Linear Equations

Lesson 58: Slope



Name: Date:



Lesson 55, Practice 1: Solving One-Step Equations by Multiplying and Dividing

Use inverse operations to find the missing values in an equation. Multiplication and division are inverse operations.

Example:10x=7010x=70x=7 10 10

Solve each multiplication equation.

1. 5x=20 2. 7x=35

3. 27=9x 4.6x=12

5. 4x=20 6.48=8x

7. 40=10x 8. 10x=20



Name: Date:


Lesson 55, Practice 2: Solving One-Step Equations by Multiplying and Dividing

Use inverse operations to find the missing values in an equation. Multiplication and division are inverse operations.

Example:x÷11=5 (x÷11)•11=5•11 x=55

Solve each division equation.

1. x÷9=7 2. x÷8=4

3. x÷7=5 4. x÷5=3

5. =6 6.=7

7. x÷7=4 8.x÷7=6


x5

x8




Answer Keys: Solving One-Step Equations by Multiplying and Dividing

Lesson 55, Practice 1 1. x=4 2. x=5 3. x=3 4. x=2 5.x=5 6. x=6 7. x=4 8. x=2

Lesson 55, Practice 2 1. x=63 2. x=32 3. x=35 4. x=15 5. x=30 6. x=56 7. x=28 8. x=42




Name: Date:



Lesson 56, Practice 1: Solving Two-Step Equations

In two-step equations, first you add or subtract, and then you multiply or divide.

Example:6x+1=19 6x+1=19 -1-1 6x=18 66

x=3

Solve each equation.

1. 7p+9=44 2. 2a–5=-3

3. 9y–5=40 4.8t–6=26

5. 7v–9=26 6.4b+2=10

7. 6s+6=12 8. 3q+8=14



Name: Date:


Lesson 56, Practice 2: Solving Two-Step Equations

Solve each equation.

1. 9c–7=11 2.+6=11

3. 10n+9=69 4.8e–8=0

5. –2=3 6.+8=11

7. 8d+5=37 8.4a–6=6


g20

w3

m14




Answer Keys: Solving Two-Step Equations

Lesson 56, Practice 1 1. p=5 2. a=1 3. y=5 4. t=4 5.v=5 6. b=2 7. s=1 8. q=2

Lesson 56, Practice 2 1. c=2 2. g=100 3. n=6 4. e=1 5. w=15 6. m=42 7. d=4 8. a=3




Name: Date:



Lesson 57, Practice 1: Graphing Linear Equations

Set up a table to find the x and y values for a linear equation. Find at least three ordered pairs, and then graph the line on the coordinate plane.

Example:y=2x+3 x y

-2-1

03

15

Graph each equation on the coordinate planes on the next page.

1. y=-%dx–2 2. y=-5x+7

3. y=3 4.x=4

5. y=$dx–4 6.y=-!sx+3

7. y=!sx+4 8. y=!fx–3

-8-7-6 -5-4-3 -2-101234567 8

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

x-axis

y-axis



Name: Date:

-8-7-6 -5-4-3 -2-101234567 8

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

x-axis

y-axis


Lesson 57, Practice 1: Graphing Linear Equations (cont.)


-8-7-6 -5-4-3 -2-101234567 8

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

x-axis

y-axis



Name: Date:


Lesson 57, Practice 2: Graphing Linear Equations

Graph each equation on the coordinate graphs on the next page.

1. y=2x+3 2.y=-4

3. y=x+1 4. y=-3x+5

5. y=-5x–3 6.y=x+4

7. y=2x+4 8.y=-2x+!f




Name: Date:

-8-7-6 -5-4-3 -2-101234567 8

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

x-axis

y-axis


Lesson 57, Practice 2: Graphing Linear Equations (cont.)


-8-7-6 -5-4-3 -2-101234567 8

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

x-axis

y-axis




Answer Keys: Graphing Linear Equations




-8-7-6 -5-4-3 -2-101234567 8

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

x-axis

y-axis

2.1.

3.

4.

8.

-8-7-6 -5-4-3 -2-101234567 8

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

x-axis

y-axis

5.

6.

7.

-8-7-6 -5-4-3 -2-101234567 8

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

x-axis

y-axis

1.

2.

3.

4.

6.

7.

8.

-8-7-6 -5-4-3 -2-101234567 8

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

x-axis

y-axis

5.



Name: Date:



Lesson 58, Practice 1: Slope

You can find the slope of a line using two points on a line. Subtract the y-coordinates of the two points to find the rise. Subtract the x-coordinates of the two points to find the run.

Example:(1,2),(3,5)= = Find the slope of the line that contains the given points.

1. (-4,-1),(3,2) 2. (3,2),(1,-2)

3. (1,3),(3,-6) 4.(-5,2),(4,-7)

5. (1,1),(5,1) 6.(3,4),(3,6)

7. (0,1),(2,4) 8. (2,2),(3,3)

5–23–1

3 rise2 run



Name: Date:


Lesson 58, Practice 2: Slope

Find the slope of the line that contains the given points.

1. (2,0),(3,0) 2.(2,3),(3,0)

3. (-1,0),(-3,1) 4. (-1,-1),(-3,2)

5. (-1,2),(1,4) 6.(0,-3),(-4,-4)

7. (-3,-3),(3,-3) 8.(0,3),(3,4)





Answer Keys: Slope


1. #j

2. $s=2

3. - (s

4. - (l=-1

5. )f

6. @;

7.#s

8.!a=1


1. )a

2.- #a

3.- !s

4. - #s

5. @s = �

6. !f=!f

7. )h

8. !d


--

--

Unit 9: Linear Inequalities

Lesson 59: Graphing Inequalities on a Number Line

Lesson 60: Solving One-Step Inequalities by Adding and Subtracting

Lesson 61: Solving One-Step Inequalities by Multiplying and Dividing



Name: Date:

Unit 9: Linear Inequalities—Lesson 59, Practice �

CD Exercises Unit 9: Linear Inequalities

Lesson 59, Practice 1: Graphing Inequalities on a Number Line

Use an open circle to graph < or >. Use a closed circle to graph ≤ or ≥.

Example:x<5 Graph the following inequalities.

1. x<1 2. x ≤ 3

3. x<4 4.x < -3

5. x>-1 6.x<10

7. x>4 8.x ≥ 2

-5 -2 0 2 5

-4 -2 0 2 4 -4 -2 0 2 4

-4 -2 0 2 4 -4 -2 0 2 4

-4 -2 0 2 4 -10-50510

-4 -2 0 2 4 -4 -2 0 2 4



Name: Date:


Lesson 59, Practice 2: Graphing Inequalities on a Number Line

Graph the following inequalities.

1. x>1 2.x ≥ 4

3. x > 2 4. x ≥ 1

5. x ≤ 9 6.x < 3

7. x>8 8.x<5


-4 -2 0 2 4 -4 -2 0 2 4

-4 -2 0 2 4 -4 -2 0 2 4

-8-4048 -4 -2 0 2 4

-8-404 8 -4 -2 0 2 4




Answer Keys: Graphing Inequalities on a Number Line

Lesson 59, Practice 1 1. 2.

3. 4.

5. 6.

7. 8.

Lesson 59, Practice 2 1. 2.

3. 4.

5. 6.

7. 8.

Unit 9: Linear Inequalities—Lesson 59, Answer Keys

-4 -2 0 2 4

-4 -2 0 2 4

-4 -2 0 2 4

-10-50510

-4 -2 0 2 4

-4 -2 0 2 4

-4 -2 0 2 4

-8-4048

-4 -2 0 2 4

-4 -2 0 2 4

-4 -2 0 2 4

-4 -2 0 2 4

-4 -2 0 2 4

-8-4048 -4 -2 0 2 4

-4 -2 0 2 4



Name: Date:



Lesson 60, Practice 1: Solving One-Step Inequalities by Adding and Subtracting

Solving an inequality is very similar to solving an equation. Use inverse operations to find the missing values.

Example: x + 1 > 25 x + 1 > 25 -1 -1 x > 24 Solve each inequality.

1. x – 7 < 14 2. p – 5 < 13

3. s – 8 < 40 4. a – 6 > 44

5. t – 7 ≥ 7 6. g – 7 ≤ 21

7. n – 9 ≥ 15 8. z + 5 > 23



Name: Date:


Lesson 60, Practice 2: Solving One-Step Inequalities by Adding and Subtracting

Solve each inequality.

1. y – 4 ≥ 16 2. b + 10 > 16

3. m – 10 ≤ 32 4. q + 1 ≥ 28

5. v + 10 < 90 6. c + 9 ≥ 14

7. j – 6 ≤ 50 8. r + 1 > 9





Answer Keys: Solving One-Step Inequalities by Adding and Subtracting

Lesson 60, Practice 1 1. x < 21 2. p < 18 3. s < 48 4. a > 50 5. t ≥ 14 6. g ≤ 28 7. n ≥ 24 8. z > 18

Lesson 60, Practice 2 1. y ≥ 20 2. b > 6 3. m ≤ 42 4. q ≥ 27 5. v < 80 6. c ≥ 5 7. j ≤ 56 8. r > 8

Unit 9: Linear Inequalities—Lesson 60, Answer Keys



Name: Date:

Unit 9: Linear Inequalities—Lesson 6�, Practice �


Lesson 61, Practice 1: Solving One-Step Inequalities by Multiplying and Dividing

Solving inequalities is similar to solving equations. Use inverse operations to find the missing values in the inequalities. If you multiply or divide by a negative number, reverse the inequality sign.

Example:8x>33 8x>33 x>4.125 88 Solve each inequality.

1. 8a>12 2. -4t>9

3. 9y<34 4.-7n>4

5. 9q ≥ 37 6.-6k ≥ 22

7. 10b ≥ 5 8.-8c ≥ 45



Name: Date:


Lesson 61, Practice 2: Solving One-Step Inequalities by Multiplying and Dividing

Solving inequalities is similar to solving equations. Use inverse operations to find the missing values in the inequalities. If you multiply or divide by a negative number, reverse the inequality sign.

Example:x ÷ 5 ≤ 3 5(x ÷ 5) ≤ 3(5) x ≤ 15

Solve each inequality.

1. y÷6>32 2.x÷-7<34

3. d÷6>14 4. k÷-9>20

5. g ÷ 9 ≥ 59 6.z ÷ -10 ≥ 77

7. f ÷ 9 ≥ 13 8.u ÷ -9 ≥ 64

Unit 9: Linear Inequalities—Lesson 6�, Practice �




Answer Keys: Solving One-Step Inequalities by Multiplying and Dividing

Lesson 61, Practice 1 1.a>1.5 2. t<-2.25 3.y<3.78 4.n<-0.57 5. q ≥ 4.11 6. k ≤ -3.67 7.b ≥ 0.5 8.c ≤ -5.625

Lesson 61, Practice 2 1. y>192 2.x>-238 3.d>84 4. k<-180 5.g ≥ 531 6.z ≤ -770 7.f ≥ 117 8.u ≤ -576

Unit 9: Linear Inequalities—Lesson 6�, Answer Keys

middle school mathematics skills wkbk with answers

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