name period - west seneca central school district

Num

ber SeNSe

Name ____________________________________________

Period ____________

Number

S

eNSe

+ x

÷

IN

TE

GE

RS

—

L

ike

Sign

s

Diff

eren

t Si

gns

L

ike

Sign

s

Add

and

ta

ke th

e si

gn

Subt

ract

and

ta

ke si

gn o

f la

rges

t

abso

lute

val

ue

Cha

nge

to

Add

ition

by:

“K

eep—

Cha

nge–

C

hang

e”

Ans

wer

is

Po

sitiv

e

Ans

wer

is

N

egat

ive

-2 +

(-4)

= -6

4

+ 6

= 10

-4 +

8 =

4

6

+ (-

12) =

-6

(-

9) -

(-2)

=

(-

9) +

(+2)

= -7

8 x

6 =

48

(-

45) ÷

(-9)

= 5

9 x

(-3)

= -2

7

(-72

) ÷ 1

2 =

-6

D

iffer

ent

Sign

s

mstupski

Stamp

mstupski

Stamp

mstupski

Stamp

Unit B Vocabulary:

1

Math www.CommonCoreSheets.com

Name:

Answers

1-10 92 83 75 67 58 50 42 33 25 1711-12 8 0

1) 78.9 - 55.779 = 23.121

2) 73 + 48.7 = 121.7

3) 41.3 - 20.65 = 20.65

4) 46 + 39.5 = 85.5

5) 72 - 67.01 = 4.99

6) 65 + 56.8 = 121.8

7) 58 - 45.183 = 12.817

8) 79.3 + 10.21 = 89.51

9) 17 - 1.2 = 15.8

10) 92 + 8.83 = 100.83

11) 67.15 - 24.302 = 42.848

12) 96 + 37.367 = 133.367

1. 23.121

2. 121.7

3. 20.65

4. 85.5

5. 4.99

6. 121.8

7. 12.817

8. 89.51

9. 15.8

10. 100.83

11. 42.848

12. 133.367

Adding & Subtracting DecimalsSolve each problem.

13

Math www.CommonCoreSheets.com

Name:

Answers

Modified 1-10 90 80 70 60 50 40 30 20 10 0

1) 78.9 - 55.779 = 23.121

2) 73 + 48.7 = 121.7

3) 41.3 - 20.65 = 20.65

4) 46 + 39.5 = 85.5

5) 72 - 67.01 = 4.99

6) 65 + 56.8 = 121.8

7) 58 - 45.183 = 12.817

8) 79.3 + 10.21 = 89.51

9) 17 - 1.2 = 15.8

10) 92 + 8.83 = 100.83

20.65 15.8 23.121 85.5 89.51

12.817 121.7 100.83 4.99 121.8

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Adding & Subtracting DecimalsSolve each problem.

14

Math

Name:

www.CommonCoreSheets.com

Answers

1-10 92 83 75 67 58 50 42 33 25 1711-12 8 0

1) 63 .9× 7 .0

0+ 44730

447 .30

2) 44 .84× 9 .84

17936358720

+ 4035600441 .2256

3) 88 .6× 5 .01

8860

+ 443000443 .886

4) 39 .6× 5 .20

07920

+ 198000205 .920

5) 28 .15× 5 .5

14075+ 140750

154 .825

6) 14 .36× 4 .9

12924+ 57440

70 .364

7) 63 .14× 2 .08

505120

+ 1262800131 .3312

8) 18 .65× 6 .8

14920+ 111900

126 .820

9) 16 .92× 8 .4

6768+ 135360

142 .128

10) 80 .1× 2 .8

6408+ 16020

224 .28

11) 5 .9× 3 .9

531+ 1770

23 .01

12) 5 .6× 6 .2

112+ 3360

34 .72

1. 447.30

2. 441.2256

3. 443.886

4. 205.920

5. 154.825

6. 70.364

7. 131.3312

8. 126.820

9. 142.128

10. 224.28

11. 23.01

12. 34.72

Multiplying with DecimalsSolve each problem.

15

Math

Name:

www.CommonCoreSheets.com

Answers

Modified 1-9 89 78 67 56 44 33 22 11 0

1) 63 .9× 7 .0

0+ 44730

447 .30

2) 44 .84× 9 .84

17936358720

+ 4035600441 .2256

3) 88 .6× 5 .01

8860

+ 443000443 .886

4) 39 .6× 5 .20

07920

+ 198000205 .920

5) 28 .15× 5 .5

14075+ 140750

154 .825

6) 14 .36× 4 .9

12924+ 57440

70 .364

7) 63 .14× 2 .08

505120

+ 1262800131 .3312

8) 18 .65× 6 .8

14920+ 111900

126 .820

9) 16 .92× 8 .4

6768+ 135360

142 .128

447.30 126.820 154.825

131.3312 441.2256 70.364

142.128 205.920 443.886

1.

2.

3.

4.

5.

6.

7.

8.

9.

Multiplying with DecimalsSolve each problem.

16

6-1 Repeating Decimals

Key Concept Part One Repeating Decimals

92

= 112

=

7

Part Two Work Space:

8

Part Three

=

9

Practice 6-‐1 Repeating Decimals

Gary brings 391pounds of hamburger to cook at Bobby’s cookout. Bobby already bought 5

114pounds.

a.) Express each amount as a decimal.

b.) How much hamburger do they have total? Round to the nearest hundredth.

c.) If they are making hamburgers that are each 31pound, how many hamburgers can they make?

10

6-2 Terminating Decimals

Key Concept A TERMINATING DECIMAL is a decimal the ENDS! Part One Part Two

11

Part Three

12

Any Rational Number (a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal. Just divide the numerator by the denominator.

Directions:

-‐ Change the following fractions to decimals. -‐ Put a “T” or “R” next to your answer for either terminating or repeating decimals.

1) 51 2)

21 3)

53

4) 41 5)

32 6)

85

7) 92 8)

52 9)

103

10) 72 11)

74 12)

127

13) 5021

14) 43 15)

54

16) 65 17)

98 18)

83

13

Comparing Integers (A)Compare the pairs of integers using <, >, or =

14 12 5 4 10 9 -12 -13

-15 -14 -5 -6 -8 -7 13 15

6 7 0 2 10 9 9 8

-2 -3 1 3 -14 -13 -4 -3

-4 -3 -4 -2 -10 -11 15 14

1 0 7 5 -8 -7 -3 -1

-13 -15 -5 -3 11 10 12 13

-4 -5 3 5 -3 -1 0 1

10 9 -2 -1 3 2 15 13

8 6 -14 -12 -10 -8 14 13

Math-Drills.com14

Student Name: __________________________ Score:

Free Math Worksheets @ http://www.mathworksheets4kids.com

Use > or < or = sign to compare the integers:

- 5 - 5 - 9 - 1 - 2 - 6

- 7 - 4 - 1 - 6 - 7 - 2

- 6 - 3 - 2 - 5 - 7 - 3

- 5 - 9 - 8 - 8 - 6 - 9

- 4 - 6 - 6 - 3 - 1 - 7

- 3 - 8 - 9 - 8 - 4 - 1

- 7 - 9 -3 - 9 - 8 - 5

- 2 - 7 - 9 - 2 - 8 - 1

- 6 - 5 - 5 - 4 - 3 - 2

Compare

15

Student Name: __________________________ Score:

Free Math Worksheets @ http://www.mathworksheets4kids.com

Answers

- 5 = - 5 - 9 < - 1 - 2 > - 6

- 7 < - 4 - 1 > - 6 - 7 < - 2

- 6 < - 3 - 2 > - 5 - 7 < - 3

- 5 > - 9 - 8 = - 8 - 6 > - 9

- 4 > - 6 - 6 < - 3 - 1 > - 7

- 3 > - 8 - 9 < - 8 - 4 < - 1

- 7 > - 9 -3 > - 9 - 8 < - 5

- 2 > - 7 - 9 < - 2 - 8 < - 1

- 6 < - 5 - 5 < - 4 - 3 < - 2

16

4-1 Rational Numbers

Part One

W I R

17

Example

18

Rational Number Practice

Part I - Place each of the following numbers in the correct column(s). Some numbers might belong in more than one column, so be careful! Make sure you list each number in EVERY column it belongs in.

0 3 -3 1.5 5.1− 32

32

− 25.0 25.0−

Whole Numbers Integers Rational Numbers

Part II - Place each of the following numbers in the correct set below.

0 3 -3 1.5 5.1− 32

32

− 25.0 25.0−

Real Numbers

Integers

Whole Numbers

Rational Numbers

19

Rational

Number

Whole

Yes/No?

Integer Yes/No?

Rational: Yes/No?

WHY?

(Terminating vs. Non-terminating) (Repeating vs. Non-repeating)

1) 0.36

2) 36.0

3) -7

4) 6.8556546

5) 0.121314151...

6) 3.6198

7) 0.24682

8) 3.0

9) 1.45454545…

10) 0.12112111211112

20

4-1 Absolute Values and Opposites

Part Two

21

Part Three Define Opposites:

22

Name: __________________________ Score:

Free Math Worksheets @ www.mathworksheets4kids.com

Find the value:

1)

|4| =

2)

|−13| =

3)

−|10| =

4)

−|−7| =

5)

|11| =

6)

|−2| =

7)

−|12| =

8)

−|5| = −

9)

|1| =

10)

|−14| =

11)

−|8| = −

12)

−|−13| =

13)

|3| =

14)

|−7| =

15)

−|4| =

16)

−|−15| =

17)

|9| =

18)

|−12| =

19)

−|14| =

20)

−|−2| =

21)

|5| =

22)

|−8| =

23)

−|11| =

24)

−|−10| =

Absolute Value

23

Name: __________________________ Score:


Find the value:

1)

|−7| − |3| =

2)

|12| + |8| =

3)

|13| − |−7| =

4)

|−14| + |−4| =

5)

|−9| + |7| =

6)

|6| − |1| =

7)

|11| + |−12| =

8)

|−10| − |−2| =

9)

|−13| + |4| =

10)

|10| + |8| =

11)

|12| − |−7| =

12)

|−15| + |−4| =

13)

|9| − |4| =

14)

|14| + |3| =

15)

|10| − |−6| =

16)

|−11| + |−3| =

17)

|−15| − |7| =

18)

|9| − |2| =

19)

|14| + |−5| =

20)

|−11| − |−6| =

21)

|−5| + |4| =

22)

|12| − |8| =

23)

|7| − |−1| =

24)

|−10| + |−5| =

Absolute Value

24

Practice with Absolute Value

Directions: Find the absolute value of each of the following. 1) | + 6 | 2) | - 4 | 3) - | 19 | 4) - | - 5.3 |

5) - | 42 | 6) | 20 - 19 | 7) - | 60 + 13 | 8) | 10.6 - 3 |

9) | 87 -

87 |

10) | 100 | - | -8 | 11) | 100 | + | -8 | 12) - | 4.6 - 4 |

13) 5 | - 4 | 14)

2|10| −

15) -2 | 15 - 8 | 16) - | 8 - 2 |

25

4-1 Opposites

Examples : -6 and 6 since -6+6=0

½ and -½ since ½+-½=0

Absolute Value

The absolute value of an integer is the numerical value without regard to whether the sign is negative or positive.

On a number line it is the distance between the number and zero.

The symbol for absolute value is to enclose the number between vertical bars such as |-20| = 20 and read "The absolute value of -20 equals 20".

Examples: |-19| = |25| = 53

− = |0.02| = |5-2| = |4| + |-9| =

Order of Operations (PEMDAS)

Step 1: Parentheses; Operations within the grouping symbols. ( ) [ ],,

Step 2: Exponents, Evaluate all powers. Step 3: Multiplication and Division in order from left to right. Step 4: Addition and Subtraction in order from left to right.

* Using these rules with ensure that numerical expressions have only one value. * Simplify:

A. 5 + (12 - 3) B. (5 - 1)³ ÷ 4 C. ( )[ ] 1223 −+−•

D. 20 – 2(4 - 1) * 3 E. 5 * 3² - 7 F. 10210 3

−

−

26

Order of Operations

Directions: Solve each expression using the order of operations (use PEMDAS to help you) 1) 321025 +÷−

2) )23(15 +÷

3) 2412 •÷

4) 45218 +•−

5) 12824 −•÷

6) 2)31220( ÷÷−

7) 4556325100 −•−•+

8) 245315 −•÷

9) 277 23 −

10) 395)34( 2

+

••

27

Order of Operations

Directions: Solve each expression using the order of operations (use PEMDAS to help you)

1) 2478 ÷+•

2) 6)34(2 −+

3) 323 •

4) 2)43(2 +

5) 4

5102 ÷+

6) 4)416( 2 ÷+

7) 10)24(6 32 −−

8) 7

)423( 2 −•

9) 12)546(916 2 ÷•−−

10) ⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−

1141058 2

23

28

4-2 Additive Inverse Property of Addition & Adding Integers

Examples:

Adding Integers using a Number Line:

Adding Integers using “chips”: =+− 58

Zero Pairs:

=−+ 47

=−+− 510 =+− 1012

29

Lesson 4-2 Adding Rational Numbers on a Number Line

5 and (-5) are called: - Additive Inverse Examples: - Opposites - Zero Pairs

• To ADD a positive integer start at the first number and move to the

_____________________ on the number line.

• To ADD a negative integer start at the first number and move to the

_____________________ on the number line.

Directions: Use these number lines to solve the following problems.

1. –2 + +5 =

2. –9 + –3 =

3. +5 + –7 =

4. –4 + +4 =

5. –8 + –2 =

6. +1 + –8 =

30

Try to solve #7 without a number line.

7. -25 + +30 =

You Try:

1) Which of the following number sentences represents the number line above? A) − 4 + 2 = 6 B) − 4 + 6 = 2 C) 2 + 6 = − 4 D) 2 + − 4 = 6

Directions: Use these number lines to solve the following problems.

2. –8 + +7 =

3. –2 + –6 =

4. +10 + –15

5. –6 + +9 =

6. –1 + –9 =

7. +8 + –8 =

31

Lesson 4-2 Adding Rational Numbers with Chips

Sample: 4 + − 6 = ___________

There are 4 zero pairs, which only leaves two negative chips, so the answer is − 2

Directions: Use your chips to set up each problem below. For #1-6, Draw the Integer Chip model to demonstrate how to find the solution. Then, find the solution.

1) − 5 + −8 = ______ 2) + 2 + −7 =______

3) + 8 + −3 = ______ 4) − 4 + +3 + − 2 =______

5) − 2 + −4 = ______ 6) + 4 + 5 =______

7) − 3 + 6 =______ 8) − 9 + −12 =______

9) 6 + + 13 + −4 =______ 10) 7 + − 13 =______

32

11) −5 + 12 = ______ 12) −5 + 3 =______

13) 5 + −4 + 4 = ______ 14) 5 + − 5 =______

15) −6 + −11=______ 16) +6 + +11 =______

17) −7 + −6 + 9 =______ 18) −8 + −2 + −4 =______

19) At 10 pm on New Years Eve, the temperature in West Seneca was 24 degrees. At midnight, the temperature dropped 36 degrees! What was the temperature at midnight?

Write a number sentence to describe this situation: ______________________

Solve:

20) Bob got on an elevator on the 5th floor. He traveled 2 floors up, and 4 floors down before he reached his destination. At which floor did Bob get off the elevator?

Write a number sentence to describe this situation: ______________________

Solve:

33

ADDING INTEGERS

SAME SIGNS DIFFERENT SIGNS

( ) ( )=+++ 19

( ) ( ) =++− 66 ( ) ( ) =−++ 47

( ) ( ) =−++ 97 ( ) ( ) =−+− 51

( ) ( ) =+++ 99

34

Adding Integers (A)Use an integer strategy to find each answer.

(-3) + (+12) = (-15) + (-10) = (+15) + (-10) =

(-15) + (-3) = (+6) + (+5) = (-7) + (-5) =

(+9) + (+4) = (+9) + (+11) = (+10) + (+11) =

(-15) + (+15) = (-7) + (+5) = (-2) + (+11) =

(+11) + (-3) = (-9) + (-14) = (+14) + (+11) =

(-5) + (-7) = (-10) + (+2) = (+4) + (+13) =

(+11) + (+13) = (-7) + (-12) = (-4) + (-7) =

(-14) + (+5) = (-1) + (+10) = (-5) + (-11) =

(+5) + (-14) = (-3) + (-10) = (-8) + (-5) =

(+8) + (-12) = (-10) + (-9) = (-1) + (+3) =

Math-Drills.Com35


(-11) + (-5) = 12 + 2 = 10 + (-13) =

(-8) + (-5) = 13 + 14 = (-7) + 15 =

11 + 15 = (-3) + (-1) = (-12) + (-1) =

(-2) + (-15) = 10 + (-12) = (-5) + 7 =

13 + (-4) = 12 + 2 = 12 + (-13) =

(-9) + (-1) = 9 + (-6) = 3 + (-3) =

2 + (-13) = 14 + (-9) = (-9) + 2 =

(-3) + 2 = (-14) + (-5) = (-1) + 7 =

(-3) + (-3) = 3 + 1 = (-8) + 13 =

10 + (-1) = (-13) + (-7) = (-15) + 12 =

Math-Drills.Com36


14 + 12 = 4 + -2 = 13 + 9 =

-11 + -11 = -8 + 13 = 6 + 14 =

10 + 7 = 15 + 9 = 2 + 6 =

15 + -15 = -11 + -3 = -6 + -3 =

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

11 + -5 = 12 + -8 = 4 + 2 =

9 + 5 = 4 + -7 = -8 + -12 =

-2 + 14 = 10 + 6 = 6 + -14 =

13 + 4 = -13 + -15 = -4 + -8 =

-6 + 7 = -7 + 12 = -6 + 9 =

Math-Drills.Com37


28 + -82 = 10 + 36 = 39 + 95 =

66 + 36 = 66 + 81 = -69 + 5 =

48 + 77 = -12 + -4 = -38 + -19 =

49 + -76 = 6 + 47 = 79 + 98 =

20 + -56 = 67 + -23 = -85 + -78 =

-57 + -22 = -36 + -32 = -81 + -5 =

-11 + 98 = -26 + 17 = -49 + -20 =

-93 + -20 = -10 + 58 = -58 + -21 =

-70 + 5 = 20 + 88 = 20 + 6 =

28 + 52 = 14 + 72 = 18 + -56 =

Math-Drills.Com38

4.3 ~ Addition with Rational Numbers When adding two numbers with the same sign: When adding two numbers with different signs:

39

ADDING RATIONAL NUMBERS

Signs: Operation: Solution: SUM: 1)

95

98+−

Same or

Different

Add or

Subtract

Positive or

Negative

95

98+−

2)

106

51 −−

+

Same or

Different

Add or

Subtract

Positive or

Negative

106

51 −−

+

3) 14.07 + − 3.9 =

Same or

Different

Add or

Subtract

Positive or

Negative

14.07 + − 3.9 =

4)

10910

6519 +−

Same or

Different

Add or

Subtract

Positive or

Negative

10910

6519 +−

5)

Same or

Different

Add or

Subtract

Positive or

Negative

40

8) At 10 pm, the temperature in Alaska was − 12 degrees.

At midnight, the temperature dropped 24 degrees.

Write an addition problem that represents this situation.

What was the temperature at midnight?

9) Justin opened a bank account by depositing (putting in) $50.80 in it on Monday. He withdrew (took out) $36.11 on Tuesday. Then deposited his check worth $77.92 on Wednesday.

Write an addition problem that represents Justin’s situation.

How much money does Justin currently have in his account?

6)

Same or

Different

Add or

Subtract

Positive or

Negative

7)

Same or

Different

Add or

Subtract

Positive or

Negative

41

10) Write in words one addition problem as a real world example. Be sure it includes positive and negative numbers. Then write it as a mathematical sentence with a solution!

Sample: I deposit $20 and then withdraw $17 the next day. + 20 + − 17 = + 3

11) − 20 + + 14 + − 2 = 12) + 12 + − 4 + − 10 =

13) 7.26 + − 9.4 = 14) 17.08 + − 5.2 =

15) =+−

72

75

16) =−

+−

127

61

17) 532.6 +−

= (Remember: you can’t compare apples to oranges!)

42

Practice 4-‐3

Adding Rational Numbers

1) Which of the following numbers are not a whole number?

0, 5, -‐3, 24

Explain why.

2) Tell whether each statement is true or false.

a) All whole numbers are integers True or False

b) All rational numbers are integers True or False

c) 3.7 is a rational number True or False

d) All integers are whole numbers True or False

3) Find the sum of the following:

a) 15 + 27 = b) -‐25 + 31 = c) -‐73 + (-‐10) =

d) 35 + (-‐17) = e) -‐105 + 26 = f) -‐53 + 19 =

4) Find the sum of the following:

a) 95 + 92 = b) 3.7 + 29.5 =

c) 6.2 + (-‐17.2) = d) 65 + -‐

83 =

e) 658 +

312 = f)

749 + -‐

215 =

43

Adding Rational Numbers

Examples: Add. 1) 4 + 7 = 11 3) 4 + (-7) = -3 2) - 4 + 7 = 3 4) - 4 + (-7) = -11 Add.

1) -5 + (-6) 2) -8 + 3 3) -5 + 5 4) -14 + (-13) 5) 4 + (-5)

6) -3 + 10 7) -6 + (-15) 8) 2 + (-8) 9) -7 + 5 10) -1 + (-4)

11) 16 + (-12) 12) -4 + (-8) 13) -7 + (-5) 14) -6 + 7 15) 10 + (-6)

16) 103

109 −+ 17)

73

72 −+

− 18) 25

21 −+

19) -2.1 + 3.5 20) -0.8 + (-0.3)

44

4-‐3 Practice – Adding Rationals Find the sum of the following:

1) !!!+ !

!!= 2)

!!+ !

!=

3) !

!+ − !

!= 4)

!!+ !

!=

5) 2 !!+ 4 !

!= 6) 2 !

!+ 3 !

!"=

7) 1 !!+ 4 !

!= 8) 3 !

!+ −4 !

!=

45

4-‐4 Subtracting Integers

1) Re-‐write Subtraction expressions into Addition:

ADD THE OPPOSITE! 2) Follow the Adding Integer Steps:

Examples:

=−− 65

( )=−−− 86

=−− 122

Write and simplify a subtraction expression for the temperature at 5:00 P.M. and at 8:00 P.M. Model each expression on the thermometer

=−− 73 =−− −61 =−1510

46

Subtracting Integers (A)Use an integer strategy to find each answer.

(-6) - (+2) = (-3) - (+8) = (+5) - (-5) =

(-9) - (-8) = (+9) - (-4) = (+6) - (-9) =

(-6) - (+6) = (+8) - (-7) = (+7) - (-5) =

(-8) - (-8) = (-6) - (+3) = (+2) - (+1) =

(+5) - (+1) = (-3) - (+4) = (-6) - (+3) =

(+6) - (-2) = (-4) - (+3) = (+2) - (+9) =

(-3) - (+5) = (-6) - (+1) = (+1) - (+1) =

(-8) - (+5) = (+8) - (-8) = (-2) - (+3) =

(-9) - (-4) = (+1) - (+4) = (+3) - (+4) =

(+1) - (+3) = (+7) - (+9) = (+8) - (-9) =

Math-Drills.Com47

Subtracting Integers (A)Use an integer strategy to find each answer.

-4 - 10 = -10 - -1 = 1 - 2 =

-1 - -11 = -5 - -2 = -3 - -11 =

11 - -14 = -3 - -10 = 1 - 2 =

3 - 3 = 1 - -10 = 13 - 14 =

-2 - -14 = 10 - 12 = 13 - 12 =

4 - 15 = -5 - -1 = -14 - -7 =

-6 - -10 = 5 - 5 = 8 - -6 =

-7 - 2 = -8 - 3 = -5 - -12 =

12 - 2 = -6 - 11 = -3 - 2 =

-9 - -6 = 11 - -8 = 5 - -10 =

Math-Drills.Com48

Integer Addition and Subtraction (A)

3 + (-8) = (-9) - (-4) = 7 - 5 =

6 - (-4) = (-4) - (-2) = (-4) - 10 =

6 - 5 = (-2) - 5 = (-2) - 7 =

(-8) + (-2) = 8 + 6 = (-9) + 10 =

8 + (-10) = 2 - (-10) = 8 - 5 =

8 - (-2) = 1 - (-7) = 4 + 2 =

(-2) + 6 = (-4) - 4 = 9 - (-7) =

(-1) - 0 = 7 - 5 = (-5) + (-10) =

(-1) - (-2) = (-5) - (-6) = 9 - (-9) =

7 - 4 = (-2) + 5 = (-4) - (-10) =

8 - (-2) = (-6) + 2 = 4 + 1 =

-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS49

Integer Addition and Subtraction (B)

(-8) + 6 = (-3) - 6 = 7 + (-3) =

(-1) + (-3) = 7 + (-10) = (-8) - (-2) =

1 - (-6) = (-6) + (-1) = (-2) - (-7) =

2 + (-2) = 3 + (-6) = 7 - 4 =

(-5) - (-8) = 2 - (-6) = (-8) - 10 =

2 - (-1) = (-1) - 8 = (-10) + 10 =

4 - 9 = 3 + 6 = 5 - 0 =

6 - 3 = 5 + 2 = (-2) + 1 =

(-4) + (-2) = (-8) + (-8) = (-4) - (-1) =

10 + 4 = 7 + 9 = (-9) - 1 =

8 - 5 = (-10) - (-3) = (-7) + 4 =

-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS.COM MATH-DRILLS50

4.5 Subtracting Rationals

Rewrite as an addition problem, then decide if the answer is positive, negative, or zero.

51

Adding & Subtracting Rational Numbers

1) ( ) ( )61811 −−+−−

2) ( ) 571010 −−−−

3) 98.36 −

4) ( )5.28.5 −+

5) ( )7.38.1 −−

6) 8.27 −

7) ( ) ( ) 4.52.78.0 −−+−

8) ( ) 013.48.07.1 +−−

9) 58

23

+⎟⎠

⎞⎜⎝

⎛−

10) ⎟⎠

⎞⎜⎝

⎛−−21

47

11) 47

51+⎟⎠

⎞⎜⎝

⎛−

12) 54

52−

52

Adding & Subtracting Rational Numbers:

1)

2)

3)

4)

5)

6)

7)

8)

8)

9)

10)

11)

12)

13)

53

14)

15)

16)

( )5.85.8 −−−

17)

18)

19)

20)

21)

22)

23)

24)

25)

26)

What is the difference between -‐424 and 125 on the number line? Explain how you found your answer!

54

4-‐6 Distance on a Number Line

55

Practice 4-‐6

Distance on a Number Line

Ex 1) Find the distance between 18 and -‐25 on a number line.

Ex 2) Find the distance between -‐12.4 and -‐2.6 on a number line.

Ex 3) Kim is standing on a diving platform that is 15 feet above the pool. She dives in and

her dive takes her 6 feet below the water. How far apart is it from where Kim started to

where she finished the dive?

56

Absolute Value/Integer Practice

1.) Insert <, >, or = between the pair of numbers. a) −13 ____ 19 b) −2.7 ____ −2. 6 c) 1 !

! ____ − !

!

d) 3 + 8 ____ 2 − 11 e) −3.2 ____ −3 !

! f) 3 − (−4) ____ −8

2.) Place each set of numbers in order from smallest to largest. Set 1: -‐0.4, − !

!, 3, −0.5 ___________________________________________________

Set 2: −12 , −10 , 6.5, −6. 5 _______________________________________________ Set 3: 2 !

!, 2.7 , − !

!, -‐1 ___________________________________________________

3) Write 2 absolute value expressions that could be used to find the distance between 3.9 and 8.3. 4) Circle all expressions that represent the distance between -‐8 and 7? a) −8 + 7 b) 7 + 8 c) −7 + 8 d) 8 − 7 e) 7 − 8 f) −8 − 7 5) Which pairs of numbers are 13.7 units apart on a number line? Circle all that apply. a) -‐26.3 and -‐12.6 b) -‐26.3 and 12.6 c) -‐3.2 and -‐10.5 d) 3.2 and 10.5 e) -‐3.2 and 10.5 f) 26.3 and -‐12.6 6) Suppose a diver is swimming 13.2 feet below sea level. A whale is 851 feet below sea level. How much lower is the whale than the diver? 7) Which pair of numbers is farther apart? a) -‐20,593 and 814.18 b) -‐20,593 and -‐814.18

57

Topic 4: RATIONAL NUMBER REVIEW

1. Determine whether the given number belongs to each set. Write Yes or No in each box.

Whole Number Integer Rational Number

12

-‐125

67

2. Compare the numbers below using the <, >, or = symbol. a.) b.) │-‐2│___ │-‐18│ b.) 25 ___ │-‐25│

c.) │-‐14 │___ -‐9 d.) -‐16 ___ -‐18

3. Evaluate: 810 +− = __________

4. Evaluate: │-‐7│+ │1│= __________

5. Which of these situations can be represented by the opposite of 15?

Check all answers that apply.

o A. You win a $15 bet. o B. A football player is tackled for a loss of 15 yards. o C. You deposit $15 into your bank account. o D. An elevator descends 15 floors.

58

6. Which of the following are Sums of Additive inverses? Check all answers that apply. o A. 6+ (-‐8) o B. 6 + (-‐6) o C. -‐8 + (-‐8) o D. 8 + (-‐8)

7. Complete the number line below to show the addition problem 9 + (-‐3). Then solve the

problem.

-‐3 -‐2 -‐1 0 1 2 3 4 5 6 7 8 9 10

9 + (-‐3) = ______

8. Use the chip board below to find the sum of 3 + (-‐12).

○○○ ○○○○ ○○○○ 3 + ( -‐12) = ______

○○○○ 9. Suppose a deep sea diver dives from the surface to 50 feet below the surface. He then dives down 120

more feet. The diver’s depth is represented by the sum -‐50 + (-‐120). Find the sum.

-‐50 + (-‐120) = ________

10. -‐8 + (-‐10) = ______

11. -‐9 + 9 = _________

12. -‐16 + 10 = _______

13. Write each subtraction problem as an addition problem, then solve it.

Subtraction problem Addition problem Answer

a.) -‐8 -‐ 4 = _______________________ = _______

b.) 12 -‐ -‐ 5 = _______________________ = _______

c.) -‐3 -‐ -‐15 = _______________________ = _______

59

Topic 4 Review

1) What type of number is − !

!? Circle all that apply.

Integer Rational Whole 2) Fill in the blank with <, >, or =. −1 _____ −16 3) Which pairs of numbers are additive inverses? 9, 9 6, -‐6 -‐9, -‐9 -‐9, 9 -‐6, -‐6 4) In her garden, Pam planted a seed 4 !

!in. below the ground. After one month, the plant has grown a

total of 10 !!in. How many inches is the plant above the ground?

5) The temperature in town is 28.3°F during the day and -‐6.7°F at night. Find the difference in the temperatures. 6) Find the distance between -‐55 and -‐24 on a number line. 7) Evaluate the following: a) 13 + −7 b) −12 − −16 c) −3 !

!+ −4 !

! d) !

!− !

!

60

5-1 Multiplying Integers

Part One

Part Two

61

Key Concept

Part Three = = = = = = = = =

62

©J X2Y0c1q2Q 8KvuMt8af vSTogfbtQw9airweG NLDLeCX.E q EAQlylL 1reiVgchgtWsX 4rdeRsAegrZvoe5dT.X I 0MNaTdAeB hwfi5tVh8 dI6nIfkiBnliutlex SPArAeC-GATlVgFeYbvrzaG.Q Worksheet by Kuta Software LLC

Kuta Software - Infinite Pre-Algebra Name___________________________________

Period____Date________________Multiplying Integers

Find each product.

1)

6 × −4 2)

4 × 2

3)

3 × −4 4)

−6 × 4

5)

5 × −4 6)

−3 × 4

7)

−5 × 6 8)

−2 × −1

9)

−8 × −2 10)

11 × 12

11)

−7 × 5 12)

9 × −6

13)

10 × 5 14)

9 × 2

15)

−12 × 7 16)

8 × −12

17)

9 × 10 × 6 18)

−6 × −10 × −8

19)

7 × 9 × 7 20)

6 × 6 × −2

21)

−5 × −4 × −10 22)

9 × 9 × −5

23)

8 × 3 × 8 24)

7 × 5 × −5

63

5-2 Multiplying Rationals

Key Concept Part One Write if each product is positive or negative. = = = = = = = =

Part Two Find the product.

Part Three

64

Multiplying Rational Numbers

1) ⎟⎠

⎞⎜⎝

⎛−•87

32

2) ⎟⎠

⎞⎜⎝

⎛−•−212

81

3) ⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛322

512

4) ( )3415 −

5) ⎟⎠

⎞⎜⎝

⎛−•−910

109

6) ⎟⎠

⎞⎜⎝

⎛−⎟

⎠

⎞⎜⎝

⎛512

316

7) 1812

92

−•

8) ⎟⎠

⎞⎜⎝

⎛−−4135

65

Multiplying Rational Numbers

Multiply.

1)

=•2112

43

-‐

2)

=•−81

41

3)

=−•−322

211

4)

=−•−322

213

5)

( )( )=06.05.0

6)

( )( )=−− 9.007.0

7)

What is the sign of ba 2 when

72 −== ba ? Evaluate!

8) A farmer has 140 bushels of wheat to sell. He sells an

average of 5116 bushels each day.

Represent the total change in the number of bushels he has for sale after 6 days.

66

Multiplying Rational Numbers-‐ word problems

1) The width of a vegetable garden is 31 times its length. If the length of the garden is

437 ft, what is the width?

2) Mark left 83 of a pizza in the refrigerator. On Friday, he ate

21 of what was left.

What fraction of the entire of the pizza did he eat on Friday?

3) Alano wants to make one and a half recipes of the pasta salad recipe shown below.

Fill in each blank with the amount of ingredient needed to make the recipe.

Ingredient Amount Alano’s Recipe Broccoli cup

411

Cooked Pasta

cup433

Salad Dressing

cup32

Cheese cup311

67

5-3 Dividing Integers

Key Concept

Part One A B C D E F G H I

68

Part Two Part Three

An elevator descends 1,000 feet in 8 seconds. Express the movement of the elevator as a unit rate.

69

©q h2e0f1522 WKyuIt4a2 ZS4ozfCtVwtazr1eI QL3LACR.o R PAIl3lX qrUiogthytxsF 2rVeysRevr2vAegd7.C C 8MVaEdHeq 6wUiUtOhk GIXnJfqienHiOt0eQ rPOrBeJ-8ATlcgbe5bQrRa6.M Worksheet by Kuta Software LLC

Kuta Software - Infinite Pre-Algebra Name___________________________________

Period____Date________________Dividing Integers

Find each quotient.

1)

35 ÷ −5 2)

−8 ÷ 4

3)

−24 ÷ 4 4)

−8 ÷ −2

5)

8 ÷ 4 6)

−24 ÷ 8

7)

−21 ÷ 7 8)

6 ÷ −6

9)

−132 ÷ −11 10)

−60 ÷ −15

11)

−52 ÷ −4 12)

60 ÷ 12

-1-

70

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13)

6 ÷ −1 14)

75 ÷ 15

15)

65 ÷ −13 16)

12 ÷ 4

17)

−168 ÷ −12 18)

−8 ÷ 2

19)

−105

720)

−4

−1

21)

−10

−222)

−144

12

23)

24

−1224)

60

−15

-2-

71

5-4 Dividing Rationals

Part One

Part Two

72

Part Three

73

5-5 Operations with Rationals

A complex fraction is a fraction within another fraction. Always re-write them as a division problem. Then apply “Keep-Switch-Flip”

Extra Practice ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺

1) 43

2) 1210

−

85

315

3) 92

− 4) 813

531− 11

32−

74

Practice with Complex Fractions:

1. 12 4

2. 38

−2

3. −6

23

4. 5

− 57

5.

−23 2

6. 13

−3

7. −4

15

8.

− 56 − 14

9.

− 35 23

75

10. 15

− 23

11. − 12 25

12. 45 34

13. 12 23

14. − 35− 47

15. − 1011 12

16. −35

− 13

17. − 13 34

18. 45

− 13

76

19. 212 23

20. − 23 1 34

21. −125 1−3

22. 15

2 13

23. 325 34

24.

−312 3 45

25. 438

−1 89

26. −423 3 38

27.

−523 3 56

77

Order of Operations Practice

1) 8 + 4 x 22 - 6 2) 2 + 24 ÷ (6 - 4)3

3) 30 - 6 ÷ 2 x 32 4) 52 - (2 + 3) ÷ 5 8 - 2

5) 17 − (5 + 3)6 ÷ 42 6) 2 + 5(6 + 1) ÷ 7

7) (3 – 5)2

÷ 2 • 2

9) 432 −

97

31−

78

Order of Operations Practice

1) 8 + 4 x 22 - 6 2) 2 + 24 ÷ (6 - 4)3

3) 30 - 6 ÷ 2 x 32 4) 52 - (2 + 3) ÷ 5 8 - 2

5) 17 − (5 + 3)6 ÷ 42 6) 2 + 5(6 + 1) ÷ 7

7) (3 – 5)2

÷ 2 • 2 8) Use the distributive property toeliminate the parenthesis:

2( x + 7 – y) =

Now evaluate if x = -6 and y = 9.

79

Order of Operations with Rational Numbers

( )3295

−= FC 3259

+= CF

1) Convert 14°F into Celsius. 2) Convert 10°C into Fahrenheit.

3) Convert -13°F into Celsius. 4) Convert -30°C into Fahrenheit.

5) 124

86+ 6) 4

32 −

321836 •÷− 97

31−

7) Use the distributive property to eliminate the parenthesis:

½( x - 8 + y) =

Now evaluate if x = -10 and y = 12.

80

Name: __________________________ Score:


1)

−13 + | − 2 + 5| − 6 =

2)

|−8| + |−14| − 9 =

3)

|−7| + |−11| =

4)

|−9| − |−5 + 7| + |12| =

5)

|32 − 95 + 6| + |−15| − 4 =

6)

|−41| − |18| + 12 =

7)

| − 64 + 7| + 2 − 6 =

8)

17 + |−14 − 65| − 8 =

9)

|−44 + 62| + |11| − |28| =

10)

|−71| − |−23 + 57| − 22 =

11)

82 + |−15 − 75| − |3| =

12)

54 + 47 − | − 25 + 19| =

13)

|−3 + 14| + |8 + 5| − 2 =

14)

−9 + 74 − |87 − 33 − 7| =

15)

|56| − |−21 − 10| − 8 =

16)

47 + |−72| − 69 =

17)

|−8 + 11 − 4| + |4 + 7| =

18)

|12 − 4| − |−8 + 8| − 1 =

19)

|31| − |−51| + 82 =

20)

|−7 + 14| + |8| − |2 + 9| =

Solve each absolute value problem

81

Name: __________________________ Score:


Find the value:

1)

|−8| × |9| =

2)

|30| ÷ |5| =

3)

|11| × |−4| =

4)

|−21| ÷ |−7| =

5)

|−3| × |5| =

6)

|10| ÷ |2| =

7)

|3| × |−6| =

8)

|−24| ÷ |−8| =

9)

|−12| × |9| =

10)

|10| ÷ |10| =

11)

|7| × |−6| =

12)

|−9| ÷ |−1| =

13)

|−6| × |−5| =

14)

|36| ÷ |3| =

15)

|4| × |−4| =

16)

|−27| ÷ |−9| =

17)

|−4| × |6| =

18)

|56| ÷ |8| =

19)

|5| × |−7| =

20)

|−55| ÷ |−5| =

21)

|−10| × |3| =

22)

|12| ÷ |2| =

23)

|5| × |−8| =

24)

|−12| ÷ |−6| =

Absolute Value

82

Name: __________________________ Score:


1)

|56 − 15| × 8 +|�|

�=

2)

|�|

�× |4 − 1| =

3)

|−8| ×|��|

|�|− |7| =

4)

|��×�|

�×|�|

|��|=

5)

|−1 + 4| +|�|

|��| =

6)

3 +|��|

�× 7 =

7)

|�×�|

|�|+

|�|

�=

8)

−|3| × |6 − 2| =

9)

|3| ×|��|

�=

10)

|��|

�− |8| × | − 5| =

11)

|��|

�+

|��|

�− | − 3 × 4| =

12)

|��|

�×

|�|=

13

9 ×|��|

|�|=

14)

|��|

|�|+

|��|

�× 8 =

15)

|13| − 7 ×|��|

�=

16)

|��|

�− |9 × 2| + |4| =

17)

|��|

|��|− |3| =

18)

|��|

|�|× 5 × | − 2 − 3| =

19)

|9 + 2| −|��|

|�|=

20)

|22 + 1| +||

|�|× 6 =


83

Name: __________________________ Score:


1)

|2 − 3| +||

|�| =

2)

| �|

|�|+

|��|

�× 8 =

3)

2 +|�|

× |−1| =

4)

−|−5| × |7 − 1| =

5)

−|−4| ×|��|

�=

6)

|� |

�− |−9| × | − 6| =

7)

2 × −|6 + 3| −|� |

|�|=

8)

|��|

||×||

|�|=

9)

|�|

+

|� |

�− |−2 × 6| =

10)

| �|

� − |2 × 4| + |4| =

11)

|18| ×| ��|

�=

12)

−5 + |−1 + 6| ×|�|

=

13)

−|3| ×|��|

×

| �|

|�|=

14)

| ��|

||× 3 =

15)

|12 − 19| × 4 +| �|

�=

16)

|−5 − 2| +||

�× |8| =

18)

|��|

|�|− |6| =

18)

| ×�|

�×

|�|

|��|=

19)

|9 − 5| +|�|

|�| =

20)

|�|

|�|+

|� |

× 6 =


84

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R ÷

OF

IN

TE

GE

RS

+

OR

- O

F I

NT

EG

ER

S

85

name period - west seneca central school district

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