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Module 3 Expressions
Homework Key
Math A Honors
2015 - 2016
Created in collaboration with Utah Middle School Math Project
A University of Utah Partnership Project
San Dieguito Union High School District
SDUHSD Math A Honors Module #3 – TEACHER EDITION 2
3.1A Homework: Matching Numerical Expressions to Stories* Name: Period: Four students, Alex, Brittany, Charlie, and Darlene, wrote a numerical expression for each story problem. Look at each student’s expression and determine whether or not it is appropriate for the given story problem. Explain why the expression “works” or “doesn’t work” using complete sentences. 1. I earned $6. Then I bought 4 candy bars for $0.50 each. How much money do I have left?
Expression Evaluate
Does it work?
Why or Why Not?
a. 6 – (0.50 + 0.50 + 0.50 + 0.50) $4 Yes
This subtracts the sum of 0.50 four times.
b. 6 – (0.50 – 0.50 – 0.50 – 0.50) $7 No
We need to subtract the sum of 0.50 four times.
c. 6 – 4(0.50) $4 Yes
It is like a only multiplying instead of repeated subtraction.
2. I earned $5. Then I spent $1 a day for 2 days in a row. How much money do I have now?
Expression Evaluate
Does it work?
Why or Why Not?
a. 5 – (1 – 1) $5 No
We need to subtract the sum of the two dollars.
b. 5 – (1 + 1) $3 Yes
We are subtracting the sum of the two dollars.
Write an expression that represents the situation for each problem. Then evaluate the expression to solve the problem. Write the answer in a complete sentence. There are various accurate expressions for these problems. They should each result in the value given. 3. Josh made ten 3-pointers and a 2-pointer at his basketball game. How many points did he score?
10(3) + 1(2) 32 points
4. I bought three apples for $0.25 each and 3 pounds of cherries for $1.75 a pound. How much money did I spend? 3(0.25) + 3(1.75) $6.00
SDUHSD Math A Honors Module #3 – TEACHER EDITION 3
5. Jim won 30 tickets. Evan won y tickets less than Jim did. How many tickets did Evan win?
Expression
Do you think it
will work?
Evaluate y = 6
Did it work?
Why or why not?
a. 30 – y --- 24 tickets Yes This is an accurate representation of
the expression
b. y 30 --- 24 tickets No Jim won more tickets than Evan, thus we must subtract from Jim’s amount.
c. y + 30 --- 36 tickets No Evan won less tickets than Jim, thus
we need to subtract.
d. 30 ÷ y --- 5 tickets No The difference between their amounts
is absolute; we must subtract.
Write an expression for each problem. Drawing a model is optional. Answer in a complete sentence.
6. I bought m gallons of milk for $2.59 each and a carton of eggs for $1.24. How much did I spend? m(2.59) + 1.24
7. Paul bought s sodas for $1.25 each and a bag of chips for $1.75. How much did he spend? s(1.25) + 1.75
8. Bob and Fred went to the basketball game. Each bought a drink for d dollars and nachos for n dollars. How much did they spend on two drinks and two orders of nachos? 2d + 2n or 2(d+n)
Spiral Review: Simplify each expression. Show all steps. 9. 2 ∙ 3 2 1 63
10. 2 ∙ 3 2 1 3
11. 2 ∙ 3 2 1 27 12. 4 ∙ 9 8 1 3
SDUHSD Math A Honors Module #3 – TEACHER EDITION 5
3.1B Homework: Algebra Tile Exploration Name: Period: Use the key below to interpret or draw the algebraic expressions in your homework. Key for Tiles:
x2 = x2
= -x2
Write an expression for what you see and then write the expression in simplest form. 1. x – 1 or x + (–1)
2. -2
3.
4.
5.
6.
x
1
1
1
1
1
x
x
x
x
x
x
x
x
x
x
1 1
1 1
1 1
x
x
x
x
1 1 1
1 1
x
x
x
111
x
x
1 1
1
x
x
x
x 1
xx
1 11 1
x
x
x
x
x
x
x – 2 or x + (–2)
3x – 3 or 3x + (-3)
x2 + x
–2x + 3
-x2
SDUHSD Math A Honors Module #3 – TEACHER EDITION 6
Draw a model for each of the expressions using the tile key. Simplify the expression if you can. 7. 2x + 4 8. 2x – 3 + 5
2x+2
9. 2x + 1 + 3 – 5 2x - 1
10. -3x + 2 + 2x - x + 2
1. –2x + 3 + 5x – 2 3x + 1
12. 5x – 3 – 4 + x 6x - 7
13. x + 4 + (–3x) – 7 -2x - 3
14. –x – 3 + 2x – 2 x – 5
15. 4x – 3 – 7x + 4 -3x + 1
SDUHSD Math A Honors Module #3 – TEACHER EDITION 7
Simplify each expression without using models. 16. 9 16 27 13 8 5
22 24 22
17. 2 3 6 9 5 7
7 8 13
Matching: Write the letter of the equivalent simplified expression on the line. 18. _e___ 3x – 5x
19. _a___ 4a – 12a
20. _ j___ 3x + 5x
21. _i___ 16a + a
22. _f___ 2x – 2y + y
23. _b___ 2x – 2 – 4
24. _h___ x – y + 2x
25. _c___ –y + 2y – x
26. _g___ 5x + 4y – 3x – x + 3y – 6y
27. _d___ 4x + 3y + 5x – 7y
a) –8a
b) 2x – 6
c) –x + y
d) 9x – 4y
e) –2x
f) 2x – y
g) x + y
h) 3x – y
i) 17a
j) 8x
Simplify each expression by combining like terms. 28. 13 9 22b 29. 45 12 33y
30. 11 14 13 –2u + 11 31. 6 4 2 10a – 2b
32. 1 3 5 33.
34. 3.4 21.4 3.4 2.2 –21.4x – 3.4y + 5.6
35.
36. 2 0.5 3 4.75 9.8 2.5x + 1.75y + 9.8
37. 14 9 15 16 –2w + 24
38. 2 39. 4 6 2 5 19 6m − 18
40. 6 16 9 18 2 -z + 2 or 2 - z 41. 88.5 22.4 4.04 26.3 92.54z - 22.4y + 26.3
42. 2 2 3 8 10x + 1 43. 65 4.2 65 2.2 5.4 3 5.4
SDUHSD Math A Honors Module #3 – TEACHER EDITION 8
44. Identify the terms, constants, coefficients, and like terms in each algebraic expression.
Expression Terms Constants Coefficients Like Terms
a. 7 3 2 1
7x, –3x, 2y, –1 –1 7, -3, 2 7x, –3x
b. 7 2 3 5 -7z, -2z, -3z, –5 –5 -7, -2, -3 -7z, -2z, -3z
c. 8 9 7 6
8, -9b, 7a, 6b 8 -9, 7, 6 -9b, 6b
d.
w, -x, -y, -z None 1, –1, –1, –1 None
45. Find the value for a for which the expressions 2a and 2 + a have the same value. Show work to
support your answer. 2
SDUHSD Math A Honors Module #3 – TEACHER EDITION 10
Section 3.1 Review Name: Period: For #1-3, simplify each expression.
1. 12 3 7 2 13 2 2.
3. ∙
∙
2169 3 -1 For #4-6, evaluate each expression if c = 6, d = 3, e = 4, and f = 5. Show all work. 4. 4de + 3f 5. 4(de + 3f) 6. 4c3 – 2e 63 108 856 For #7-12, simplify each expression. 7. 11 7 8 9 2
9 10 8. 8 3 5 7 3
3 10 3
9. 1 5
4
10. 5 7 9 8 14
11. 8 3 12 5 4 7 16 1
12. 4 3 7 2 10
For #13-14, write an expression. Simplify, if possible. State your answer in a complete sentence. 13. Chloe bought 14 puzzles. Chloe’s brother
Oliver bought y less puzzles than Chloe. How many puzzles did Oliver buy? 14 Oliver bought 14 puzzles
14. Hazel and her friends went to a Los Angeles Kings game. They bought x hamburgers for $8.75 each and x nachos for $5 each. How much did they spend? 8.75 5 Hazel and her friends spent $13.75
SDUHSD Math A Honors Module #3 – TEACHER EDITION 11
15. Sally bought 4 cupcakes for $3 each and 2 slices of pie for $1 each. Circle all of the expressions that accurately represent this situation.
a) 4 + 4 + 4 + 2
b) 4(3) + 2(1)
c) 3 + 3 + 3 + 3 + 1 + 1 d) (4 + 3)(2 + 1)
For #16-18, identify the terms, constants, coefficients, and like terms in each algebraic expression.
Expression Terms Constants Coefficients Like Terms
16. 5x + 3y + 2x – y + 4
5x, 3y, 2x, -y, 4
4
5, 3, 2, -1
5x, 2x, 3y, -y
17. 8p + 12 - 3p – 6p + 7
8p, 12, -3p, -6p,
7
12, 7
8, -3, -6
8p, -3p, -6p
12, 7 18. x + y – z + 9
x, y, -z, 9
9
1, 1, -1
None
For #19-20, write a simplified expression for each model. Key for Tiles:
= 1
= –1
19. -2x + 2
20. x - 2
– X
– X
– X
X
-1
-1
1
1
1
1
1
X
– X -1 -1
-1
1 1
-1
X -1
1
-1
SDUHSD Math A Honors Module #3 – TEACHER EDITION 12
For #21-24, write an expression for what you see and then write the expression in simplest form. 21. 2 1 7 Model:
Simplified expression: 5 1
22. 3 3 4 Model:
Simplified expression: 4 7
23. 4 3 2 5 2
Simplified expression: 6 5
24. 2 5 2
Simplified expression: 2 3
-1
-1
-1
-1
-1
-1
-1
-1
-1 -1 -1
-1 -1
– X
– X
-1 -1 -1 -1 -1
1 1
SDUHSD Math A Honors Module #3 – TEACHER EDITION 13
3.2A Homework: Iterating Groups* Name: Period: Draw a model that represents each problem. Simplify each expression. 1. 3(x + 1) 3x + 3
2. 2(3x + 2) 6x + 4 3. 4(x + 3) 4x + 12
4. 2(3x – 1) 6x – 2 or 6x + (–2)
5. 3(2x – 3) 6x - 9 6. 5(x – 1) 5x - 5
1 X
1 X
1 X
1
X
1 X
X
1
X
1 X
X
1 X 1 1
1 X 1 1
1 X 1 1
1 X 1 1
-1 X
X
X
-1 X
X
X
-1
X
X -1 -1
-1
X
X -1 -1
-1
X
X -1 -1
-1X
-1X
-1X
-1X
-1X
SDUHSD Math A Honors Module #3 – TEACHER EDITION 14
Simplify each expression. 7. 12(x – y) 12x – 12y 8. r(c – d) rc - rd
9. 8(6 – k) -8k + 48 10. 10(3p + 5) 30p + 50
11. 6(0.3c + 1.2d) 1.8c + 7.2d 12. r(r – 7) 7
13. 0.2(2 + 3e) 0.6e + 0.4 14. 12 4 -x + 3
Spiral Review: In the number squares below, each row, column, and diagonal must have the same sum. Complete each number square and state the common sum. 15.
5 -9
-1
-3 -7
16.
-5 6
4 3
2 0 5
-3 -6
Sum: Answers given in class
Sum: Answers given in class
SDUHSD Math A Honors Module #3 – TEACHER EDITION 15
3.2B Warm Up: Iterating Groups with Rectangles
3.2B Homework: More Simplifying* Name: Period: Simplify the following expressions. Models are optional. Show your work.
1. (51x + 34)
6x + 4
2. – 3(2x + 1) 6x – 3
3. – 3(2x – 1) 6x + 3
4. – (x + 4) x – 4
5. – (x – 4) x + 4
6. – (4 – x) 4 + x or x – 4
7. – 2(4x – 3) 8x + 6
8. – 5.1(3x + 2) 15.3x – 10.2
9. – (4x – 5)
14x +
10. 5x + 1 (x + 3)
6 x +
11. 5x + 2(x – 3) 7x – 6
12. 5x – 2(x + 3) 3x – 6
13. 5x – 2(x – 3) 3x + 6
14. 3x + 2 – 4x + 2(3x + 1) 5x + 4
15. –7x + 3 + 2x – 3(x +2) 8x – 3
SDUHSD Math A Honors Module #3 – TEACHER EDITION 16
16. 10x – 4 – 7x – 4(2x 3) 5x + 8
17. 4x – 5(2x 5) – 3x + 4 9x + 29
18. x – 7 – 2(5x – 3) + 4x 5x – 1
SDUHSD Math A Honors Module #3 – TEACHER EDITION 17
For #19-20, read and answer each question carefully. 19. The price for each notebook is p dollars. The number of notebooks bought by Lucy, Joe, and Kate is
represented by a, b, and c. Which expression represents the total price?
a. b. 3 c. 3 d.
20. There are 3 groups of students that are planting trees. Each student plants 2 trees. The number of
students in each of the 3 groups is represented by i, j, and k. Which expression represents the total number of trees planted?
a. 2 b. 2 3 c. 2 d. 6
Spiral Review: Find the area and perimeter. Use a formula, show the substitution step and remember the units on the final answer. 21. 32 m 45 m 22. 12 in
18 in
23. 7.4 cm 8.2 cm 13.1 cm
Area: 1440 m2 Perimeter: 154 m
Area: 108 in2 Perimeter: 54 in
Area: 96.94 cm2 Perimeter: 42.6 cm
SDUHSD Math A Honors Module #3 – TEACHER EDITION 18
3.2B Extra Practice: Simplified Expressions * Name: Period: Matching: Write the letter of the equivalent expression on the line: 1. B 3 6
2. I 3 6
3. J 3 1
4. A 3 1
5. G 6 3
6. H 6 18
7. E 6 18
8. F 6 1
9. C 3 2
10. D 3 2
A. 3 3
B. 3 18
C. 2 6
D. 2 6
E. 6 1
F. 6
G. 6 18
H. 6 1
I. 3 18
J. 3 3
Practice: Simplify each expression. 11. 7 3
7 21 12. 8 8
8 64 13. 6 6
6 6
14. 3 4 3 12
15. 9.8 5.2 9.8 50.96
16. 4 6 6 24 24
17. 7 7 7
18. 2 6
3
19. 9 4 7 63 36
20.
21. 1 4 4
22. 5
553
23. 2 3 2 6 4
24. – 3 6 3 6
25. 4 1 4 4
26. 1.6 2 2 3.2 3.2
27. 3 5 2 15 6
28. 7 3 2 21 14
29. 3 1 3
30. 14 12 14 168
31. 6 4 4 24
SDUHSD Math A Honors Module #3 – TEACHER EDITION 19
Simplify. 32. 5 10 2 4 3
4 14 33. 5 10 2 4 3
10 6
34. 2 5 2 4 2 2
35. 7 3 5 8 6 10 5 3 11
36. 4 2 5 8 20
37. 6 4 2 12 24
38. 8 6 2 12 16
39. 3 5 3 15 9
40. 6 8
3 4
41. 1 2 2
42. 3 6 3 6
43. 3 5 3 5
44. 7 2 7 2
45. 7 5 7 35
46. 3 4 2 5 8 17
47. 12 6 4 2 12 12
48. 5 8 6 6 3
49. 4 3 5 5 7
50. 2 6 8 10 12 6
51. 5 1 2 6 7 6
SDUHSD Math A Honors Module #3 – TEACHER EDITION 21
3.2C Homework: Properties and Proofs* Name: Period: Complete the table below:
1. Identity Property of Addition: Rule: 0
Show the Identity Property of Addition with 2.17 2.17 + 0 = 2.17 3 0 3
Show the Identity Property of Addition with 3
2. Identity Property of Multiplication: Rule: ∙ 1
23 ∙ 1 23
Show the Identity Property of Multiplication with 23
Show the Identity Property of Multiplication with 3b 3 ∙ 1 = 3
3. Multiplicative Property of Zero:
Rule: ∙ 0 0
43.581 ∙ 0 0
Show Multiplicative Property of Zero with 43.581
4 ∙ 0 0
Show the Multiplicative Property of Zero with 4xy
4. Commutative Property of Addition:
4.38 + 2.01 is the same as: 2.01 + 4.38 x + z is the same as:
5. Commutative Property of Multiplication: ab = ba
∙ is the same as: ∙
6k is the same as: ∙ 6
6. Associative Property of Addition: (a + b) + c = a + (b + c)
(1.8 + 3.2) + 9.5 is the same as: 1.8 + (3.2 + 9.5 ) (x + 1) + 9 is the same as: x + (1 + 9)
7. Associative Property of Multiplication:
(2.6 · 5.4) · 3.7 is the same as: 2.6· (5.4· 3.7)
is the same as:
Use the listed property to fill in the blanks.
8. Multiplicative Inverse Property: 1 5 = 1 ¼ ( 4 ) = 1
9. Additive Inverse Property: a + (–a) = 0
+ = 0 x + –x = 0
10. Substitution Property: 2 + 3 = 5 (3 + 4)y = 7y
SDUHSD Math A Honors Module #3 – TEACHER EDITION 22
Name the property/definition demonstrated in each statement. Use the complete name.
11. 9 ∙ 7 7 ∙ 9 Commutative Property of Multiplication
12. 2 3 2 3 Definition of Subtraction
13. 25 + (–25) = 0 Additive Inverse Property
14. 515
1 Multiplicative Inverse Property
15. (x + 3) + y = x + (3 + y) Associative Property of Addition
16. 1 mp = mp Identity Property of Multiplication
17. (-20 + 7)y = -13y Substitution Property
18. 0 + 6b = 6b Identity Property of Addition
19. 7x 0 = 0 Multiplicative Property of Zero
20. 4(3z)=(43)z Associative Property of Multiplication
21. x + 4 = 4 + x Commutative Property of Addition
22. 3(x + 2) = 3x + 6 Distributive Property
23. Define the operation @ in this way: If A and B are any integers, then A@B = A – B + 1. For
example:9@3 = 9 – 3 + 1 = 7
a. Find 2@4 Answers given in class
b. Find 3@(2@4).
c. Find (3@2)@4.
d. Based on the two questions above, does it appear that the associative property works for the operation @? Explain.
e. Find a number E so that E@(5@E) = 1. Explain how you found your answer.
SDUHSD Math A Honors Module #3 – TEACHER EDITION 23
Using the properties, complete the following algebraic proofs stating the property that is used to move to the next step. 24. -5x + 8 + x = -5x + 8 + 1x _____________________________________________
= -5x + 1x + 8 _____________________________________________
= (-5 + 1)x + 8 _____________________________________________
= -4x + 8 _____________________________________________
25. 7z – 5(3 + z) = 7z – 15 - 5z _____________________________________________ = 7z + (-15) + (-5z) _____________________________________________ = 7z + (-5z) + (-15) _____________________________________________ = [7 + (-5)]z + (-15) _____________________________________________ = 2z + (-15) _____________________________________________ = 2z – 15 _____________________________________________ Spiral Review: Fill in the table:
Simplified Fraction Decimal Percent
26. 45
0.8 80%
27. 8899
0. 88 888899
%
28. 2150
0.42 42%
29. 13
0. 3 3313%
30. 6310
6.3 630%
Identity Property of Multiplication
Commutative Property of Addition
Distributive Property
Distributive Property
Distributive Property
Substitution Property
Substitution Property
Definition of Subtraction
Commutative Property of Addition
Definition of Subtraction
SDUHSD Math A Honors Module #3 – TEACHER EDITION 24
3.2D Homework: Modeling Backwards Distribution* Name: Period: Write each in reverse (factored) distributed form. Use a model to justify your answer. Label all part of the model.
1. 2x + 4 2(x + 2)
2. 3x + 12 3(x + 4)
3. 2x + 10 2(x + 5)
4. 3x + 18 3(x + 6)
5. x2 + 2x x(x + 2)
6. x2 + 5x x(x + 5)
Simplify each expression. Draw and label a model to justify your answer. 7. 2x + 3x 5x
8. (2x)(3x) 6x2
X
X
X
X
X
SDUHSD Math A Honors Module #3 - TEACHER EDITION 25
1. Looking at #7 and #8, explain how these expressions are the same and how are they different. You may want to reference your models in your explanation.
Simplify the following expressions without a model: 2. 4(x + 7)
4x + 28 3. 7(x – 3)
7x - 21 4. -2(x + 4)
-2x - 8
5. 3x2(x + 2y) 3x3 + 6x2y
6. 3p(p + 3q) 3p2 + 9pq
7. a(a – 12) a2 – 12a
8. 3m(m + 2) 3m2 + 6m
9. x(x + 9) x2 + 9x
10. 12(4k + 13) 48k + 156
Factor (reverse distribute) the following expressions completely. 11. 5x + 35
5(x + 7) 12. a2 + 4a
a(a + 4) 13. 9x – 81
9(x – 9)
14. 4x + 18 2(2x + 9)
15. 42y + 18 6(7y + 3)
16. 6y2 - 9y 3y(2y – 3)
17. 10x + 30 10(x + 3)
18. 12f2 + 18f 6f(2f + 3)
19. 14g3 – 8g 2g(7g2 – 4)
Spiral Review: 20. Which statement(s) is/are false? If false, give a counterexample (an example that proves it doesn’t
work) and explain your example.
a. The opposite of a non-zero whole number is negative.
b. The sum of a number and its additive inverse is one.
c. The product of a number and its multiplicative inverse is one.
d. The sum of a number and zero is the original number.
SDUHSD Math A Honors Module #3 - TEACHER EDITION 26
Section 3.2 Review Name: Period:
1. The neighbors have a triangular yard with a perimeter of 4 3 2. Which of the following could be side lengths of the yard? Circle all that apply.
a. 4y – 2x + 1, 4x – 4, and 2x + 1 b. -4 + 2x – y, 5y + 3x, and –2x + 2 c. 6 – 2x, –y + 7x, and 5y – 2x – 8 d. 3(x + y–1), -(2x–2), and x – y – 1 e. –2(2y – 3x + 1), –3(–2y + x + 2), and 2y + 6
2. Name the property to justify each step. (Yes, spelling counts!) Statement/Steps Algebra Property to justify change from one step to the next:
a. 2x(1)+ 20 + 4x
Multiplicative Identity 2x + 20 + 4x
b. 2x + 20 + 4x
Commutative Property of Addition 2x + 4x + 20
c. 2x + 4x + 20
Associative Property of Addition (2x + 4x)+20
d. (2x + 4x) + 20
Distributive Property 2x(1 + 2) + 20
e. 2x(1 + 2) + 20
Substitution Property 2x(3) + 20
f. 2x(3) + 20
Commutative Property of Multiplication (3)2x + 20
3. Write each expression in reverse distributed (factored) form. Draw a model using tiles to justify your
answer.
a. 5 15 b. 4 c. 20 30 d. 14 28 5 3 4 10 2 3 14 2
4. Which expression(s) below is (are) equivalent to 5 10 :
a. 10 5
b. 2 c. – 2 d. 2 1
e. 10 5
f. 5 10
SDUHSD Math A Honors Module #3 - TEACHER EDITION 27
5. Jason tells you the expression 4 7 can be expanded to 28 4 using the Distributive Property. Is he correct? Explain.
Jason is incorrect. Distributive Property is multiplication over addition or subtraction. The correct Simplification of the expression is -28yz 6. Model each expression and simplify: a. 4 3 3 Model: Simplified expression: 3 7
b. 2 4 2 1 Model: Simplified expression: 2 2 1
c. 3 2 1 Model: Simplified expression: 6 3
7. Write each expression in reverse distributed (factored) form. Draw a model to justify your answer. a. 5 15 Reverse distributed form: 5 3 Model:
b. 4 Reverse distributed form: 4 Model:
For #8-10, write a simplified expression. Verify that your expression is equivalent to the one given by evaluating both expressions using x = 5. 8. 3x + (2 – 4x)
-x + 2 Evaluation: -3 9. -3x + (2 + 4x)
x + 2 Evaluation: 7 10. 3x – (-2 + 4x)
-x + 2 Evaluation: -3 For each proof, identify the property used in each line. Write the complete name. 11.
1 1∙
1 ∙
Associative Property of Multiplication Multiplicative Inverse Property Identity Property of Multiplication
12. 1 ∙ 1 1
1 1
∙ 0
0
Identity Property of Multiplication Distributive Property _____ Additive Inverse Property Multiplicative Property of Zero
SDUHSD Math A Honors Module #3 - TEACHER EDITION 28
Simplify the following expressions. 13. 5 3 6 6
2 14. 5 3 5 8
8 13
15. 4 7 2 5 3 2 5
16. 7 7 5 35 14
17. 3 2 4 4 6 4 7 2 10
18. 17 2 12 12 15 14 14
19. 3 6 5 2 4 3 2 5
20. 10 10 3 20 3
21. 31 5 4 12 13 23 8 8 8
22. 3 2 5 5 10 3 8
23. 3 6
2 4
24. 6 1 2 12 6
25. 0.25 7 0.25 1.75
26. 3 3 3 9
27. 4 1 6 24 4
28. 0.8 0.5 0.7 0.56 0.4