AnswersAG Q1 Keystone Algebra 1 Block 26-27 DDiamondEquivalent Expressions and the Distributive Property

Equivalent Expressions and the Distributive Property Answers

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1
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Check all that apply.

A
Distribute 9, by multiplication, to the variable, a, and to the constant, 8.
B
Write the two multiplications, 9(a) + 9(8)
C
The expression 9(a) is written as 9a.
D
The expression 9(8) equals 72.
E
The equivalent expression is 9a + 8.
F
The equivalent expression is 9a + 72.
2
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There are 12✔ 3x

A
1
B
2
C
✔ 3
D
x
3

There are 12✔ 36

A
1
B
2
C
✔ 3
D
6
4

The equivalent expression is 4x3x + 1✔ 3x + 33x + 4.

A
4x
B
3x + 1
C
✔ 3x + 3
D
3x + 4
5

The equivalent expression is 5x40x✔ 5(x + 7)5(x + 35).

A
5x
B
40x
C
✔ 5(x + 7)
D
5(x + 35)
6

Which expression is equivalent to 5(2n + 1)?

A
2n + 1
B
2n + 5
C
10n + 1
D
10n + 5
7

Question text not available

Answers:
5x divided by the GCF is , and 35 divided by the GCF is .:5x and 35
5x divided by the GCF is , and 35 divided by the GCF is .:5
5x divided by the GCF is , and 35 divided by the GCF is .:x
5x divided by the GCF is , and 35 divided by the GCF is .:7
5x divided by the GCF is , and 35 divided by the GCF is .:5(x + 7)
8

Model the expression as 12✔ 3x

Answers:
Selection 1:3
Selection 2:3
Selection 3:3
.:3x + 3
9

Which expression is equivalent to 15n – 20?

A
2(8n – 6)
B
6(2n – 9)
C
5(3n – 4)
D
5(4n – 3)
10

Find the GCF of 5355x✔ 5x and 35.

Answers:
5x divided by the GCF is , and 35 divided by the GCF is .:5x and 35
5x divided by the GCF is , and 35 divided by the GCF is .:5
5x divided by the GCF is , and 35 divided by the GCF is .:x
5x divided by the GCF is , and 35 divided by the GCF is .:7
5x divided by the GCF is , and 35 divided by the GCF is .:5(x + 7)
11

Are the expressions equivalent? Use j = 3 and j = 8 to determine if they are. 7(j – 2) 4j – 5

A
No, because when j = 8, the values of the expressions are different.
B
Yes, because when j = 3, the value of both expressions is 7 and when j = 8, the value of both expressions is 42.
C
Yes, because when j = 3, the value of both expressions is 7.
D
Yes, because when j = 8, the values of the expressions are different.
12

Use the distributive property to write an equivalent expression. Complete the statement. 4(9 + d) The equivalent expression is 49 + d49 + 4d36 + d✔ 36 + 4d.

A
49 + d
B
49 + 4d
C
36 + d
D
✔ 36 + 4d
13

When w = 10, both expressions have a value of .

Answer:

84

14

Is Jordan’s work correct? Choose the correct answer.

A
Yes, Jordan’s work is correct.
B
No, Jordan forgot to divide 48 by 6.
C
No, Jordan forgot to subtract 6 from 48.
D
No, Jordan forgot to multiply 6 and 48.
15

Check all points that you included in your response.

A
To use the distributive property, distribute multiplication by 2 to both terms inside the parentheses.
B
The products are 2(11) and 2(y).
C
The equivalent expression is 22 + 2y.
16

Check all points that you included in your response.

A
If both expressions have the same value after substituting and simplifying for x = 6 and x = 10, then they are equivalent.
B
When x = 6, the value of both expressions is 88.
C
When x = 10, the value of both expressions is 120.
D
Therefore, the expressions are equivalent.
17

Now, factor out the GCF by dividing each term in the expression by ✔ 55x3540.

A
✔ 5
B
5x
C
35
D
40
18

5✔ x5x35

A
5
B
✔ x
C
5x
D
35
19

5✔ 7x35

A
5
B
✔ 7
C
x
D
35

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