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SSAT Middle Level Math : How to find the distributive property

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Example Questions

Example Question #1 : Distributive Property

$3\times(4+\frac{1}{3})= ?$

Possible Answers:

$12+\frac{1}{3}$

$15+\frac{2}{3}$

Correct answer:

Explanation:

Using the distributive property we get: $(3\times4)+(3\times \frac{1}{3})=12+1=13$

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Example Question #2 : Distributive Property

Which of the following expressions is equivalent to the expression -6 (-3x+7) ?

Possible Answers:

18x -7

18x +7

18x - 42

18x +42

-18x - 42

Correct answer:

18x - 42

Explanation:

By the distributive property of multiplication over addition,

$-6 (-3x+7) = -6 \cdot (-3x) +(-6)\cdot 7 = 18x + (-42)= 18x - 42$

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Example Question #3 : Distributive Property

Which of the following expressions is equivalent to the expression 8 (-2x+7) ?

Possible Answers:

-16x+56

16x+7

-16x+7

16x-7

-16x-56

Correct answer:

-16x+56

Explanation:

By the distributive property of multiplication over addition,

$8 (-2x+7) = 8 (-2x)+8\cdot 7 = -16x + 56$

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Example Question #4 : Distributive Property

Simplify the expression: 11y - 3y + 4y

Possible Answers:

18y

-132y

-132y^3

12y

Correct answer:

12y

Explanation:

Apply the distributive property:

11y - 3y + 4y

$= \left (11 - 3 + 4 \right ) y$

$= \left (8 + 4 \right ) y$

=12 y

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Example Question #4 : Distributive Property

Simplify the expression: 7 (y+5)

Possible Answers:

y+12

y+35

7y+12

7y+35

7y+5

Correct answer:

7y+35

Explanation:

Apply the distributive property:

7 (y+5)

$= 7 \cdot y+7 \cdot5$

= 7 y+35

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Example Question #5 : Distributive Property

Which of the following is an example of an application of the distributive property?

Possible Answers:

$13 \times (54 \times 14) = \left (13 \times 54 \right ) \times 14$

$1 \times (54 \times 14) =54 \times 14$

$13 + (54 \times 14) = (54 \times 14) + 13$

$13 \times (54 + 14) = 13 \times 54 + 13 \times 14$

$13 + (54 \times 14) = 13 +(14 \times 54)$

Correct answer:

$13 \times (54 + 14) = 13 \times 54 + 13 \times 14$

Explanation:

According to the distributive property, for any values of a,b,c ,

$a (b + c) = a \cdot b + a \cdot c$

If we set a=13,b=54,c=14 , this become the statement

$13 \times (54 + 14) = 13 \times 54 + 13 \times 14$ ,

so this is the correct choice.

All of the other statements are true for different reasons:

$13 \times (54 \times 14) = \left (13 \times 54 \right ) \times 14$ is true because of the associative property of multiplication.

$13 + (54 \times 14) = 13 +(14 \times 54)$ is true because of the commutative property of multiplication.

$13 + (54 \times 14) = (54 \times 14) + 13$ is true because of the commutative property of addition.

$1 \times (54 \times 14) =54 \times 14$ is true because of the identity property of multiplication.

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Example Question #6 : Distributive Property

Simplify the expression:

8x - 7 (3x+ 6) - 5

Possible Answers:

-13 x + 1

-13 x - 1

-13 x - 47

-13 x + 37

-13 x - 37

Correct answer:

-13 x - 47

Explanation:

Distribute, then collect like terms:

8x - 7 (3x+ 6) - 5

$=8x - 7 \cdot 3x - 7 \cdot 6 - 5$

=8x - 21x - 42 - 5

$= \left ( 8 - 21 \right ) x - 42 - 5$

= -13 x - 47

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Example Question #7 : Distributive Property

Diana is thirty-three years older than her son Colin, who is three times as old as her niece Sharon. If is Diana's age, how old is Sharon?

Possible Answers:

$\frac{1}{3}D - 33$

$\frac{1}{3}D + 11$

$\frac{1}{3}D - 11$

3D - 99

3D-33

Correct answer:

$\frac{1}{3}D - 11$

Explanation:

Colin's age is thirty-three years less than Diana's age of , so Colin is D -33 years old; Sharon is one-third of this, or $\frac{1}{3 }\left (D -33 \right )$ . Using distribution, this can be rewritten as

$\frac{1}{3 }\left (D -33 \right ) = \frac{1}{3 } \cdot D - \frac{1}{3 } \cdot 33 = \frac{1}{3}D - 11$ .

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Example Question #8 : Distributive Property

Nina is twenty-one years younger than her mother Caroline, who is one-third as old as their neighbor Mr. Hutchinson. If is Nina's age, how old is Mr. Hutchinson?

Possible Answers:

$\frac{1}{3}N - 7$

$\frac{1}{3}N - 21$

3N + 63

3N + 21

3N + 7

Correct answer:

3N + 63

Explanation:

Caroline is twenty-one years older than Nina, so her age is N + 21 . Mr. Hutchinson is three times as old as Caroline, so he is $3\left (N + 21 \right )$ . Using distribution, this can be rewritten as

$3\left (N + 21 \right ) = 3 \cdot N + 3 \cdot 21= 3N + 63$ .

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Example Question #8 : Distributive Property

Which of the following expressions is equivalent to x(2-k) ?

Possible Answers:

x(k+2)

2x-kx

2x-2k

2(k-x)

Correct answer:

2x-kx

Explanation:

When distributing, the number outside the parentheses is multiplied by both of the numbers inside without changing any signs.

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SSAT Middle Level Math : How to find the distributive property

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Distributive Property

Example Question #2 : Distributive Property

Example Question #3 : Distributive Property

Example Question #4 : Distributive Property

Example Question #4 : Distributive Property

Example Question #5 : Distributive Property

Example Question #6 : Distributive Property

Example Question #7 : Distributive Property

Example Question #8 : Distributive Property

Example Question #8 : Distributive Property

All SSAT Middle Level Math Resources

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