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SSAT Middle Level Math : Distributive Property

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Example Questions

Example Question #1 : Distributive Property

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

Possible Answers:

$\displaystyle 8$

$\displaystyle 21$

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

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

$\displaystyle 13$

Correct answer:

$\displaystyle 13$

Explanation:

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

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Example Question #1 : Distributive Property

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

Possible Answers:

$\displaystyle -18x - 42$

$\displaystyle 18x - 42$

18x +42 $\displaystyle 18x +42$

18x +7 $\displaystyle 18x +7$

18x -7 $\displaystyle 18x -7$

Correct answer:

$\displaystyle 18x - 42$

Explanation:

By the distributive property of multiplication over addition,

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

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Example Question #3 : How To Find The Distributive Property

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

Possible Answers:

-16x+56 $\displaystyle -16x+56$

-16x+7 $\displaystyle -16x+7$

16x-7 $\displaystyle 16x-7$

-16x-56 $\displaystyle -16x-56$

16x+7 $\displaystyle 16x+7$

Correct answer:

-16x+56 $\displaystyle -16x+56$

Explanation:

By the distributive property of multiplication over addition,

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

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Example Question #1 : How To Find The Distributive Property

Simplify the expression: $\displaystyle 11y - 3y + 4y$

Possible Answers:

$\displaystyle 4y$

-132y^3 $\displaystyle -132y^3$

12y $\displaystyle 12y$

18y $\displaystyle 18y$

-132y $\displaystyle -132y$

Correct answer:

12y $\displaystyle 12y$

Explanation:

Apply the distributive property:

$\displaystyle 11y - 3y + 4y$

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

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

=12 y $\displaystyle =12 y$

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Example Question #2 : How To Find The Distributive Property

Simplify the expression: 7 (y+5) $\displaystyle 7 (y+5)$

Possible Answers:

y+12 $\displaystyle y+12$

7y+35 $\displaystyle 7y+35$

y+35 $\displaystyle y+35$

7y+12 $\displaystyle 7y+12$

7y+5 $\displaystyle 7y+5$

Correct answer:

7y+35 $\displaystyle 7y+35$

Explanation:

Apply the distributive property:

7 (y+5) $\displaystyle 7 (y+5)$

$= 7 \cdot y+7 \cdot5$ $\displaystyle = 7 \cdot y+7 \cdot5$

$\displaystyle = 7 y+35$

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Example Question #2 : How To Find The Distributive Property

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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

so this is the correct choice.

All of the other statements are true for different reasons:

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

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

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

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

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Example Question #2 : How To Find The Distributive Property

Simplify the expression:

$\displaystyle 8x - 7 (3x+ 6) - 5$

Possible Answers:

$\displaystyle -13 x - 47$

$\displaystyle -13 x - 37$

$\displaystyle -13 x + 1$

$\displaystyle -13 x + 37$

$\displaystyle -13 x - 1$

Correct answer:

$\displaystyle -13 x - 47$

Explanation:

Distribute, then collect like terms:

$\displaystyle 8x - 7 (3x+ 6) - 5$

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

$\displaystyle =8x - 21x - 42 - 5$

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

$\displaystyle = -13 x - 47$

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Example Question #3 : How To Find The Distributive Property

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

Possible Answers:

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

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

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

3D-33 $\displaystyle 3D-33$

3D - 99 $\displaystyle 3D - 99$

Correct answer:

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

Explanation:

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

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

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Example Question #3 : How To Find The Distributive Property

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

Possible Answers:

3N + 63 $\displaystyle 3N + 63$

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

3N + 7 $\displaystyle 3N + 7$

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

3N + 21 $\displaystyle 3N + 21$

Correct answer:

3N + 63 $\displaystyle 3N + 63$

Explanation:

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

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

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Example Question #4 : How To Find The Distributive Property

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

Possible Answers:

2(k-x) $\displaystyle 2(k-x)$

2x-2k $\displaystyle 2x-2k$

2x-kx $\displaystyle 2x-kx$

x(k+2) $\displaystyle x(k+2)$

Correct answer:

2x-kx $\displaystyle 2x-kx$

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 : 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 #1 : Distributive Property

Example Question #3 : How To Find The Distributive Property

Example Question #1 : How To Find The Distributive Property

Example Question #2 : How To Find The Distributive Property

Example Question #2 : How To Find The Distributive Property

Example Question #2 : How To Find The Distributive Property

Example Question #3 : How To Find The Distributive Property

Example Question #3 : How To Find The Distributive Property

Example Question #4 : How To Find The Distributive Property

All SSAT Middle Level Math Resources

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