How to find the distributive property - SSAT Middle Level Quantitative

Card 0 of 196

Which of the following expressions is equivalent to the expression ?

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By the distributive property of multiplication over addition,

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

Which of the following expressions is equivalent to the expression ?

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By the distributive property of multiplication over addition,

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

Which of the following expressions is equivalent to ?

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

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

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

Simplify the expression:

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Apply the distributive property:

$= 7 \cdot y+7 \cdot5$

Simplify the expression:

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Apply the distributive property:

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

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

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

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According to the distributive property, for any values of ,

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

If we set , 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.

Simplify the expression:

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Distribute, then collect like terms:

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

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

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?

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Colin's age is thirty-three years less than Diana's age of , so Colin is 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$ .

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?

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

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

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

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The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=4$

After we reduce each addend by the greatest common factor we can rewrite the expression:

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Tap to see back →

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=4$

After we reduce each addend by the greatest common factor we can rewrite the expression:

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Tap to see back →

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=4$

After we reduce each addend by the greatest common factor we can rewrite the expression:

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Tap to see back →

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=4$

After we reduce each addend by the greatest common factor we can rewrite the expression:

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Tap to see back →

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=5$

After we reduce each addend by the greatest common factor we can rewrite the expression:

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Tap to see back →

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=5$

After we reduce each addend by the greatest common factor we can rewrite the expression:

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Tap to see back →

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=5$

After we reduce each addend by the greatest common factor we can rewrite the expression:

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Tap to see back →

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=5$

After we reduce each addend by the greatest common factor we can rewrite the expression:

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Tap to see back →

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=6$

After we reduce each addend by the greatest common factor we can rewrite the expression:

Use the distributive property to express the sum as the multiple of a sum of two whole numbers with no common factor.

Tap to see back →

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

In this case, the greatest common factor shared by each number is:

$$\text{GCF}$=6$

After we reduce each addend by the greatest common factor we can rewrite the expression: