How to find the distributive property

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SSAT Middle Level Quantitative › How to find the distributive property

Questions 1 - 10
1

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

None of these

Explanation

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:

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

2

Which of the following expressions is equivalent to ?

Explanation

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

3

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

Explanation

According to the distributive property, for any values of ,

If we set , this become the statement

,

so this is the correct choice.

All of the other statements are true for different reasons:

is true because of the associative property of multiplication.

is true because of the commutative property of multiplication.

is true because of the commutative property of addition.

is true because of the identity property of multiplication.

4

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

Explanation

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:

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

5

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

None of these

Explanation

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:

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

6

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

Explanation

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:

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

7

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

Explanation

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:

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

8

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

Explanation

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:

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

9

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?

Explanation

Caroline is twenty-one years older than Nina, so her age is . Mr. Hutchinson is three times as old as Caroline, so he is . Using distribution, this can be rewritten as

.

10

Simplify:

Explanation

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