DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER SUBTRACTION WORKSHEETS

About "Distributive property of multiplication over subtraction worksheets"

Distributive property of multiplication over subtraction worksheets are much useful to the kids who would like practice problems on distributive property of multiplication

Distributive property of multiplication over subtraction is a very useful property that lets us simplify expressions in which we are multiplying a number by the difference of two other numbers.

The property states that the product of a number and the difference of two other numbers is equal to the difference of the products.

More clearly,

Distributive property of multiplication over subtraction worksheets - Problems

1. Evaluate using distributive property : 7(10 - 2)

2. Evaluate using distributive property : 6(x - y)

3. Evaluate using distributive property : m(n - p)

4. Evaluate using distributive property : 5(x² - y²)

5. Evaluate using distributive property : m(m² - m)

6. Write the given verbal phrase into algebraic expression

"3 times the difference of two different numbers"

7. If 4 times the difference of a number and 5 is 32, find the number.

8. Write the given verbal phrase into algebraic expression

"6 times 3 less than 4 times of a number"

9. If 7 times 6 less than 3 times of a number is 147, find the number.

10. If 9 times the difference of 7 and 4 times of a number is 27, find the number.

Distributive property of multiplication over subtraction worksheets - Answers

Problem 1 :

Evaluate using distributive property : 7(10 - 2)

Solution :

7(10 - 2) = 7(10) - 7(2)

7(10 - 2) = 70 - 14

7(10 - 2) = 56

Problem 2 :

Evaluate using distributive property : 6(x - y)

Solution :

6(x - y) = 6x - 6y

Problem 3 :

Evaluate using distributive property : m(n - p)

Solution :

m(n - p) = mn - mp

Problem 4 :

Evaluate using distributive property : 5(x² - y²)

Solution :

5(x² - y²) = 5x² - 5y²

Problem 5 :

Evaluate using distributive property : m(m² - m)

Solution :

m(m² - m) = m.m² - m.m

m(m² - m) = m³ - m²

Problem 6 :

Write the given verbal phrase into algebraic expression

"3 times the difference of two different numbers"

Solution :

Let "x" and "y" be the two different numbers.

Then,

The difference of two different numbers = x - y

3 times the sum of two different numbers = 3(x - y)

Problem 7 :

If 4 times the difference of a number and 5 is 32, find the number.

Solution :

Let "x" be the required number.

According to the question, we have

4(x - 5) = 32

4x - 20 = 32

4x = 52

x = 13

Hence the required number is 13.

Problem 8 :

Write the given verbal phrase into algebraic expression

"6 times 3 less than 4 times of a number"

Solution :

Let "x" be the number.

Then,

4 times of number = 4x

3 less than 4 times of number = 4x - 3

6 times 3 less than 4 times of a number = 6(4x - 3)

6 times 3 less than 4 times of a number = 24x - 18

Problem 9 :

If 7 times 6 less than 3 times of a number is 147, find the number.

Solution :

Let "x" be the required number.

According to the question, we have

7(3x - 6) = 147

21x - 42 = 147

21x = 189

x = 9

Hence the required number is 9.

Problem 10 :

If 9 times the difference of 7 and 4 times of a number is 27, find the number.

Solution :

Let "x" be the required number.

According to the question, we have

9(7 - 4x) = 27

63 - 36x = 27

36 = 36x

1 = x

Hence the required number is 1.

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