# DISTRIBUTIVE PROPERTY OF MULTIPLICATION WORKSHEETS

## About "Distributive property of multiplication worksheets"

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

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

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

## Distributive property of multiplication 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 + z²)

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

6. Write the given verbal phrase into algebraic expression

"3 times the sum of two different numbers"

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

8. Write the given verbal phrase into algebraic expression

"6 times the sum of three different numbers"

9If 7 times the sum of 3 times of a number and 6 is            147, find the number.

10. If 9 times the sum of 7 and 4 times of a number is            135, find the number.

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

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

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

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

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

16. Write the given verbal phrase into algebraic expression

"3 times the difference of two different numbers"

17If 4 times the difference of a number and 5 is 32, find the number.

18. Write the given verbal phrase into algebraic expression

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

19If 7 times 6 less than 3 times of a number is 147, find the number.

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

## Distributive property of multiplication 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)  =  84

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 + z²)

Solution :

5(x² + y² + z²)  =  5x² + 5y² + 5z²

Problem 5 :

Evaluate using distributive property : m(m² + m + 5)

Solution :

m(m² + m + 5)  =  m.m² + m.m + 5m

m(m² + m + 5)  =  m³m² + 5m

Problem 6 :

Write the given verbal phrase into algebraic expression

"3 times the sum of two different numbers"

Solution :

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

Then,

The sum of two different numbers  =  x + y

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

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 7 :

If 4 times the sum 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  =  12

x  =  3

Hence the required number is 3.

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 8 :

Write the given verbal phrase into algebraic expression

"6 times the sum of three different numbers"

Solution :

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

Then,

The sum of three different numbers  =  x + y + z

6 times the sum of three different numbers  =  6(x + y + z)

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 9 :

If 7 times the sum of 3 times of a number and 6 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  =  105

x  =  5

Hence the required number is 5.

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 10 :

If 9 times the sum of 7 and 4 times of a number is 135, find the number.

Solution :

Let "x" be the required number.

According to the question, we have

9(7 + 4x)  =  135

63 + 36x  =  135

36x  =  72

x  =  2

Hence the required number is 2.

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 11 :

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 12 :

Evaluate using distributive property : 6(x - y)

Solution :

6(x - y)  =  6x - 6y

Problem 13 :

Evaluate using distributive property : m(n - p)

Solution :

m(n - p)  =  mn - mp

Problem 14 :

Evaluate using distributive property : 5(x² - y²)

Solution :

5(x² - y²)  =  5x² - 5y²

Problem 15 :

Evaluate using distributive property : m(m² - m)

Solution :

m(m² - m)  =  m.m² - m.m

m(m² - m)  =  m³ - m²

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 16 :

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)

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 17 :

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.

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 18 :

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

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 19 :

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.

Let us look at the next problem on "Distributive property of multiplication worksheets"

Problem 20 :

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.

After having gone through the stuff given above, we hope that the students would have understood "Distributive property of multiplication worksheets".

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