DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION WORKSHEETS

About "Distributive property of multiplication over addition worksheets"

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

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

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

More clearly,

Distributive property of multiplication over addition 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"

7. If 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"

9. If 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.

Distributive property of multiplication over addition 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) = m³ + m² + 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)

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.

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)

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.

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.

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