Exams CBSE Distributive Property of Multiplication: Definition, Formula, Examples

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Last Modified 25-01-2023

Distributive Property of Multiplication: Definition, Formula, Examples

Distributive Property of Multiplication: The distributive property is also known as the distributive law of multiplication or division over addition and subtraction. The name itself implies distributing something over another entity. With distributive property, you can solve any expression that is in the form of a(b + c).

The distributive property is one of the most commonly used properties in mathematical calculations. Using the detailed information about the distributive property of multiplication provided in this article, you can learn all the formulas and solve examples to master the topic.

Distributive Property of Multiplication: Definition

Distributive property is the algebraic property used to multiply a number with the sum or difference of two or more numbers within a parenthesis. We can say that the distributive property helps in simplifying the problems by breaking the expressions into addition or subtraction of products or vice versa.

This property multiplies the number outside the parentheses by the numbers that are to be added or subtracted inside the parenthesis. Hence, to solve the expression using distributive property, you need to find the products and then add or subtract, as required.

Distributive Property of Multiplication: Formula

According to this property, the number multiplied by the sum or addition of two or more values is equal to the sum or addition of their products. The formulas used for the distributive property of multiplication are given below.

Distributive property of multiplication over addition: a(b + c) = ab + ac
Distributive property of multiplication over subtraction: a(b – c) = ab – ac

Distributive Property of Multiplication: Types

The different types of distributive properties of multiplication are explained below.

1. Distributive Property of Multiplication over Addition

This property is used when you multiply a number over the addition of two or more numbers.

Example:

7(5 + 2) = (7 x 5) + (7 x 2)

7(7) = 35 + 14

49 = 49

2. Distributive Property of Multiplication over Subtraction

This property is used when you multiply a number over the subtraction of two or more numbers.

Example:

3(5 – 3) = (3 x 5) – (3 x 3)

3(2) = 15 – 9

6 = 6

Download NCERT Solutions for Class 7 Maths Chapter 1 PDF

Solved Examples

Example 1: Verify a − (− b) = a + b for the values of a = 21 and b = 18.

Solution: Given: a = 21, b = 18

LHS: a − (− b) = 21 − (−18) = 39

RHS: a + b = 21 + 18 = 39

Therefore, LHS = RHS

Thus, verified.

Example 2: Prove that 18 × [7 + (−3)] = [18 × 7] + [18 × (−3)]

Solution: Given: 18 × [7 + (−3)] = [18 × 7] + [18 × (−3)]

LHS: 18 × [7 + (−3)]

= 18 × 4

= 72

RHS: [18 × 7] + [18 × (−3)]

= 126 + (−54)

= 72

Therefore, LHS = RHS

Hence, proved.

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FAQs on Distributive Property of Multiplication

Some frequently asked questions on the distributive property of multiplication are given below.

Q1. What is the distributive property of multiplication?
A. Distributive property of multiplication says that the multiplication of a number by the addition or subtraction of two or more numbers is equal to the sum or difference of their products, respectively.

Q2. What is the formula of the distributive property of multiplication?
A. The distributive property of multiplication over addition is given by a(b + c)= ab + ac.
The distributive property of multiplication over subtraction is given by a(b – c)= ab – ac.

We hope the detailed information on the distributive property of multiplication helped you clear your doubts. To practice and solve more such formulas, log on to embibe.com.