Distributive Property of Multiplication
2026-02-28 09:07 Diff
https://brightchamps.com/en-us/math/numbers/distributive-property-of-multiplication

323 Learners

Last updated on December 9, 2025

The distributive property of multiplication states that multiplying a number by a sum gives the same result as multiplying each addend separately and then adding the products. This property applies to both addition and subtraction. In this article, we will discuss its formula, applications, and significance.

What is the Distributive Property of Multiplication?

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

Distributive Property of Multiplication Formula

Using the distributive property, an expression of the form A(B + C) can be expanded as:

A × (B + C) = A × B + A × C

This property also applies to subtraction:

A × (B – C) = A × B – A × C

where A, B, and C are any real numbers.

Distributive Property of Multiplication Over Addition 

The distributive property of multiplication shows that when the sum is multiplied by another number, each term in the sum can be multiplied individually by that number, and the results can then be added together for the same outcome.

Consider the example 5(6 + 4). We can expand it as follows:

5 × (6 + 4) = (5 × 6) + (5 × 4) = 30 + 20 = 50

Here, we distribute the numbers 5 to both 6 and 4 and then sum up their products separately.

Using BODMAS rule also gives the same result

5 × (6 + 4) = 5 × (10) = 50

As both methods give the same result, the distributive property is true.

Explore Our Programs

Distributive Property of Multiplication Over Subtraction 

The distributive property of multiplication over subtraction states that you can multiply a number by each value separately and subtract the results. This is the same as multiplying the number by the difference between the two values. The formula we use for the distributive property of multiplication over subtraction is:

A × (B – C) = A × B – A × C

For example:

Solve 7 × (15 – 5) using both methods:

As per this property, the result on both LHS and RHS is the same.

On the left-hand side (LHS), we evaluate directly:

7 × (15 – 5) = 7 × (10) = 70

In RHS, we apply the distributive property:

(7 × 15) – (7 × 5) = 105 – 35 = 70

Since both sides give the same result, we confirm that the property holds.

Tips and Tricks to Master Distributive Property of Multiplication

The distributive property of multiplication is used to break large numbers into smaller factors for multiplication. This property is helpful in arithmetic, algebra, mental math, and solving equations. Here are a few tips and tricks to master the distributive property of multiplication. 
 

  • When multiplying complex numbers, students can use the distributive property to split a complex number into a sum of smaller numbers. For example, rewrite 27 × 6 as (20 + 7) × 6. 
     
  • Use the area model to visualize, by drawing a rectangle and breaking it into sections to see how each part is multiplied. 
     
  • Always distribute the outside number to every term inside the bracket. This helps avoid missing terms or making sign mistakes.
     
  • Teachers can use color coding to show how distributive work is applied, highlighting multiplication for each term inside the brackets in different colors.
     
  • Parents can use real-life examples to demonstrate the property. For example, breaking the shopping prices to show how the distributive property works.

Common Mistakes and How to Avoid Them in Distributive Property of Multiplication

Mostly, students make mistakes in calculating the sum and product of the numbers. Here are a few common mistakes and ways to avoid them:

Real-Life Applications of Distributive Property of Multiplication

Understanding the distributive property enhances students' ability to simplify complex calculations. It applies not only to math but also to real life. Some real-life applications are:

  • When shopping for multiple items, we apply the distributive property of multiplication to determine the total cost. For example: Purchasing 3 units of each of two items priced at $30 and $12, 3 (30 + 12) = (3 × 30) + (3 × 12) = 90 + 36 = 126, which indicates that the total cost is $126.
     
  • The distributive property can be used to divide the task evenly among students.
     
  • In construction, the distributive property is used to calculate areas when rooms are divided into sections. For example: Dividing the area of a single part: 10 (3 + 2) = (10 × 3) + (10 × 2) = 30 + 20 = 50.
     
  • When packing items into boxes, the distributive property helps us quickly calculate the total number of items. For example, if each box contains 5 notebooks and 3 folders, and there are 12 boxes, then: 12(5 + 3) = (12 × 5) + (12 × 3) = 60 + 36 = 96 items in total.
     
  • In sports, the distributive property simplifies the calculation of total points across multiple games. For example, if a player scores 2 goals and 1 assist in each of 7 games, then: 7(2 + 1) = (7 × 2) + (7 × 1) = 14 goals and 7 assists.

Download Worksheets

Problem 1

Solve 8 × (9 + 6) using the distributive property.

Okay, lets begin

 8 × (9 + 6) = 120

Explanation

Apply the distributive property formula:

A × (B + C) = AB + AC

Using the distributive property, distribute the number 8 to both terms within the brackets.

8 × (9 + 6) = (8 × 9) + (8 × 6)

Now, multiply the terms:

72 + 48 = 120

So, 8 × (9 + 6) = 120.

Well explained 👍

Problem 2

Expand 6 × (y + 5) using the distributive property.

Okay, lets begin

6 × (y + 5) = 6y + 30.

Explanation

We apply the distributive property to expand the expression:

A × (B + C) = AB + AC

Substituting the given values:

6 × (y + 5) = (6 × y) + (6 × 5)

Now, simplify the expression:

6y + 30

So, 6 × (y + 5) = 6y + 30.

Well explained 👍

Problem 3

Solve - 4 × (10 – 2) using the distributive property.

Okay, lets begin

 –4 × (10 – 2) = –32

Explanation

To solve this expression, we apply the distributive property:

–4 × (10 – 2) = (–4 × 10) + (–4 × -2)

Now, multiply the terms:

–40 + 8 = –32

So, –4 × (10 – 2) = –32. 

Well explained 👍

Problem 4

Solve 12 × (5 + 7 - 6) using the distributive property.

Okay, lets begin

 12 × (5 + 7 – 6) = 72

Explanation

We first simplify inside the brackets:

5 + 7 – 6 = 6

So, 12 × (5 + 7 × 6) = 12 × 6 = 72.

We can also solve this using distributive property: 

A × (B + C) = AB + AC

⇒ 12 × (5 + 7 – 6) = (12 × 5) + (12 × 7) + (12 × –6)

= 60 + 84 – 72 = 72

Well explained 👍

Problem 5

Solve 3 × (x - 6) using the distributive property.

Okay, lets begin

3 × (x – 6) = 3x – 18

Explanation

Apply the distributive property of multiplication:

A × (B - C) = AB - AC

We have: A = 3, B = x, and C = 6.

Now distribute 3 to both terms inside the parentheses:

3 × (x – 6) = (3 × x) – (3 × 6)

Multiply the terms:

3x – 18

So, 3 × (x – 6) = 3x – 18.

Well explained 👍

FAQs on Distributive Property of Multiplication

1.What do you mean by Distributive Property of Multiplication?

The distributive property states that multiplying a number by the sum of two or more addends is equivalent to multiplying each addend independently by the number and then adding the results.

2.Give the formula for the Distributive Property of Multiplication.

The formula to solve an expression of the form A(B + C):

A × (B + C) = AB + AC

This property also applies to subtraction:

A × (B – C) = AB – AC

where A, B, and C are any real numbers.

3.What is the significance of the Distributive Property of Multiplication in math?

The distributive property of multiplication helps in solving algebraic expressions by breaking them down into simpler terms. 
 

4.Can we apply the distributive property in real life?

Yes, we can apply the distributive property to real-life situations such as calculating the total costs in shopping, and area calculations in construction.

5.Give an example of the distributive property of multiplication.

Apply the distributive property to solve 4 × (3 – 5):
4 × (3 – 5) = 4 × 3 – 4 × 5 
12 – 20 = –8
4 × (3 – 5) = –8

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.