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Last updated on July 5th, 2025

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Distributive Property of Multiplication

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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.

Distributive Property of Multiplication for Filipino Students
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What is the Distributive Property of Multiplication?

The distributive property is multiplying a number by sum equals to multiplying the number by each addend separately and then adding the products. It breaks down and simplifies expressions. To distribute anything is to divide or assign a portion of something. We apply this property to describe the way by which multiplication extends to addition and subtraction.

 

 

Distributive Property of Multiplication Formula


Using the distributive property of multiplication, we solve an expression of the form A(B + C) by expanding it as:
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.

 

 

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) by expanding it:
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.

 

 

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) = ab – ac. 
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.
 

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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.
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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:

Mistake 1

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Misapplication of the Property
 

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Students forget to apply the property to both terms, resulting in wrong answers. So, make sure that you multiply both terms in the brackets. For example: 4 (5 – 3) = (4 × 5) – (4 × 3) = 20 - 12 = 8. Here, 4 gets multiplied by each term in the bracket to find the difference.
 

Mistake 2

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Forgetting to Simplify
 

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Students tend to forget to simplify the terms. To avoid the confusion, do not forget to simplify the expression after distributing the multiplier. For example: 2(6 – 4) = 12 – 8 = 4.

Mistake 3

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Missing the Parentheses
 

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Not using the brackets in the expression properly can lead to errors. So, make sure to use brackets to show which terms the number is being multiplied by. For example: 3(6 – 5) = 3(6) – 3 (5) = 18 – 15 = 3.
 

Mistake 4

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Not Applying the Minus Sign Correctly

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Students forget to apply the minus sign inside the parentheses, and it leads to errors. To avoid this error, retain the subtraction operation while distributing the multiplier to both terms. For example: 5 (7 – 3) = 5 (7) – 5 (3).
 

Mistake 5

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Confusing Addition and Subtraction
 

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Students typically misapply addition or subtraction inside the parentheses, and it results in errors. So, identify the operation inside the brackets and then apply the distributive property. For example: 6 (8 – 2) = 6(8) – 6 (2)  = 48 – 12 = 36.
 

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Solved Examples of Distributive Property of Multiplication

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Problem 1

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

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 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.
 

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Problem 2

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

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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.
 

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Problem 3

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

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 -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.
 

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Problem 4

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

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 12 (5 + 7 - 6) = 72
 

Explanation

We first simplify inside the brackets:
5 + 7 – 6 = 6
Now, we apply the distributive property:
12 (6) = 12 × 6 = 72
So, 12 (5 + 7 - 6) = 72.
 

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Problem 5

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

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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.
 

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FAQs on Distributive Property of Multiplication

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

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

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

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

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

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6.How can children in Philippines use numbers in everyday life to understand Distributive Property of Multiplication?

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7.What are some fun ways kids in Philippines can practice Distributive Property of Multiplication with numbers?

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8.What role do numbers and Distributive Property of Multiplication play in helping children in Philippines develop problem-solving skills?

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9.How can families in Philippines create number-rich environments to improve Distributive Property of Multiplication skills?

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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.

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Fun Fact

: She loves to read number jokes and games.

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