## Distributive property -Meaning and examples

Table of Contents

## Introduction

The distributive property is useful when dealing with algebra and complex equations. Distributive property helps greatly to break the equations down into smaller parts to solve the equation. It is used in advanced and higher multiplication, addition and algebra.

## Meaning of distributive property

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

The distributive property helps in making difficult problems simpler. You can use the distributive property of multiplication to rewrite expression by distributing or breaking down a factor as a sum or difference of two numbers.

Here, for instance, calculating 8 × 27 can be made easier by breaking down 27 as 20 + 7 or 30 − 3. Distributive property can be also known as the distributive law of multiplication, it’s one of the most commonly used properties in mathematics.

## Examples of Distributive Property

The following are examples of distributive property.

- Distributive property of addition
- Distributive property of subtraction
- Distributive property of multiplication over addition
- Distributive property of multiplication over subtraction
- Distributive property of fractions

Let’s focus on the distributive property of multiplication as explained by Splash Learners.

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.

Let’s look at the distributive property with this example: distributive property of multiplication. According to the distributive property 2 × (3 + 5) will be equal to 2 × 3 + 2 x 5

2 × (3 + 5) = 2 × 8 = 16

2 × 3 + 2 × 5 = 6 + 10 = 16

In both cases we get the same result, 16, and therefore we can show that the distributive property of multiplication is correct.

Another example: Imagine one student and her two friends each have seven pens and four pencils. How many pieces of fruit do all three students have in total? In their school bags, they each have 7 pens and 4 pencils. To know the total number of pieces of pens and pencils, we need to multiply the whole thing by 3.

When you break it down, you’re multiplying 7 pens and 4 pencils by 3 students. So, you end up with 21 pens and 12 pencils for a total of 33 pieces of stationaries.

The distributive property of multiplication over addition can be used when you want to multiply a number by a sum. For example, if you want to multiply 3 by the sum of 10 + 2.

According to this property, you can add the numbers and then multiply by 3. 3(10 + 2) = 3(12) = 36. Or, you can first multiply each addend by the 3. (This is called distributing the 3.) Then, you can add the products.

The multiplication of 3(10) and 3(2) will each be done before you add. 3(10) + 3(2) = 30 + 6 = 36. Note that the answer is the same as before.

The distributive property of multiplication over subtraction is like the distributive property of multiplication over addition. You can subtract the numbers and then multiply, or you can multiply and then subtract as shown below. This is called “distributing the multiplier.”

5( 6 – 3) = 5(6) – 5(3)

The same number works if the is on the other side of the parentheses, as in the example below.

(6 – 3) 5 = 6(5) – 3(5)

In both cases, you can then simplify the distributed expression to arrive at your answer. The example below, in which 5 is the outside multiplier, demonstrates that this is true.

The expression on the right, which is simplified using the distributive property, is shown to be equal to 15, which is the resulting value on the left as well.

5( 6 – 3) = 5(6) – 5(3)

5(3) = 30 – 15

15= 15

## References

www.splashlearn.com/math. Retrieved on 24th January, 2020.

www.Khan academy.org/math/pre-algebra.

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