Distributive Property – Property of Integers

The distributive property means distribution of the given operation over another mathematical operation within a bracket.

Multiplication is Distributive Over Addition

Lets consider a, b and c are three integers, by distributive Property:

a x (b +c) = (a x b) + (a x c) = ab + ac

Therefore, we can say multiplication is distributive over addition of integers.

Distributive property of multiplication over addition states that integers are added first and then multiplied or multiply first with each number within the bracket and then added.

We can see that whether we follow the distributive property or order of the operation, the result is the same.

Here we are distributing the process of multiplying 4 evenly between 5 and 6.

Here, a = 4, b = 5 and c = 6

Put the value in the equation

a x (b + c) = (a x b) + (a x c) = ab + ac

a x (b + c) = 4 x (5 + 6)

= 4 x 5 + 4 x 6

= 20 + 24

= 44

or

4(5 + 6) = 4(11) = 44

= 20 + 24

= 44

Both are equal. Therefore, multiplication is distributive over addition.

Multiplication is Distributive Over Subtraction

Distributive property of multiplication over subtraction states that integers are subtracted first and then multiplied or multiply first with each number within the bracket and then subtracted.

Let a, b and c are three integers, by distributive Property

a x (b – c) = (a x b) – (a x c) = ab – ac

Therefore, multiplication is distributive over subtraction of integers.

Let’s understand distributive property with examples.

Put the value in the equation

Example: Three integers 7, 6 and 5. Here a = 7, b = 6 and c = 5.

By distributive property

a(b – c) = 7(6 – 5)

Here we are distributing the process of multiplying 7 evenly between 6 and 5.

= 7 x 1

= 7

(ab – ac) = 7 x 6 – 7 x 5

= 42 – 35

= 7

When we apply distributive property we have to multiply a with both b and c and then subtract i.e.

(a x b) – (a x c) = ab – ac.

We can see that whether we follow the distributive property or order of the operation the result is the same.

Therefore, multiplication is distributive over subtraction.