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Mar06

# Distributive Property of Multiplication with Examples

In today’s post, we will look at some examples of the distributive property. But first, we have to remember what this property consists of.

As you know, multiplication has different properties, among which we point out:

• Commutative Property
• Associative Property
• Neutral Element
• Distributive Property

Well, the distributive property is that by which the multiplication of a number by a sum will give us the same as the sum of each of the sums multiplied by that number.

For example:

3 x (4 + 5) = 3 x 4 + 3 x 5

But we can also apply the distributive property in the other direction, then calling out a common factor, and thus:

2 x 6 + 2 x 9 = 2 x (6 + 9)

Let’s look at two examples:

Distributive: 8 x (13 – 1) = 8 x 13-8 x 1 = 8 x 13-8

Remove common factor: 12 x 3 x 2 + 3 x 6 + 7 x 3 = 3 x (12 x 2 + 6 + 7)

#### To understand this better, let’s see an example of Distributive Property in a Word Problem: Mary is preparing for her birthday party, at which she will distribute sweets to all her friends. To do this, she will put 5 strawberry, 4 lemon and 3 peppermint candies in each bag.  She has decided to give away 10 bags of candy. How many candies are given away altogether?

To solve the problem, it is important that we know the number of candies of each kind in each bag, and the number of bags. Therefore, we can solve this problem in two different ways:

• We find the total number of candies that she will put in each bag, and then multiply by the number of bags:

5 + 4 + 3 = 12 candies in each bag

12 x 10 = 120 candies in total

• We find the total number of candies of each flavor and then add:

5 pieces of strawberry candies in 10 bags: 5 x 10 = 50 strawberry candies

4 lemon candies in 10 bags: 4 x 10 = 40 lemon candies

3 peppermint candies in 10 bags: 3 x 10 = 30 peppermint candies

We add all the candy: 50 + 40 + 30 = 120 candies in total

We see that the two paths have obtained the same result, so we can choose the path that we find easier.