# Distributive property

The distributive property states that multiplying a number by an addition problem is the same as multiplying the number by each addend in the addition problem and then adding the products.

Notice that the distributive property combines both multiplication and addition.

Find some good examples here showing you how to use this property. Study these examples really well! As a result, you will be able to solve similar problems with ease. Take a look at the figure above. While trying to find the area of the figure, you will end up using the distributive property.

In the figure, the number that we distribute is 6 and the addends are 4 and 10. The way to distribute is to multiply 6 by 4 and 6 by 10. Finally, you can add the products if you want to get an answer.

Area = width × length

Since width = 6 and length = 4 + 10, area = 6 × (4 + 10)

6 × (4 + 10) = 6 × 4 + 6 × 10

6 × (4 + 10) = 24 + 60

6 × (4 + 10) = 84

You can do the math also by adding 4 and 10 and multiply what you get by 6.

6 × (4 + 10) = 6 × 14

6 × (4 + 10) = 84

Although the answer is indeed 84, this way of solving the problem does not show the distributive property.

## Using the distributive property to solve a couple of word problems

Example #1:

You go to the supermarket to buy some items that you need. One bag of apples costs 3 dollars and one gallon of olive oil costs 15 dollars. If you get 4 bags of apples and 4 gallons of olive oil, how much money do you pay the cashier?

Total cost = # of items you get × (cost for apples + cost for olive oil)

Total cost = 4 × (3 + 15) = 4 × 3 + 4 × 15

Total cost = 4 × (3 + 15) = 12 + 60

Total cost = 4 × (3 + 15) = 72

Example #2:

Robert has 8 notebooks and his brother has 6 notebooks. If we double both amount, how many do they now have altogether?

This word problem can be written as 2 × ( 8 + 6)

2 × ( 8 + 6) = 2 × 8 + 2 × 6

2 × ( 8 + 6) = 16 + 12

2 × ( 8 + 6) = 28

Notice again that we get the same answer if we add 8 and 6 and multiply the result by 2. However, this way of solving the problem will not show the distributive property.

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