Distributive property

We will explain the distributive property with three good examples. Study these examples well.

Example #1:

Look at the following illustration. How would you get the area?

Area = width × length

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

You can do the math two ways

You can add 4 and 10 and multiply what you get by 6.

Otherwise, you can use the distributive property illustrated above by multiplying 6 by 4 and 6 by 10 and adding the results

Example #2:

You go to the supermarket. 1 bag of apples costs 4 dollars. 1 gallon of olive oil costs 10 dollars. You get 6 bags of apples and 6 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 = 6 × (4 + 10) = 6 × 4 + 6 × 10 = 24 + 60 = 84 dollars.

Same answer you would get for example #1!

Example #3:

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

We get 2 × ( 8 + 6) = 2 × 8 + 2 × 6 = 16 + 12 = 28

Notice that we get the same answer if we add 8 and 6 and multiply the result by 2

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