The distributive property

​What is the distributive property?
Let's say you want to find 5(6+8). You could use the order of operations to solve by adding the numbers in parentheses first.
5(6+8)
5(14)
70

Or you could use the distributive property. Multiply the number outside of the parentheses by each number inside of the parentheses. Then add those products. Look at the steps below.
5(6+8)
5(6)+5(8)
30+40
70
So, 5(6+8)=70!

​The distributive property works with subtraction in the parentheses, too.
8(10–4)
8(10)–8(4)
80–32
48

Check your work with the order of operations:
8(10–4)
8(6) 48
So, 8(10–4)=48!

​The distributive property with variables
The distributive property is useful when simplifying expressions with variables. When using variables, you may not be able to do the operation inside the parentheses first.
Let's try an example.

​So, 8(y+4z)=8y+32z!

​Using the distributive property to multiply large numbers

You can use the distributive property to help multiply large numbers.

Let's try it with 6×57. First, split 57 up into smaller pieces.

6×57

6×(50+7)

Then use the distributive property to solve!

6(50+7)

6(50)+6(7)

300+42

342

You can use area models to see why this works. The model below shows 6×57.

​You can also show 6×57 as 6×(50+7).

​Multiply the 6 by 50 and by 7.

​Then add to find the total area.
300+42=342

So, 6×57=342!