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Arithmetic properties

### The distributive property

The distributive property tells us how to solve equations in the form of a(b + c).  The distributive property is sometimes called the distributive law of multiplication and division.

Normally when we see an equation like this …

we just evaluate what’s in the parentheses first, then solve it:

This is following the official “order of operations” rule that we’ve learned in the past.

With the distributive property, we multiply the ‘4’ first:

We distribute the 4 to the 8, then to the 3.
Then we need to remember to multiply first, before doing the addition!

We got the same answer, 44, with both approaches!

Why did we do it differently when we could have easily worked out what was in the brackets first?
This is preparation for when we have variables instead of numbers inside the parentheses.

Practice the Distributive Property now

Another example before we start to use variables:

Example of the distributive property using variables:

More examples
a)

b)

c)

Tips

• We usually use the distributive property because the two terms inside the parentheses can’t be added because they’re not like terms
• Make sure you apply the outside number to all of the terms inside the parentheses/brackets

Next step:
Practice using the distributive property

Try our stack of practice questions with useful hints and answers! Like this one:

Or watch Sal go through some examples: