Understanding the Distributive Property

When multiplying a number by a sum or difference, we use the distributive property.

The distributive property states that for any three numbers 'a', 'b' and 'c'

• a (b + c) = (a b) + (a c)
• a (b − c) = (a b) − (a c)

For example, in the math statement 7 (4 + 9), we are multiplying 7 with a sum of 4 and 9. Here we can use the distributive property as follows.

7 (4 + 9) = (7 4) + (7 9) = 28 + 63 = 91

Similarly, in the math statement 5 (8 3), we are multiplying 5 with a difference of 8 and 3. Here we can use the distributive property as follows.

5 (8 3) = (5 8) (5 3) = 40 15 = 25

In an expression for example, 6 (3 + 5), we can simplify using the order of operations rule PEMDAS or use distributive property.

If  PEMDAS rule is followed

6 (3 + 5) = 6 (8) = 48

(We simplify the parentheses first and then do multiplication operation next)

If distributive property is used

6 (3 + 5) = (6 3) + (6 5) = 18 + 30 = 48

Either way, the answer is the same.

Sometimes it is easier to use the distributive property to simplify than using the order of operations rule PEMDAS.

Simplify 4 (3 + 50) using distributive property

Solution

Step 1:

In 4 (3 + 50), it is easier to simplify using distributive property as follows

4 (3 + 50) = (4 3) + (4 50) = 12 + 200 = 212

Step 2:

If PEMDAS rule is used

4 (3 + 50) = 4 53 = 212