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