Introduction
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 = ab + ac
- a b−c = ab − ac
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 = 74 + 79 = 28 + 63 = 91
Similarly, in the math statement 5 83, we are multiplying 5 with a difference of 8 and 3. Here we can use the distributive property as follows.
5 83 = 58 53 = 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
Wesimplifytheparenthesesfirstandthendomultiplicationoperationnext
If distributive property is used
6 3+5 = 63 + 65 = 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.Problem
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 = 43 + 450 = 12 + 200 = 212
Step 2:
If PEMDAS rule is used
4 3+50 = 4 53 = 212
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