Question

How do you use the distributive property to multiply `3*215`?

Answer 1

`(63xx10)+(3xx5) = 645`

Explanation:

Multiplication is said to be distributive over addition since:

`a(b+c) = ab+ac`

In this question are asked to use this property to multiply `3xx215`

As an example, I will choose to express `215` as `210+5`
(NB: I could have choosen any other valid sum but this one will demonstrate the process well)

Now consider: `210 = 7xx5xx3xx2`
(These are known as its 'prime factors')

Because multiplication is distributive over addition I can write:
`3xx215 = 3xx(210+5)`

`= 3xx( 7xx5xx3xx2+ 5)`

`= (63xx10) + (3xx5)`

`=630 + 15 = 645`

Answer 2

The distributive property means to multiply everything by the same thing. so `3 xx 200 + 3 xx 10 + 3 xx 5`# = 645

Explanation:

The problem can be rewritten as `3 xx ( 200 + 10 + 5)`

Using the distributive property 3 must be multiplied by every term in the parenthesis . so that equals

`3 xx 200 + 3 xx 10 + 3 xx 5`

3 x 200 = 600
3 x 10 = 30
3 x 5 = 15 add all three parts

600 + 30 + 15 = 645