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

Aug 25, 2016

#### Answer:

$\left(63 \times 10\right) + \left(3 \times 5\right) = 645$

#### Explanation:

Multiplication is said to be distributive over addition since:

$a \left(b + c\right) = a b + a c$

In this question are asked to use this property to multiply $3 \times 215$

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: $210 = 7 \times 5 \times 3 \times 2$
(These are known as its 'prime factors')

Because multiplication is distributive over addition I can write:
$3 \times 215 = 3 \times \left(210 + 5\right)$

$= 3 \times \left(7 \times 5 \times 3 \times 2 + 5\right)$

$= \left(63 \times 10\right) + \left(3 \times 5\right)$

$= 630 + 15 = 645$

Aug 25, 2016

#### Answer:

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

#### Explanation:

The problem can be rewritten as $3 \times \left(200 + 10 + 5\right)$

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

$3 \times 200 + 3 \times 10 + 3 \times 5$

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

600 + 30 + 15 = 645