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

2 Answers
Aug 25, 2016

Answer:

#(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#

Aug 25, 2016

Answer:

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