Question

Explain why it works to break apart a number by place values to multiply

Answer 1

Answer:

We are still multiplying the sum of the addends whose result is those numbers. In other words, we are multiplying those same numbers too.

Step-by-step explanation:

Because when we break apart a number by placing values to multiply like when we do in partial products, we are still multiplying the sum of the addends whose result is those numbers. In other words, we are multiplying those same numbers too.

Check below that Partial Products example:

$46*32=\\46=(40+6)\\32=(30+2)\\(40+6)(30+2)=1200+80+180+120$

Answer 2

It works because even if the numbers are broken apart, you are still multiplying the numbers by their values, it's only different because once broken apart, it's in expanded form instead of standard form. It also makes multiplication easier since you don't have to deal with such large numbers.