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

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:

[tex]46*32=\\46=(40+6)\\32=(30+2)\\(40+6)(30+2)=1200+80+180+120[/tex]

fichoh fichoh · Answer 2 · 2021-10-28T13:59:46+02:00

Breaking a number apart by place values then multiply gives the same product as multiply the numbers directly because under multiplication condition, each digit in a number multiplies every other digit in the other value.

Using the expression as an example :

(17 × 12)

17 = 10 + 7 (tens and unit respectively)

12 = 10 + 2 (tens and unit respectively)

17 × 2 = (10 + 7)(10 + 2)

(10 + 7)(10 + 2) = (10×10) + (10×2) + (7×10) + (7×2)

(10×10) + (10×2) + (7×10) + (7×2) = 100 + 20 + 70 + 14 = 204

Therefore, the product will give the same result always.

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