Question

Explain how modeling partial products can be used to find the products of greater numbers ?

Answer 1

You can break large numbers into a sum of a multiple(s) of 10 and the last digit of the number. For example, you can break 26 as 20+6, or 157 as 100+50+7.

Then, using the distributive property, you can turn the original multiplication into a sum of easier multiplications. For example, suppose we want to multiply 26 and 37. This is quite challenging to do in your mind, but you can break the numbers as we said above:

$26\times 37=(20+6)(30+7) = 20\times 30+20\times 7+30\times 6+6\times 7$

All these multiplications are rather easy, because they either involve multiples of 10 of single-digit numbers:

$20\times 30+20\times 7+30\times 6+6\times 7 = 600+140+180+42=962$