Multiplication Methods

Before we start, do this question (at least go through the motions in your head):

45 x 23

Did you line them up first so the four was above the two and the five was above the three? Then did 3 x 5, then 3 x 4, then dropped to the next line and wrote a 0, then continued to multiply the rest then added 135 to 900 to get your answer, right? That's how most adults today learned to multiply a two-digit number by another two-digit number. Easy. Now... can you explain the mathematics involved in doing that? What happened to make that work?

Think of it another way.

You know that that 45 can be shown as tens and ones: 40 and 5. 23 can be shown as 20 and 3.

If we divide them up first into their tens and ones, we can multiply them separately, then add them back up later. Often as adults we attack things in bits at a time instead of doing it all at once, so let's do that now.

40 x 20 =  800
40 x 3 = 120
5 x 20 =  100
5 x 3 = 15

If we add 800 + 120 + 100 + 15, we get 1035, which is the same answer we got above.

Does it make more sense to look at it this way? Think of it in terms of groups of items if it doesn't. Think about 40 chocolates or 40 marbles.

If your child is having trouble with multiplication, try to show them this method of multiplication. Same results, different way of getting to the answer.