How to multiply two- or three-digit numbers
I like to think of multiplication as addition in disguise. For example when you multiply two numbers say 7 times 3, you are actually adding 7 to itself 3 times. This is true for any number that's being multiplied by another one. You're simply adding one number to itself a certain number of times.
For single digit numbers you can probably do this quite easily. However when it comes to multiplying a two-digit number by a single digit number or multiplying two double digit numbers, things can get tricky. For those situations I have what I like to call the divide and conquer approach. Lets just jump into some examples.
Examples
23 * 8 -> There are two ways to do this. We'll do the easier(and recommended) method first. Break the problem down
to (20 * 8) + (3 * 8).
We now have: 20 * 8 = 160 (8 *2 = 16 and add zero at the end) and
3 * 8 = 24
Add the two results to get our final answer: 160 + 24 = 184 (160 + 20 = 180 + 4 = 184)
What we did here was break 23 down to a multiple of 10 plus a remainder.
Now let's try the second method. Feel free to use whichever one you find easier for you.
Change the problem to 23 * 10
We now have: 23 * 10 = 230 ( multiplying by ten is fairly simple. Just add zero to the end of the number)
We added 2 to the 8 to make it 10 so we could multiply easier. Now we must multiply 23 * 2 to get 46.
To get the final answer we subtract the two results: 230 - 46 = 184.
Basically what we did was: 23 * 8 = (23 * 10) - (23 *2). I personally find the first method to be much easier
but I usually use both methods when I want to verify my answer.
39 * 7 -> This example is actually easier to do using the second method above.
Round 39 up to 40.
We now have: 40 * 7 = 280 (4 * 7 = 28 then add zero at the end)
Now we added 1 to get 40 so we must multiply the amount we added to the 7 and subtract that result to get
the final answer.
40 * 7 = 280
1 * 7 = 7
Subtract the second result from the first to get the final answer: 280 - 7 = 273
Once you get into the habit of doing this it becomes a lot easier than it seems now.
Now let's do it using the first method that I showed you before.
We have: 30 * 7 = 210 and
9 * 7 = 63
Now add the two results: 210 + 63 = 273
44 * 3 -> We break 44 up to get (40 * 3) + (4 * 3)
Add the two results to get our final answer: 120 + 12 = 132
26 * 5 -> Break 26 up to get (20 *5) + (6 * 5)
Add the two results to get the final answer: 100 + 30 = 130
Another way of multiplying a number by five is this:
Double the five to 10 because multiplying any number by 10 means just adding a zero to the end of the
number
We now have 26 * 10 = 260
Because 5 is half of 10 simply divide the answer by 2. In other words the final answer is half
of the intermediate answer: 130
Another way of thinking about it is to remember "my little rule" in the Addition section. We doubled
the 5 at the beginning so we must half the intermediate answer to get the final answer. (Check in the
"Miscellaneous" section of the site to see some more examples of multiplying by 5)
27 * 23 -> Break the problem into (27 * 10) + (27 * 10) + (27 * 3)
Now break [27 * 3] down as we have been doing before:
(27 * 10) + (27 * 10 ) + (20 * 3) + (7 *3)
We now have: 270 + 270 + 60 + 21
540 + 60 + 21
600 + 21
Final answer: 621
147 * 26 -> Break the problem down to the following:
(a) (147 * 10) + (147 * 10 ) + (147 * 6)
(b ) 1470 + 1470 + (147 * 5) + (147 * 1)
(c) 2940 + 735 + 147
(d) 2975 + 147
(e) 8122
Let go over the steps:
(a) We broke 26 down to 10 + 10 + 6
(b) We multiplied 147 * 10 two times and broke 6 down to 5 + 1
(c) We added the two results of (147 * 10) + (147 *10). We also did the calculation of (147 * 5)
(d),(e) We simply added all our results to get the final answer.
186 * 112 -> We'll break 112 down into 100 + 10 + 2
(186 * 100) + (186 * 10) + (186 * 2)
18600 + 1860 + 372
