Ever wondered if there’s a quick way to multiply two numbers in the teens, like:
14 x 17, or 18 x 16?
Turns out, there is. Stick around a minute, and you’ll learn it. Let’s try it for:
18 x 16.
The trick involves doing two operations with the numbers in the ones place of the teen numbers. The numbers in the ones place are 8 (in the ones place of 18) and 6 (in the ones place of 16).
First, ADD the two digits in the ones place.
8 + 6 = 14.
Take that sum, 14, and add it to 10: 14 + 10 = 24.
Tack a zero on to the end. 24 becomes 240. (Keep that number in mind.)
Next MULTIPLY the two digits in the ones place:
8 x 6 = 48.
Now just add this product, 48, to the 240.
240 + 48 = 288.
That’s the answer. This may seem a little tricky and a little weird, at first, but it gets easy after a few times. Trust me …
O.K., fine, don’t trust me. But just try it one more time, with 14 x 17, and see for yourself.
4 + 7 = 11. 11 + 10 = 21.
21 becomes 210.
Then 4 x 7 = 28, and 210 + 28 = 238.
That’s all there is to it.
Now try these:
a) 13 x 16
b) 12 x 17
c) 14 x 19
d) 12 x 19
e) 13 x 14
f) 17 x 18
g) 19 x 17
h) 15 x 19
j) 16 x 17
k) 18 x 19
Answers:
a) 13 x 16 = 208
b) 12 x 17 = 204
c) 14 x 19 = 266
d) 12 x 19 = 228
e) 13 x 14 = 182
f) 17 x 18 = 306
g) 19 x 17 = 323
h) 15 x 19 = 285
j) 16 x 17 = 272
k) 18 x 19 = 342
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Comments on: "How to Multiply Two Teen Numbers — FAST" (4)
Wonderful trick!
I wonder if there is a proof for the validity of this method?
Thanks!
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Yes, there is a proof.
To understand this proof, it helps to view the multiplication of any two 2-digit numbers in an interesting new way.
Take a problem like 18 x 16.
First, view each number as the sum of its two digits. In other words, view 18 as
[10 + 8], and view 16 as [10 + 6].
Once you do that, you can view 18 x 16 as the same as [10 + 8] x [10 + 6]
O.K., now if you recall the concept of F.O.I.L, from Algebra 1, you’ll remember that it gives you a way to multiply using the pattern: Firsts, Outers, Inners, Lasts. Sound vaguely familiar?
Using this pattern of F.O.I.L, from algebra, you can now look at the product of
[10 + 8] x [10 + 6] as a four-part process:
Firsts give you 10 x 10 = 100
Outers give you 10 x 6 = 60
Inners give you 10 x 8 = 80
Lasts give you 6 x 8 = 48
Add up those four sub-products, and you get 288, the answer to 18 x 16.
O.K., fine you say. But what does that have to do with the trick I offered?
Well, everything, if you think about it.
Think for a moment about the part of the trick that asks you to add the 6, 8, and 10 to get 24, then tack on a 0, to get 240. In terms of F.O.I.L, this is the same as the first three steps: the Firsts give you 10 x 10 = 100; the Outers give you 10 x 6 = 60; and the lasts give you 10 x 8 = 80. Add up those products and you get 240, which is the same thing you get in the trick: 24 with a 0 at the end: 240.
Then the last step, multiplying the 6 x 8, gives you the 48, and that is the last step of F.O.I.L: the step where you multiply the “Lasts,” the 6 x 8.
So essentially, the trick I have explained is just a shortened form of doing F.O.I.L. for multiplication with teen numbers.
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i got all the answers correct on your page and its a pretty cool trick but at the bottom when you explain, and say add them all up … 240 + 48 is 288, not 248 .. so im confused bout that
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Hi Isaac. Good observation. Fixed it. – Josh
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