Multiplication Trick #5 — How to Multiply Two-Digit Numbers by 11
This is the fifth in my series on multiplication tricks. I suggest that you make mental math “tricks” a steady part of your math instruction. Benefits students will reap include:
— delight with the tricks themselves
— enhanced confidence in working with numbers
— students who otherwise don’t like math — or don’t like it much — often find the tricks irresistibly fun and interesting
WHAT THE TRICK LETS YOU DO: Multiply two-digit numbers by 11.
HOW YOU DO IT: To multiply a two-digit number by 11, first realize that the answer will have three digits. The first (left-most) digit of the answer is the first digit of the number; the last (right-most) digit of the answer is the last digit of the number; and the middle digit is the sum of the first and last digits.
But those are just words … here’s a living, breathing example …
Example: 11 x 25
Look at 25. The first digit is 2; the last digit is 5.
First digit of answer is 2, so thus far we know the answer looks like: 2 _ _
Last digit of answer is 5, so now we know the answer looks like: 2 _ 5
Middle digit is 7, since 2 + 5 = 7.
The answer is the three-digit number: 2 7 5, more casually known as 275.
It’s that easy!
ANOTHER EXAMPLE: 11 x 63
First digit of answer is 6, so thus far we know the answer looks like: 6 _ _
Last digit of answer is 3, so now we know the answer looks like: 6 _ 3
Middle digit is 9, since 6 + 3 = 9.
The answer is the three-digit number: 6 9 3, or just 693.
Try these for practice:
11 x 24
11 x 31
11 x 52
11 x 27
11 x 34
11 x 26
11 x 62
11 x 24 = 264
11 x 31 = 341
11 x 52 = 572
11 x 27 = 297
11 x 34 = 374
11 x 26 = 286
11 x 62 = 682
NOTE: If you’re clever (and we’re sure that you are), you have probably realized that this trick, as described, works only when the digits add up to 9 or less. So what do you do when the digits add up to 10 or more? Some of you may figure this out on your own. For those who need a little help, the answer to this will be included in an upcoming blog post.
Josh Rappaport is the author of five books on math, including the Parents Choice-award winning Algebra Survival Guide. If you like how Josh explains these problems, you’ll certainly like the Algebra Survival Guide and companion Workbook, both of which are available on Amazon.com Just click the links in the sidebar for more information!