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

**TRICK #5:**

**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

Answers:

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.

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