999 x 121 Made Easy with this Math Shortcut

mental math series, part 7

The number 9 has a reputation for being difficult to multiply by. Which is a shame because it is actually an incredibly easy number to multiply. In fact, using a simple trick we can multiply by 99 or 999 just as easily. Can you believe that? And the trick only takes a couple minutes to learn!

So let’s get to it!

The 9’s Trick

Multiplying by 9 is really the same as multiplying by 10 minus 1. For example, let’s begin by multiplying 9 x 12.

First rewrite 9 as 10 minus 1. Make sure to include parenthesis!

Then distribute 12 through.

And finally complete the arithmetic.

Let’s try another one. How about 25 x 9?

Rewrite 9 as 10 minus 1.

Distribute the 25 and subtract.

99 times a number

We can extend this to multiply by 99 if we’d like. Just simply rewrite 99 as 100 minus 1. For example, let’s try 99 x 150? That seems sufficiently difficult to do mentally without the trick.

Distribute 150 and subtract.

999 times a number

Finally, let’s try this trick on 999, such as 999 x 121. As you may have guessed, the trick is to rewrite 999 as 1000 minus 1.

Multiply 121 through.

You’ll need to borrow, so imagine the problem in your head with the following place values.

Therefore our answer 999 • 121 is 120,879.

As you can imagine, you can use the pattern to further extend the rule to multiply by any number with all 9's digits.

Next Lesson: Starter Tricks for Mental Division

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