What Is "Casting Out Nines"? Part 2

Learn more about using the “casting out nines” method to quickly and easily check your answers to multiplication and division problems.

Jason Marshall, PhD
4-minute read
Episode #83

How to Use Casting Out Nines to Check Subtraction and Division

So that’s how addition and multiplication work with casting out nines, what about subtraction and division? The easiest way to check your answers to subtraction and division problems is to transform them into equivalent addition and multiplication problems.

For example, the easiest way to check the answer to the subtraction problem 522 – 291 = 231 is to transform this into the equivalent addition problem, 522 = 231 + 291. All we’ve done here is to add 291 to both sides of the original subtraction problem. Or to check the answer to the division problem 798 / 21 = 38, start by turning this into the equivalent multiplication problem, 21 x 38 = 798. All we’ve done here is to multiply both sides of the original division problem by 21. If casting out nines tells you that the answers to the addition or multiplication problems may be correct, then you also know that the answers to the equivalent subtraction and division problems may also be correct.

Number of the Week

This week’s number is actually a conversion that will let you quickly figure out how much water you could potentially collect from your roof when it rains. If you multiply the square footage of your house by 0.62, the number you get will be the approximate number of gallons of water you could collect from your roof for every inch of rainfall. For example, if you live in a 1,000 square foot house, you could potentially collect 0.62 x 1,000 = 620 gallons of water for every inch of rainfall.

Why is that useful to know? Because that’s a lot of water! And because it’s fairly easy to divert water from your gutters into rain barrels that you can then use to water your yard...for free!

Wrap Up

Okay, that’s all the math we have time for today. Remember to become a fan of the Math Dude on Facebook where you’ll find a new featured number or math puzzle posted every weekday. And if you’re on Twitter, please follow me there too. Finally, if you have math questions, feel free to send them my way via Facebook, Twitter, or by email at mathdude@quickanddirtytips.com.

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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

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About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.