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How to Do Multiplication and Division in Modular Arithmetic

Learn more about performing modular arithmetic, how it’s related to finding remainders in division, and how it can help you predict the future.

By
Jason Marshall, PhD,
Episode #054

Practice Problems

So what about the problem that Jeff’s daughter was confronted with…the one about finding the day of the week some number of days from today? Well, unfortunately we’re out of time, so I’m going to let you think about how what we’ve talked about today can help solve that problem—and we’ll talk about how to figure it all out in the next article.

But before we finish, here are a couple of practice problems for you to work on to help you make sure you understand everything we’ve talked about:

  1. What’s (150 + 25) (mod 10)?

  2. What’s (150 – 25) (mod 10)?

  3. What’s (150 x 25) (mod 10)?

  4. What’s (150 / 25) (mod 10)?

Use the connection between modular arithmetic and the remainder in division to solve these problems. You can find the answers at the very end of the article. After checking them, feel free to leave a comment at the bottom of the page and let me know how you did.

Wrap Up

If you have questions about how to solve these practice problems or any other math questions, please email them to me at mathdude@quickanddirtytips.com, send them via Twitter, or become a fan of the Math Dude on Facebook and get help from me and the other math fans there.

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!

Practice Problem Answers

  1. Since 150 + 25 = 175, (150 + 25) (mod 10) = 175 (mod 10). The remainder in 175 / 10 is 5, therefore (150 + 25) (mod 10) ≡ 5.

  2. Since 150 – 25 = 125, (150 – 25) (mod 10) = 125 (mod 10). The remainder in 125 / 10 is 5, therefore (150 – 25) (mod 10) ≡ 5.

  3. Since 150 x 25 = 3750, (150 x 25) (mod 10) = 3750 (mod 10). The remainder in 3750 / 10 is 0, therefore (150 x 25) (mod 10) ≡ 0.

  4. Since 150 / 25 = 6, (150 / 25) (mod 10) = 6 (mod 10). The remainder in 6 / 10 is 6, therefore (150 / 25) (mod 10) ≡ 6.

Clock image from Shutterstock

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