How to Find Quotients

By Pamela Martin
Image of father and son doing a math problem.

A quotient is the result of dividing one number, known as the dividend, by another, called the divisor. Put most simply, the quotient is the answer to a division problem. If you can remember to “drive my super cool buggy,” finding quotients is simple.

Divide the divisor into the dividend; this is the D for “drive” in the mnemonic. Estimate how many sets you make from the dividend, each continuing the divisor. Begin by estimating for just the first digit or two. For example, in the equation 138 divided by 3, estimate how many sets of three you can make from 13. Write that number above the line of the bracket or after the equals sign, depending on how you’ve formatted the problem. In this case, you would write four.

Multiply the estimate times the divisor; now you’ve used the M for “my.” To continue the example, you will now multiply 4 x 3. Write the number -- this time, it’s 12 -- under the first numbers of the dividend.

Subtract the product from the first numbers of the dividend, to complete the S, or “super,” step of the mnemonic. In the example, you will answer 13-12. Write the result under the subtraction problem.

Compare the number you just wrote to the divisor -- C for “cool.” This number should be less than the divisor. If it is, you are ready for the next step. If it isn’t, you need to go back to the estimating step and choose a larger number -- usually just one more set -- before repeating the multiply, subtract and compare steps.

Bring down the next digit in the dividend to complete the B for “buggy” in the mnemonic. In the example, you would bring down the eight, writing it next to the one you got when you subtracted.

Repeat the steps until you’ve used all of the digits in the dividend. If you still have not reached zero in your subtracting, you have a remainder, which means that the dividend cannot be divided evenly into sets the size of the divisor.


You can express the remainder in several ways. One is to write the number after the initial r., for remainder. Another is to write it as a fraction, with the remainder as the numerator, or top number, and the divisor as the denominator, or bottom number.


Don't skip the comparing step, or you might get confused on the next "divide."

About the Author

Pamela Martin has been writing since 1979. She has written newsletter articles and curricula-related materials. She also writes about teaching and crafts. Martin was an American Society of Newspaper Editors High School Journalism Fellow. She holds a Bachelor of Arts in Teaching in elementary education from Sam Houston State University and a Master of Arts in curriculum/instruction from the University of Missouri.