Dividing with remainders, like 87 ÷ 5
In 4th grade, children learn to divide numbers up to four digits by one-digit numbers, like 87 ÷ 5 = 17 with 2 left over, and to explain it with a drawing or an equation.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 4th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
What is 87 ÷ 5?
- 17
- 17 R 2
- 17.2
Why this matters
Sharing things out fairly is something your child already cares about, and division with remainders is the math behind it: 87 stickers among 5 friends, or how many boxes 150 cupcakes will fill. It sets up dividing by two-digit numbers in 5th grade, and later dividing decimals and fractions. Checking by multiplying back, 17 × 5 + 2 = 87, is a habit that will serve them for years.
Where kids can get stuck
- Leaving a remainder bigger than the divisor, such as 87 ÷ 5 = 16 remainder 7, when 7 holds another 5.
- Dropping a zero in the answer, so 624 ÷ 6 becomes 14 instead of 104.
- Skipping the check by multiplying back, so 1,452 ÷ 6 = 232 goes unnoticed though 232 × 6 is only 1,392.
How you can help
- Share real things into equal groups. Count out 50 dried beans or paper clips and ask your child to share them among 4 people, then say how many each gets and how many are left over.
- Arrange 52 pennies in 4 equal rows on the table. Ask your child how many are in each row, 13, and to explain it with an equation that matches the rows, such as 4 × 10 + 4 × 3 = 52.
- When your child finishes a division problem, ask them to prove it by multiplying the answer by the divisor and adding the remainder, to see if they get back to the starting number.
Want a little more? Try Bobby's Math Club for free practice that adapts to your child.
Questions parents ask
Why is my child learning division this way?
Taking out friendly chunks, like 10 fives or 200 sixes, lets your child divide large numbers using facts they already understand. It also shows why division works, rather than following steps like "divide, multiply, subtract, bring down" without knowing what they mean. Many children find their mistakes easier to catch this way, because each chunk can be checked on its own.
When will my child learn long division?
Some classes introduce the long-division layout in 4th grade as one way to record the work, but this year's goal is dividing by one-digit numbers with methods your child understands. In 5th grade, children divide by two-digit numbers. Using the standard long-division method fluently is usually expected in 6th grade, by which point the chunking work makes each step familiar.
What is a remainder, and how should my child write it?
A remainder is the amount left over when something cannot be shared into equal groups exactly. In 4th grade, it is usually written with an R or the word "remainder": 87 ÷ 5 = 17 R 2. A useful check is that the remainder must be smaller than the number you divided by. If it is not, another full group still fits.
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Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 4.NBT.B.6: “Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.NBT.6)