How to Find a Remainder
A remainder is what is left over when the groups are all full.
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How to do it
- Find the biggest multiple of the divisor that fits.
- Use that fact for the quotient.
- Subtract to find the remainder.
Teaching tip
Use real counters to make the groups for the first example. This sheet is aligned with Common Core 4.NBT.B.6.
About this chart
47 ÷ 5 shown as 9 groups of 5 with 2 left over, with skip counting, and how to check that a remainder is smaller than the divisor.
What kids practice
Fourth graders divide numbers up to four digits by a one-digit number, like 857 ÷ 4 = 214 R1. They learn to break a big division into smaller parts with area models, then use long division: divide, multiply, subtract, bring down. They also learn what a remainder means in a story, and check their answers with multiplication.
Watch for
- Forgetting a 0 in the quotient, like writing 15 instead of 105 for 525 ÷ 5.
- A remainder that is bigger than the divisor. That means the quotient digit should be one bigger.
- Bringing down two digits at once.
- Lining up quotient digits over the wrong place.
It's free to print, as many copies as you need. See the full long division guide for 4th grade.
More sheets in this set
- See it all
1. How to Divide Tens and HundredsRows from 54 ÷ 6 = 9 up to 54,000 ÷ 6 = 9,000 with the zeros in red, plus problems like 400 ÷ 5 where the fact already uses a zero. 
2. Divide Tens and HundredsBasic facts like 54 ÷ 6 = 9 with related problems like 540 ÷ 6 and 5,400 ÷ 6. More includes a missing dividend.
4. RemaindersDivision facts with remainders, like 47 ÷ 5 = 9 R2. More uses quotients up to 12.- See it all
5. How to Divide with an Area Model984 ÷ 4 worked out with a rectangle split into 800, 160 and 24, and why the parts on top add up to the quotient. 
6. Area Model DivisionRectangles with the area split into easy parts, like 984 = 600 + 360 + 24. Find each side length and add them to get the quotient.- See it all
7. How to Do Long Division857 ÷ 4 worked out on graph paper step by step, with how to check by multiplying and the words dividend, divisor, quotient and remainder. 
8. Long DivisionLong division on graph paper so the digits line up, with a box for the remainder. Fewer has 4 two-digit problems, Standard 6 three-digit problems, and More 9 three-digit problems with bigger divisors and zeros in the quotient.
9. Check with MultiplicationDivision answers to check. Multiply and add the remainder, then decide if each answer is right or wrong.- See it all
10. What to Do with a RemainderThree stories that all divide 29 by 6: vans that need rounding up, books where the remainder is dropped, and stickers where the remainder is the answer. 
11. What to Do with the RemainderStory problems where the remainder matters, like how many vans are needed or how many stickers are left over.
12. Division Word ProblemsDivision stories about crates, albums, shelves, money and miles, with a work space and an answer box.