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.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Fourth graders find whole-number quotients and remainders for dividends up to four digits and divisors of one digit, such as 1,732 ÷ 6. As with multiplication, the emphasis is on strategies grounded in place value and the link between multiplication and division, not yet on the formal long division algorithm.
A popular method is partial quotients: subtract friendly multiples of the divisor, such as 6 × 200 = 1,200, then 6 × 80 = 480, then 6 × 8 = 48, and add up the multipliers. Another is an area model where the divisor is one side of a rectangle and students find the missing side in chunks. Whatever is left when no more full groups fit is the remainder, and it must always be smaller than the divisor. Students check their work by multiplying the quotient by the divisor and adding the remainder, which should give back the dividend.
Writing 47 ÷ 5 = 8 remainder 7 means another group of 5 still fits. If the remainder is equal to or bigger than the divisor, the quotient should be larger.
In 824 ÷ 4 students may write 26 instead of 206 because the 2 tens cannot make a group of 4 tens. Partial quotients keep the tens place visible.
A student checks 59 ÷ 7 = 8 r 3 with 8 × 7 = 56 and thinks the answer is wrong. The check is 8 × 7 + 3 = 59.
Find 1,732 ÷ 6. Give the quotient and remainder.
Answer: 1,732 ÷ 6 = 288 remainder 4.
Partial quotients reward number sense: students can take away any friendly chunk they know, so a student who uses 6 × 100 twice gets the same answer as one who uses 6 × 200 once. Celebrate both and then compare efficiency.
Build the habit of a multiply-and-add check on every problem. Tests often include an answer with the remainder too large or a missing zero in the quotient, and the check catches both.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 169
5 × 100 = 500 leaves 345. 5 × 60 = 300 leaves 45. 5 × 9 = 45 leaves 0. The quotient is 100 + 60 + 9 = 169.
Answer: B) 288 remainder 4
6 × 288 = 1,728, and 1,732 - 1,728 = 4. The answer is 288 remainder 4. A remainder of 6 is impossible because another group of 6 would fit.
Answer: 206
4 × 200 = 800 leaves 24, and 4 × 6 = 24 leaves 0. The quotient is 206, with a 0 in the tens place.
Answer: 3
7 × 8 = 56 and 59 - 56 = 3. The remainder is 3.
Answer: C) 401 × 8 + 7
Multiply the quotient by the divisor and add the remainder: 401 × 8 + 7 = 3,208 + 7 = 3,215.
Answer: 504
9 × 500 = 4,500 leaves 36, and 9 × 4 = 36 leaves 0. The quotient is 504.
A full lesson with slides, activities and an exit ticket on division with remainders, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.NBT.B.6 with an answer key, ready in about a minute.
Make a worksheet →Turn division with remainders into a quiz students answer online that marks itself, with a class summary for you.
Build a test →The standard asks for strategies based on place value and properties of operations. Many classes introduce long division later, and fluency with the standard division algorithm is a sixth grade expectation (6.NS.B.2).
One digit. Dividing by two-digit divisors is part of fifth grade under 5.NBT.B.6.