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Division · Grade 4

4 Digit Division Word Problems With and Without Remainders

Teach students to interpret a remainder in the context of the story.

4 problemsAnswer key includedPrintable worksheetA4 & US Letter
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Teaching notes for parents and teachers

How to teach it

Label the total and group size before dividing. Have the student describe the complete groups and what is left, then choose a suitable activity range.

Example to work through together

Use the model below as you explain the example. Have your student point to the quantities as you discuss them.

Total: 1,237 counters. Group size: 6 counters.

1,237 ÷ 6 = 206 R 1
206 × 6 + 1 = 1,237

Quotient: 206 full groups. Remainder: 1 counter.

Ask your student

What does the remainder represent here?

If your student needs help

If the student ignores the remainder, ask where the leftover objects belong in the model.

Use smaller totals to explain a remainder

Choose Smaller totals: remainders to practice finding complete groups and the individual counters left over. Each sheet has four different questions with totals from 10 to 999 and group sizes from two to nine. Every question in this option has at least one full group and a positive remainder.

Start with the 32 ÷ 9 picture in the guide: three full groups use 27 counters, and five individual counters remain. The same idea works for a larger total. We can count full groups in batches instead of drawing every counter.

Make 35 groups in two steps

There are 247 counters to pack in groups of seven. Thirty groups use 7 × 30 = 210 counters. Subtract those counters from the total: 247 − 210 = 37. The 37 is what remains at this stage, but it is not yet the final remainder because more full groups of seven can still be made.

Each cell = 1 group of 710 groups × 7 = 70777777777710 groups × 7 = 70777777777710 groups × 7 = 70777777777730 groups use 2105 groups × 7 = 35777772 individual counters left30 + 5 = 35 full groups
Each numbered cell represents seven counters in one complete group. Three rows of ten cells make 30 groups; the shorter row adds five groups. Only the two separate dots represent individual leftover counters.

Five more groups use 7 × 5 = 35 counters. Now 37 − 35 = 2 counters remain. Add the full groups from both steps: 30 + 5 = 35. The numbers 30 and 5 are partial quotients: each counts the full groups made at that step. The 210 and 35 count the counters used in those steps.

247 ÷ 7 = 35 R 2
247 = 210 + 35 + 2
247 = (7 × 30) + (7 × 5) + 2

The diagram has 35 numbered cells, one for each full group. The first three rows are batches of ten groups, not three groups. The two loose dots are counters, not groups or fractional groups. Say the answer with both units: 35 full groups and 2 counters left.

Check the total and the size of the remainder

Rebuild the total by multiplying the quotient by the group size, then adding what is left: 35 × 7 + 2 = 245 + 2 = 247. In symbols, quotient × divisor + remainder = dividend. The remainder must also satisfy 0 ≤ remainder < divisor. Here 0 ≤ 2 < 7, so there are too few counters left to make another group of seven.

If the child stops at 30 groups with 37 left: the total check, 30 × 7 + 37 = 247, works, but the remainder check does not: 37 is at least seven. Ask how many more full groups can be made before accepting the answer.

Do not add the two leftover counters to the 35 groups: the quantities have different units. Do not automatically change 35 to 36 either. This question asks for full groups and leftovers separately. A different question about containers needed to hold every counter can require a partly filled extra container, as the 32-counter example explains.

Move between the two practice options

This smaller-total option always leaves something over. The default four-digit activity can include exact division with zero left, division with a positive remainder, or both. For either option, write the equation, keep the quotient and leftover amount separate, and use the work space for your calculation. The answer key gives the final equation and values; the examples in this guide explain the steps.

Make a practice set

Select the worksheet, answer key, or both. When both are selected, the answer key prints after the questions. Keep it separate if you want your student to work independently.

Print materials

After your student finishes

Choose one problem and ask what the quotient counts and what the remainder counts. Check the multiplication-and-addition identity together. If place-value division is secure, compare the wording with an equal-sharing story to discuss the meaning of each answer.

More about division · Grade 4 worksheets

Grade 4 selected skill connection: 4.NBT.B.6 (up to four-digit dividends and one-digit divisors in grouping contexts; smaller-remainders uses two- and three-digit totals with positive remainders). See the Common Core standards for this grade. This worksheet does not cover every requirement in the standard.