4-Digit by 4-Digit Division — With and Without Remainders
Use this worksheet to teach 4-digit by 4-digit division. Work through one example with your student before assigning independent practice. The first number has 4 digits, and the second has 4 digits.
Teaching notes for parents and teachers
Use this worksheet to teach 4-digit by 4-digit division. Work through one example with your student before assigning independent practice. The first number has 4 digits, and the second has 4 digits.
This set may include division with and without remainders. Ask your student to explain any remainder in the context of equal groups.
How to teach it
Model long division using place-value units. At each step, discuss the amount being shared or grouped, then record the quotient digit, product, and difference. Show why a zero is sometimes needed in the quotient.
Examples to explain together
Check: 3 × 2606 + 267 = 8085. The remainder is smaller than 2606.
Check: 1 × 3082 + 2375 = 5457. The remainder is smaller than 3082.
If your student needs help
If your student stops too early, check for a digit still to be brought down. If the remainder is at least as large as the divisor, show that another group can be made.
Check understanding
Ask your student to multiply the quotient by the divisor and add the remainder. The result should equal the dividend.
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.
After your student finishes
Review one problem together. Ask your student to explain the steps, then use the answer key to check the result. Revisit a difficult step before assigning another set.
About 4-Digit by 4-Digit Division — With and Without Remainders
Practice 4-digit by 4-digit division. Focus on accuracy before speed. Use the space provided to record the steps you need. The first number has 4 digits, and the second has 4 digits.
This number range includes exact divisions and divisions with a remainder. Write a remainder when needed.
How to practice
Decide how many complete groups of the divisor fit into the current amount. Write a quotient digit, multiply it by the divisor, and subtract. Bring down the next digit and repeat. A zero quotient digit may be needed to hold a place. At the end, the remainder must be smaller than the divisor.
Examples to explain together
Check: 3 × 2606 + 267 = 8085. The remainder is smaller than 2606.
Check: 1 × 3082 + 2375 = 5457. The remainder is smaller than 3082.
If your student needs help
Do not stop just because a current digit is smaller than the divisor. Check whether more digits remain to be brought down. A remainder equal to or larger than the divisor means another complete group fits.
Check understanding
Multiply the quotient by the divisor and add the remainder. This must equal the dividend.
Before independent practice
Work through one example together. Ask the student to explain one step, then try a few questions independently. Review the cause of an error before repeating the calculation. Compare the student’s written steps with the answer key where worked steps are provided; a correct answer alone does not show which strategy was used.