The idea in brief. Divide, and then read the remainder against the question. If the question asks how many full groups you can make, the remainder is left out and the quotient is the answer. If it asks how many groups you need to hold everything, the remainder needs one more group, so the answer is the quotient plus one.
Lesson video, with the working
Division with a remainder: round up or down
5 min 03 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
A baker has 1250 cookies. She packs them into boxes of 8. What is the maximum number of boxes of 8 cookies she can pack?
1250 ÷ 8 = 156 R 2
maximum number of boxes = 156 (round down)
Ans: 156 boxes
Example 1
A school orders 1070 exercise books. The books are delivered in cartons. Each carton can hold up to 9 books. What is the minimum number of cartons needed to deliver all the books?
1070 ÷ 9 = 118 R 8
118 + 1 = 119
Ans: 119 cartons
How to solve it
Set out the long division, and work from the greatest place towards the ones.
Use the times table to find the biggest number that fits. Write it on top, multiply, then subtract.
Rename what remains and bring down the next digit. Continue until the remainder is smaller than the number we divide by.
1250 divided by 8 is 156 remainder 2. The 2 cookies cannot fill another box, so there are 156 full boxes.
1070 divided by 9 is 118 remainder 8. If every book must be delivered, the 8 books need another carton.
Read what the question asks. For all the books, 118 plus 1 is 119 cartons.
Full groups: leave the remainder out. Holding everything: the remainder needs one more group.
Practice questions with worked solutions
Question 1 is free to try. The other 7 open in the free trial, each with its full working.
How can I help my child interpret P4 division with remainders?
Your child uses the division algorithm for numbers up to 4 digits divided by a 1-digit number, the MOE Primary 4 outcome 3.2.
What your child learns here
Your child uses the division algorithm for numbers up to 4 digits divided by a 1-digit number, the MOE Primary 4 outcome 3.2. In a word problem, the quotient and remainder then need interpreting. The number of complete groups and the number needed to hold everything can be different answers to different questions.
Divide from the greatest place, distributing each part and renaming what remains into the next smaller place as the calculation continues.
Keep a zero in the quotient when a place has no complete groups, rather than closing the gap and changing the quotient's value.
Recognise that the final remainder is smaller than the divisor, because enough for another full group would increase the quotient.
Decide whether a story asks for complete groups only, the amount left over or enough containers for all the items, including an unfinished group.
State the final answer with the correct unit and explain any change from the numerical quotient to a whole-number answer in context.
Does the answer make sense?
Multiply the quotient by the divisor and add the remainder; the result must be the original dividend. Your child should also check that the remainder is at least zero and smaller than the divisor before interpreting it in the story.
How to practise these questions
Basic questions cover exact division and identifying a remainder. Intermediate practice interprets packets needed to hold enough items, leftover items after full packing, an exact capacity and recovering the original number from a quotient and remainder. Challenge questions divide separate rolls into pieces or account for stickers left after two stages of packing. Your child should record what the quotient counts before deciding whether anything must be added to it. Compare the exact-capacity case with a case that leaves something over: an extra container is justified only when the leftovers need one. For the recovery question, use multiplication and addition to rebuild the original number, then divide once more to verify both the quotient and remainder.
Questions parents ask
When does my child add one to a division answer? Add one to the count of complete groups when the question requires enough containers or trips for everything and there is a non-zero remainder. The extra group holds the leftovers. If the division is exact, no extra group is needed for that reason.
When should the remainder be left out of the final count? A question about the greatest number of complete packets or full groups uses the quotient alone. The remainder tells your child how many items cannot form another complete group. It is still useful information for checking, even when it is not included in the requested count.
Why can a zero occur in the middle of the quotient? At that place there may be too little to make a complete group, while smaller places can still be divided. The zero preserves the position. Ask your child to check the final quotient by multiplication; omitting the zero changes the value and will fail that check.
