How is the divisor found from the largest remainder?

The largest remainder is the divisor minus one, so add one to the largest remainder to get the divisor.

Why must units be written?

The quotient and remainder carry different units, such as 8 boxes and 4 eggs left, so units matter.

What strategy suits the challenge items?

Write the equation, check divisor times quotient plus remainder, then decide whether the answer needs one more group.

P3 Maths Division with Remainders Paper 3: Challenge

2026-11-09

Tutor Prep Guide · P3 Maths

Ten original items, each with an answer and a one-line explanation.

Direct answers　Items 1-3 are basic, 4-6 intermediate and 7-9 challenge, with item 10 as the error review. Time yourself first, then check each answer and redo what is wrong.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: P3 Maths: Division with Remainders Word Problems
Level	P3

02　Questions (10 items)

FoundationIn a division, the largest possible remainder is 6. What is the divisor?
FoundationA number divided by 8 gives a quotient of 9 and a remainder of 7. What is the number?
Intermediate100 eggs are packed 12 to a box. How many full boxes and how many eggs left?
IntermediateThe divisor is 15, the quotient is 12 and the remainder is 5. What is the dividend?
FoundationWhat are the quotient and remainder of 135 divided by 6?
IntermediateWith 250 dollars and workbooks at 30 dollars each, how many can be bought and how much is left?
ChallengeA number divided by 9 gives a quotient of 13 and a remainder of 8. What is the number?
Challenge200 books are packed 24 to a box. How many full boxes and how many books left?
Challenge62 people travel in cars holding 9 each. What is the least number of cars needed?
Error redoA student says the largest remainder with a divisor of 6 is 6. What is correct?

03　Answers and one-line notes

#	Answer	One-line note
1	7	A remainder is always smaller than the divisor, so the largest remainder 6 means the divisor is 7.
2	79	8 times 9 + 7 = 79, and the remainder 7 is smaller than the divisor 8.
3	8 boxes, 4 eggs left	100 divided by 12 = 8 remainder 4, and the 4 eggs left would need one more box.
4	185	15 times 12 + 5 = 185, and 185 divided by 15 gives 12 remainder 5.
5	Quotient 22, remainder 3	6 times 22 = 132 and 135 minus 132 = 3, so the quotient is 22 with remainder 3.
6	8 books, 10 dollars left	250 divided by 30 = 8 remainder 10, so 8 books cost 240 dollars and 10 dollars remain.
7	125	9 times 13 + 8 = 125, and 8 is the largest remainder possible with a divisor of 9.
8	8 boxes, 8 books left	200 divided by 24 = 8 remainder 8, and 8 boxes hold 192 books.
9	7 cars	62 divided by 9 = 6 remainder 8, so 6 cars hold 54 and the 8 left need one more: 7 cars.
10	5	A remainder must be smaller than the divisor, so with a divisor of 6 the largest remainder is 5.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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