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Short and long division, and what to do with the remainder once you have it.
Question 1 of 12
A factory has 264 pencils. They are packed into packets of 19. How many full packets are there?
264 ÷ 19 = 13 remainder 17. The question asks for full packets, so the remainder is left over rather than rounded up: 17 pencils are not enough to fill another one. The answer is 13. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many packets are *needed* would have the answer 14. Ask whether the leftovers still need carrying. If they do, round up; if they are simply left, round down.
The answer is B. 264 ÷ 19 = 13 remainder 17. The question asks for full packets, so the remainder is left over rather than rounded up: 17 pencils are not enough to fill another one. The answer is 13. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many packets are *needed* would have the answer 14. Ask whether the leftovers still need carrying. If they do, round up; if they are simply left, round down.
Work out 1,056 ÷ 32.
It helps to know a few multiples of 32 before starting: 32 × 10 = 320, 32 × 20 = 640, 32 × 5 = 160. 1,056 is more than 640, so the answer is above 20. Working it through gives 1,056 ÷ 32 = 33, with nothing left over. Multiplying back confirms it: 33 × 32 = 1,056. Estimate first so you know roughly how big the answer should be.
The answer is D. It helps to know a few multiples of 32 before starting: 32 × 10 = 320, 32 × 20 = 640, 32 × 5 = 160. 1,056 is more than 640, so the answer is above 20. Working it through gives 1,056 ÷ 32 = 33, with nothing left over. Multiplying back confirms it: 33 × 32 = 1,056. Estimate first so you know roughly how big the answer should be.
Work out 1,320 ÷ 30.
It helps to know a few multiples of 30 before starting: 30 × 10 = 300, 30 × 20 = 600, 30 × 5 = 150. 1,320 is more than 600, so the answer is above 20. Working it through gives 1,320 ÷ 30 = 44, with nothing left over. Multiplying back confirms it: 44 × 30 = 1,320. Always multiply back to check. It takes seconds and catches nearly every slip.
The answer is B. It helps to know a few multiples of 30 before starting: 30 × 10 = 300, 30 × 20 = 600, 30 × 5 = 150. 1,320 is more than 600, so the answer is above 20. Working it through gives 1,320 ÷ 30 = 44, with nothing left over. Multiplying back confirms it: 44 × 30 = 1,320. Always multiply back to check. It takes seconds and catches nearly every slip.
A market stall has 595 pencils. They are packed into packets of 24. How many full packets are there?
595 ÷ 24 = 24 remainder 19. The question asks for full packets, so the remainder is left over rather than rounded up: 19 pencils are not enough to fill another one. The answer is 24. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many packets are *needed* would have the answer 25. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
The answer is D. 595 ÷ 24 = 24 remainder 19. The question asks for full packets, so the remainder is left over rather than rounded up: 19 pencils are not enough to fill another one. The answer is 24. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many packets are *needed* would have the answer 25. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
The school kitchen has 430 cakes. They are laid out into trays of 15. How many full trays are there?
430 ÷ 15 = 28 remainder 10. The question asks for full trays, so the remainder is left over rather than rounded up: 10 cakes are not enough to fill another one. The answer is 28. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many trays are *needed* would have the answer 29. Check by multiplying back: 28 × 15 = 420, plus 10 left over.
The answer is A. 430 ÷ 15 = 28 remainder 10. The question asks for full trays, so the remainder is left over rather than rounded up: 10 cakes are not enough to fill another one. The answer is 28. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many trays are *needed* would have the answer 29. Check by multiplying back: 28 × 15 = 420, plus 10 left over.
Work out 1,330 ÷ 35.
It helps to know a few multiples of 35 before starting: 35 × 10 = 350, 35 × 20 = 700, 35 × 5 = 175. 1,330 is more than 700, so the answer is above 20. Working it through gives 1,330 ÷ 35 = 38, with nothing left over. Multiplying back confirms it: 38 × 35 = 1,330. Estimate first so you know roughly how big the answer should be.
The answer is A. It helps to know a few multiples of 35 before starting: 35 × 10 = 350, 35 × 20 = 700, 35 × 5 = 175. 1,330 is more than 700, so the answer is above 20. Working it through gives 1,330 ÷ 35 = 38, with nothing left over. Multiplying back confirms it: 38 × 35 = 1,330. Estimate first so you know roughly how big the answer should be.
Work out 858 ÷ 13.
It helps to know a few multiples of 13 before starting: 13 × 10 = 130, 13 × 20 = 260, 13 × 5 = 65. 858 is more than 260, so the answer is above 20. Working it through gives 858 ÷ 13 = 66, with nothing left over. Multiplying back confirms it: 66 × 13 = 858. Estimate first so you know roughly how big the answer should be.
The answer is A. It helps to know a few multiples of 13 before starting: 13 × 10 = 130, 13 × 20 = 260, 13 × 5 = 65. 858 is more than 260, so the answer is above 20. Working it through gives 858 ÷ 13 = 66, with nothing left over. Multiplying back confirms it: 66 × 13 = 858. Estimate first so you know roughly how big the answer should be.
A market stall has 451 books. They are stacked into shelves of 10. How many full shelves are there?
451 ÷ 10 = 45 remainder 1. The question asks for full shelves, so the remainder is left over rather than rounded up: 1 books are not enough to fill another one. The answer is 45. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many shelves are *needed* would have the answer 46. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
The answer is A. 451 ÷ 10 = 45 remainder 1. The question asks for full shelves, so the remainder is left over rather than rounded up: 1 books are not enough to fill another one. The answer is 45. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many shelves are *needed* would have the answer 46. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
The school kitchen has 175 eggs. They are packed into boxes of 8. How many full boxes are there?
175 ÷ 8 = 21 remainder 7. The question asks for full boxes, so the remainder is left over rather than rounded up: 7 eggs are not enough to fill another one. The answer is 21. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many boxes are *needed* would have the answer 22. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
The answer is C. 175 ÷ 8 = 21 remainder 7. The question asks for full boxes, so the remainder is left over rather than rounded up: 7 eggs are not enough to fill another one. The answer is 21. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many boxes are *needed* would have the answer 22. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
The school kitchen has 344 eggs. They are packed into boxes of 15. How many full boxes are there?
344 ÷ 15 = 22 remainder 14. The question asks for full boxes, so the remainder is left over rather than rounded up: 14 eggs are not enough to fill another one. The answer is 22. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many boxes are *needed* would have the answer 23. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
The answer is A. 344 ÷ 15 = 22 remainder 14. The question asks for full boxes, so the remainder is left over rather than rounded up: 14 eggs are not enough to fill another one. The answer is 22. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many boxes are *needed* would have the answer 23. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
Work out 1,121 ÷ 19.
It helps to know a few multiples of 19 before starting: 19 × 10 = 190, 19 × 20 = 380, 19 × 5 = 95. 1,121 is more than 380, so the answer is above 20. Working it through gives 1,121 ÷ 19 = 59, with nothing left over. Multiplying back confirms it: 59 × 19 = 1,121. Write out the first ten multiples of the divisor before you start. It turns long division into looking things up.
The answer is C. It helps to know a few multiples of 19 before starting: 19 × 10 = 190, 19 × 20 = 380, 19 × 5 = 95. 1,121 is more than 380, so the answer is above 20. Working it through gives 1,121 ÷ 19 = 59, with nothing left over. Multiplying back confirms it: 59 × 19 = 1,121. Write out the first ten multiples of the divisor before you start. It turns long division into looking things up.
A factory has 857 eggs. They are packed into boxes of 21. How many full boxes are there?
857 ÷ 21 = 40 remainder 17. The question asks for full boxes, so the remainder is left over rather than rounded up: 17 eggs are not enough to fill another one. The answer is 40. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many boxes are *needed* would have the answer 41. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
The answer is B. 857 ÷ 21 = 40 remainder 17. The question asks for full boxes, so the remainder is left over rather than rounded up: 17 eggs are not enough to fill another one. The answer is 40. This is the part of division that costs marks — the arithmetic is usually right and the last step is not. A question asking how many boxes are *needed* would have the answer 41. Read the last sentence twice. Division questions are won and lost on what happens to the remainder.
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