The four operations, order of operations and long division – Year 6 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. Estimate 350 × 30 = 10 500. 346 × 7 = 2 422 and 346 × 20 = 6 920. Add: 2 422 + 6 920 = 9 342.
   2. Estimate 1 300 × 30 = 39 000. 1 258 × 4 = 5 032 and 1 258 × 30 = 37 740. Add: 42 772.
   3. Estimate 4 000 × 60 = 240 000. 4 023 × 6 = 24 138 and 4 023 × 50 = 201 150. Add: 225 288.
   4. 346 × 270 is ten times 346 × 27, so it is 93 420.

2. Answer to Question 2

   1. 12 into 75 goes 6 (72), remainder 3. Bring down 6 to make 36. 12 into 36 goes 3. Answer 63.
   2. 14 into 19 goes 1, remainder 5. Bring down 0 to make 50: 14 into 50 goes 3 (42), remainder 8. Bring down 4 to make 84: 14 into 84 goes 6. Answer 136.
   3. 15 into 23 goes 1, remainder 8. Bring down 4: 84 ÷ 15 = 5 (75), remainder 9. Bring down 5: 95 ÷ 15 = 6 (90), remainder 5. Answer 156 remainder 5.
   4. 16 into 30 goes 1 (16), remainder 14. Bring down 0: 140 ÷ 16 = 8 (128), remainder 12. Bring down 0: 120 ÷ 16 = 7 (112), remainder 8. Add a decimal point: 80 ÷ 16 = 5. Answer 187.5.

3. Answer to Question 3

   1. 12 × 40 = 480 and 487 − 480 = 7. Answer 40 remainder 7.
   2. The remainder 7 becomes the fraction 7/12. Answer 40 and 7/12.
   3. 8 × 60 = 480 and the remainder is 7. 7 ÷ 8 = 0.875. Answer 60.875.
   4. Dividing by a smaller number gives a bigger answer, so 487 ÷ 8 is bigger.

4. Answer to Question 4

   1. Multiplication first: 4 × 3 = 12, then 8 + 12 = 20.
   2. Brackets first: 12, then 12 × 3 = 36.
   3. Division first: 12 ÷ 4 = 3. Then 20 − 3 + 1 = 17 + 1 = 18.
   4. Brackets: 5. Then 5 × 5 = 25 and 10 ÷ 2 = 5. Add: 30.
   5. Index first: 3² = 9. Then 9 × 4 = 36. Then 2 + 36 = 38.

5. Answer to Question 5

   1. 1, 2, 3, 4, 6, 9, 12, 18, 36. (Nine factors, found in pairs: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.)
   2. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common to both: 1, 2, 3, 4, 6, 12. The HCF is 12.
   3. Multiples of 4: 4, 8, 12, ... Multiples of 6: 6, 12, ... The LCM is 12.
   4. 9, 18, 27, 36.
   5. 7 × 8 = 56.

6. Answer to Question 6

   1. 27 = 3 × 9, 39 = 3 × 13 and 51 = 3 × 17 are not prime. The primes are 23, 31 and 53.
   2. 41, 43, 47, 53, 59. (Even numbers and multiples of 5 are never prime here. 49 = 7 × 7, 51 = 3 × 17 and 57 = 3 × 19.)
   3. 12² = 12 × 12 = 144. 4³ = 4 × 4 × 4 = 64.
   4. 9 × 9 = 81, so the square root is 9.
   5. Squares: 1, 4, 9, 16, 25. Cubes: 1, 8, 27, 64.

7. Answer to Question 7

   1. 342 + 18 = 360 people.
   2. 360 ÷ 52 = 6 remainder 48. Six coaches carry only 312 people, so 48 would be left behind. We need 7 coaches.
   3. 7 × 385 = £2 695.
   4. 342 × 6 = £2 052.
   5. Total = 2 695 + 2 052 = £4 747. Each pupil pays 4 747 ÷ 342 = 13.88... so £13.88 to the nearest penny.

8. Answer to Question 8

   1. 24 × 36 = 720 + 144 = 864 pencils.
   2. 864 ÷ 18 = 48 pencils for each class.
   3. 864 ÷ 20 = 43 remainder 4. Each class receives 43 pencils and 4 pencils are left over.
   4. (24 × 36) ÷ 18 = 48. The brackets make sure that we multiply before we divide.

9. Answer to Question 9

   1. 23 × 15 = 230 + 115 = 345 rolls.
   2. 345 ÷ 6 = 57 remainder 3. She fills 57 bags and has 3 rolls left over.
   3. 57 × 180p = 10 260p, which is £102.60.
   4. 28 × 15 = 420 rolls and 420 ÷ 6 = 70 bags, exactly.

10. Answer to Question 10

    1. 1 250 − 1 025 = 225 child tickets.
    2. 1 025 × 27 = 20 500 + 7 175 = £27 675.
    3. 225 × 20 = £4 500.
    4. 27 675 + 4 500 = £32 175. Check: 1 000 × 27 = 27 000 and 250 × 20 = 5 000, giving about 32 000. The answers agree.

11. Answer to Question 11

    1. (8 × 135) + (2 × 90) = 1 080 + 180 = 1 260 seats.
    2. 1 260 × 6 = 7 560 seats to fill.
    3. 7 560 × 8 = £60 480.

12. Answer to Question 12

    1. 15 × 24 = 360 bulbs.
    2. 360 ÷ 25 = 14.4, so 14 packs are not enough. He must buy 15 packs.
    3. 15 × 25 = 375, so 375 − 360 = 15 bulbs are left over.
    4. 15 × £4 = £60.

13. Answer to Question 13

    1. 0, 12, 24, 36, 48 minutes.
    2. 0, 15, 30, 45, 60 minutes.
    3. The common multiple of 12 and 15 is the LCM: 60. They leave together again at 9:00 am.
    4. Every 60 minutes: 8:00, 9:00, 10:00, 11:00 and 12:00. That is 5 times.

14. Answer to Question 14

    1. Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
    2. The highest common factor is 24, so she makes 24 bags.
    3. 72 ÷ 24 = 3 balloons, 48 ÷ 24 = 2 hats.
    4. 84 and 48 have HCF 12, so she can make 12 bags (the HCF of 84 and 48 is smaller than 24).

15. Answer to Question 15

    1. Cakes: 126 × 2 = £252. Plants: 38 × 6 = £228. Books: 215 × 1 = £215. Car washes: 47 × 5 = £235.
    2. 252 + 228 + 215 + 235 = £930. Check: 250 + 230 + 215 + 235 = 930. The numbers match.
    3. 930 − 248 = £682.
    4. £682 is less than £700, so they did not reach the target; they were £18 short.
    5. 682 ÷ 4 = £170.50 each.

16. Answer to Question 16

    1. 1 764 ÷ 12 = 147 passengers.
    2. 15 × 147 = 1 470 + 735 = 2 205 passengers.
    3. 28 × 1 764 = 35 280 + 14 112 = 49 392 passengers.
    4. 49 392 × 30 = 1 481 760 and 49 392 × 5 = 246 960. Add: £1 728 720.
    5. 28 × 1 764 is about 30 × 1 800 = 54 000. This is close to 49 392, so the answer is sensible.

17. Answer to Question 17

    1. 7 + 3 × 4 = 7 + 12 = 19. (15 − 3) ÷ 4 + 2 = 12 ÷ 4 + 2 = 3 + 2 = 5. 18 − 6 ÷ 3 × 2 = 18 − 2 × 2 = 18 − 4 = 14.
    2. Only Dev has 19, 5 and 14.
    3. Amy worked from left to right: 7 + 3 = 10, then 10 × 4 = 40. She should have multiplied before adding.
    4. Cara added 4 + 2 = 6 first and then worked out 12 ÷ 6 = 2. The addition must come after the division.
    5. Ben subtracted before dividing: 18 − 6 = 12, then 12 ÷ 3 = 4, then 4 × 2 = 8. Division and multiplication come before subtraction.
    6. (18 − 6) ÷ 3 × 2 = 12 ÷ 3 × 2 = 4 × 2 = 8.

18. Answer to Question 18

    1. The primes between 70 and 90 are 71, 73, 79, 83 and 89. The digit sums are 8, 10, 16, 11 and 17, so the number is 71.
    2. The squares between 30 and 60 are 36 and 49. Only 36 is in the 6 times table (6 × 6 = 36), so the number is 36.
    3. The LCM of 6 and 8 is 24, so the common multiples are 24, 48, 72, 96, ... Between 50 and 100 we have 72 and 96, so there are two answers.
    4. A number with exactly three factors is the square of a prime: 7 × 7 = 49 (factors 1, 7 and 49).
    5. 2 is the only even prime. Every other even number has 2 as a factor as well as 1 and itself, so it has more than two factors.

19. Answer to Question 19

    1. 15 × 6 = 90 hours, and 90 × 34 = £3 060.
    2. 15 × 28 = £420.
    3. 3 060 + 420 = £3 480.
    4. 3 480 ÷ 12 = £290 each.
    5. £1 400 is less than £3 480, so it is not enough. The committee still needs 3 480 − 1 400 = £2 080.

20. Answer to Question 20

    1. (4 + 6) × 2 − 1 = 10 × 2 − 1 = 20 − 1 = 19.
    2. 4 + 6 × (2 − 1) = 4 + 6 × 1 = 10.
    3. The possible brackets give 15 (no change), 19 and 10. For example (4 + 6 × 2) − 1 = 15 and 4 + (6 × 2 − 1) = 15 and (4 + 6) × (2 − 1) = 10. So the three answers are 10, 15 and 19. Joe is correct.
    4. (3 + 12) ÷ 3 × 2 = 15 ÷ 3 × 2 = 5 × 2 = 10.