Adding and subtracting mixed numbers worksheet

Part A: Working out and filling in

1. 1. 7, 1, 2

   Add the wholes and the fractions separately: put 15 and 310 over a common denominator and see whether they pass 1.

   Add the wholes, 3 + 4; add the fractions over a common denominator and carry any whole: 7 12.

2. 2. 6, 1, 2

   Add the wholes and the fractions separately: put 15 and 310 over a common denominator and see whether they pass 1.

   Add the wholes, 2 + 4; add the fractions over a common denominator and carry any whole: 6 12.

3. 3. 6, 9, 10

   Put 15 and 310 over a common denominator first. Is 15 big enough? If not, borrow 1 from 9.

   15 is less than 310, so borrow 1 from 9 as a fraction, then subtract: 6 910.

4. 4. 3, 1, 5

   8 has no fraction part. Borrow 1 from it as 55 first, then subtract.

   Borrow 1 from 8 as 55: 55 − 45 = 15, and the wholes 8 − 1 − 4 = 3.

5. 5. 5, 5, 6

   Put 13 and 12 over a common denominator first. Is 13 big enough? If not, borrow 1 from 9.

   13 is less than 12, so borrow 1 from 9 as a fraction, then subtract: 5 56.

6. 6. 7, 8, 9

   9 has no fraction part. Borrow 1 from it as 99 first, then subtract.

   Borrow 1 from 9 as 99: 99 − 19 = 89, and the wholes 9 − 1 − 1 = 7.

7. 7. 5, 9, 10

   Put 45 and 910 over a common denominator first. Is 45 big enough? If not, borrow 1 from 8.

   45 is less than 910, so borrow 1 from 8 as a fraction, then subtract: 5 910.

Part B: Choose, or true or false

1. 8. C. 9 and 10

   Add the wholes, 3 + 5, first, then see whether 34 + 12 goes past 1.

   The wholes make 3 + 5 = 8; 34 + 12 is more than 1, so carry 1: the answer is between 9 and 10.

2. 9. C. 11 and 12

   Add the wholes, 6 + 4, first, then see whether 45 + 14 goes past 1.

   The wholes make 6 + 4 = 10; 45 + 14 is more than 1, so carry 1: the answer is between 11 and 12.

3. 10. C. 5 and 6

   Add the wholes, 2 + 2, first, then see whether 25 + 34 goes past 1.

   The wholes make 2 + 2 = 4; 25 + 34 is more than 1, so carry 1: the answer is between 5 and 6.

4. 11. False

   Put 12 and 1112 over a common denominator and see whether 12 is big enough; work it out yourself and compare with the right-hand side.

   12 is less than 1112: borrow 1 from the wholes first; never swap it round to 1112 − 12.

5. 12. False

   Put 34 and 1112 over a common denominator and see whether 34 is big enough; work it out yourself and compare with the right-hand side.

   34 is less than 1112: borrow 1 from the wholes first; never swap it round to 1112 − 34.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 2, 4, 5

   You need 7 − 4 15. The 7 has no fraction part, so borrow 1 as 55 first.

   Borrow 1 from 7 as 55, then subtract: 2 45 kg.

2. 14. 110 litres

   Compare the wholes, 1 and 1, then 25 and 12 over a common denominator, to see which bottle holds more.

   See which is more, then take the smaller from the bigger (borrowing if needed): 110 litres.

3. 15. 3, 7, 18

   You need 4 12 − 1 19. Put the fraction parts over a common denominator and see whether there is enough to subtract.

   4 12 − 1 19: fractions over a common denominator, borrowing 1 if needed: 3 718 m.

4. 16. 6, 1, 10

   Add the two days: wholes with wholes, fractions over a common denominator, and see whether they pass 1.

   Wholes together, fractions over a common denominator, carrying a whole: 6 110 hours.

5. 17. 7, 8, 9

   Add the two days: wholes with wholes, fractions over a common denominator, and see whether they pass 1.

   Wholes together, fractions over a common denominator, carrying a whole: 7 89 hours.

6. 18. 4, 1, 2

   You need 6 13 − 1 56. Put the fraction parts over a common denominator and see whether there is enough to subtract.

   6 13 − 1 56: fractions over a common denominator, borrowing 1 if needed: 4 12 m.