Adding and Subtracting Fractions — Solutions

1. Add fractions with the same denominator

   1. 15 + 35: 45 ▶ View Solution
   2. 38 + 18: ½ ▶ View Solution
   3. 29 + 59: 79 ▶ View Solution
   4. 512 + 712: 1 ▶ View Solution
   5. 411 + 611: 1011 ▶ View Solution
   6. 715 + 415: 1115 ▶ View Solution
   7. 310 + 910: 115 ▶ View Solution
   8. 57 + 47: 127 ▶ View Solution

2. Add fractions with different denominators

   1. 12 + 14: 34 ▶ View Solution
   2. 13 + 16: ½ ▶ View Solution
   3. 23 + 14: 1112 ▶ View Solution
   4. 34 + 16: 1112 ▶ View Solution
   5. 25 + 310: 710 ▶ View Solution
   6. 14 + 23: 1112 ▶ View Solution
   7. 56 + 38: 1524 ▶ View Solution
   8. 35 + 56: 11330 ▶ View Solution

3. Subtract fractions

   1. 34 − 14: ½ ▶ View Solution
   2. 56 − 13: ½ ▶ View Solution
   3. 78 − 12: 38 ▶ View Solution
   4. 35 − 14: 720 ▶ View Solution
   5. 56 − 34: 112 ▶ View Solution
   6. 910 − 25: ½ ▶ View Solution
   7. 712 − 14: 13 ▶ View Solution
   8. 56 − 79: 118 ▶ View Solution

4. Add mixed numbers

   1. 1½ + 2¼: 334 ▶ View Solution
   2. 213 + 116: 3½ ▶ View Solution
   3. 325 + 1310: 4710 ▶ View Solution
   4. 234 + 158: 438 ▶ View Solution
   5. 423 + 256: 7½ ▶ View Solution
   6. 179 + 323: 549 ▶ View Solution

5. Subtract mixed numbers

   1. 334 − 1½: 2¼ ▶ View Solution
   2. 456 − 213: 2½ ▶ View Solution
   3. 5½ − 334: 134 ▶ View Solution
   4. 6¼ − 258: 358 ▶ View Solution
   5. 413 − 125: 21415 ▶ View Solution
   6. 716 − 434: 2512 ▶ View Solution

6. Check the working — is it correct? If not, fix it.

   1. 13 + 14: Incorrect — correct answer: 712 ▶ View Solution
   2. Same-denominator addition: Correct ▶ View Solution
   3. 56 + 38: 1524 ▶ View Solution
   4. Is 34 + 23 less than 2?: Yes — 1512 < 2 ▶ View Solution

7. Word problems with fractions

   1. Total flour for both recipes: 1512 cups ▶ View Solution
   2. Total distance cycled: 438 km ▶ View Solution
   3. Rope remaining after cuts: 134 m ▶ View Solution
   4. Fraction playing neither sport: 720 ▶ View Solution
   5. Extra time on Saturday: 56 hr ▶ View Solution

8. Add and subtract three fractions

   1. 12 + 13 + 16: 1 ▶ View Solution
   2. 34 + 18 − 38: ½ ▶ View Solution
   3. 1 − 25 − 14: 720 ▶ View Solution
   4. 56 − 14 + 13: 1112 ▶ View Solution
   5. 23 + 34 − 56: 712 ▶ View Solution
   6. 710 + 25 − 34: 720 ▶ View Solution

9. Fraction chains and equations

   1. ☐ + 34 = 1¼: ½ ▶ View Solution
   2. ½ + ☐ = 56: 13 ▶ View Solution
   3. 23 + ☐ = 116: ½ ▶ View Solution
   4. 138 + ☐ = 2: 58 ▶ View Solution
   5. Can you add fractions by adding numerators and denominators?: No — must find common denominator first ▶ View Solution

10. Multi-step fraction word problems

    1. Final amount in container: 4 litres ▶ View Solution
    2. Total fabric and whether more is needed: 778 m total; no extra needed ▶ View Solution
    3. Total race distance and leg comparison: 113 km; first and fourth legs equal second and third legs ▶ View Solution
    4. Final fraction of tank that is full: 34 full ▶ View Solution