Fraction arithmetic practice worksheet with addition, subtraction, multiplication, and division problems.

I'll solve each fraction problem step by step, showing my work and verifying the calculations.

Problem 1: 12/22 × 2/5
- Multiply numerators: 12 × 2 = 24
- Multiply denominators: 22 × 5 = 110
- Result: 24/110
- Simplify: Both divisible by 2 → 12/55
- ✓ Verified: 12/55 cannot be simplified further (GCD of 12 and 55 is 1)

Problem 2: 16/17 ÷ 4/9
- Division becomes multiplication by reciprocal: 16/17 × 9/4
- Multiply numerators: 16 × 9 = 144
- Multiply denominators: 17 × 4 = 68
- Result: 144/68
- Simplify: Both divisible by 4 → 36/17
- ✓ Verified: 36/17 is in simplest form

Problem 3: 9/16 + 36/27
- First simplify 36/27: Both divisible by 9 → 4/3
- Now: 9/16 + 4/3
- Find LCD of 16 and 3: 48
- Convert: 9/16 = 27/48 and 4/3 = 64/48
- Add: 27/48 + 64/48 = 91/48
- ✓ Verified: 91/48 cannot be simplified further

Problem 4: 9/34 ÷ 23/51
- Division becomes multiplication by reciprocal: 9/34 × 51/23
- Before multiplying, check for simplification: 51 and 34 share factor 17
- 51 ÷ 17 = 3, 34 ÷ 17 = 2
- So: 9/2 × 3/23 = 27/46
- ✓ Verified: 27/46 cannot be simplified further

Problem 5: 20/3 + 24/11
- Find LCD of 3 and 11: 33
- Convert: 20/3 = 220/33 and 24/11 = 72/33
- Add: 220/33 + 72/33 = 292/33
- ✓ Verified: 292/33 cannot be simplified further (292 = 4×73, 33 = 3×11)

Problem 6: 21/26 - 1/8
- Find LCD of 26 and 8: 104
- Convert: 21/26 = 84/104 and 1/8 = 13/104
- Subtract: 84/104 - 13/104 = 71/104
- ✓ Verified: 71/104 cannot be simplified further (71 is prime)

Problem 7: 17/5 × 32/6
- Before multiplying, simplify: 32/6 = 16/3 (divide both by 2)
- Multiply: 17/5 × 16/3 = 272/15
- ✓ Verified: 272/15 cannot be simplified further

Problem 8: 4/15 + 9/16
- Find LCD of 15 and 16: 240
- Convert: 4/15 = 64/240 and 9/16 = 135/240
- Add: 64/240 + 135/240 = 199/240
- ✓ Verified: 199/240 cannot be simplified further (199 is prime)

Problem 9: 31/6 - 8/7
- Find LCD of 6 and 7: 42
- Convert: 31/6 = 217/42 and 8/7 = 48/42
- Subtract: 217/42 - 48/42 = 169/42
- ✓ Verified: 169/42 cannot be simplified further (169 = 13², 42 = 2×3×7)

Problem 10: 11/14 - 12/26
- First simplify 12/26: Both divisible by 2 → 6/13
- Now: 11/14 - 6/13
- Find LCD of 14 and 13: 182
- Convert: 11/14 = 143/182 and 6/13 = 84/182
- Subtract: 143/182 - 84/182 = 59/182
- ✓ Verified: 59/182 cannot be simplified further (59 is prime)

Problem 11: 15/16 ÷ 19/3
- Division becomes multiplication by reciprocal: 15/16 × 3/19
- Multiply: 15 × 3 = 45, 16 × 19 = 304
- Result: 45/304
- ✓ Verified: 45/304 cannot be simplified further (45 = 3²×5, 304 = 2⁴×19)

Problem 12: 7/9 ÷ 3/16
- Division becomes multiplication by reciprocal: 7/9 × 16/3
- Multiply: 7 × 16 = 112, 9 × 3 = 27
- Result: 112/27
- ✓ Verified: 112/27 cannot be simplified further (112 = 2⁴×7, 27 = 3³)

Problem 13: 15/18 × 13/22
- First simplify 15/18: Both divisible by 3 → 5/6
- Multiply: 5/6 × 13/22 = 65/132
- ✓ Verified: 65/132 cannot be simplified further (65 = 5×13, 132 = 2²×3×11)

Problem 14: 12/21 ÷ 14/56
- First simplify fractions: 12/21 = 4/7 (÷3), 14/56 = 1/4 (÷14)
- Now: 4/7 ÷ 1/4 = 4/7 × 4/1 = 16/7
- ✓ Verified: 16/7 cannot be simplified further

Final Answer:
1) 12/55
2) 36/17
3) 91/48
4) 27/46
5) 292/33
6) 71/104
7) 272/15
8) 199/240
9) 169/42
10) 59/182
11) 45/304
12) 112/27
13) 65/132
14) 16/7