Multiplying and Dividing Fractions — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. The reciprocal of 78 is 87.
Swapping the numerator and denominator of 78 gives 87, which is its reciprocal.
2. 34 ÷ 12 = 34 × 21 = 112.
Flip 12 to get 21, then multiply: 34 × 21 = 64, which simplifies to 32 or 112.
3. 59 ÷ 56 = 59 × 65 = 23.
Flip 56 to get 65, then multiply: 59 × 65 = 3045. The 5s cancel and 3045 simplifies to 23.
4. Dividing by 14 is the same as multiplying by 4.
The reciprocal of 14 is 41, which equals 4, so dividing by 14 is the same as multiplying by 4.
5. 710 ÷ 720 = 710 × 207 = 2.
Flip 720 to get 207, then multiply: 710 × 207 = 14070. The 7s cancel and 14070 simplifies to 2.
6. 25 ÷ 415 = 25 × 154 = 112 as a mixed number.
Flip 415 to get 154, then multiply: 25 × 154 = 3020, which simplifies to 32 or 112.
7. A number multiplied by its reciprocal always equals 1.
When you multiply any number by its reciprocal, the numerators and denominators cancel out completely, always giving a product of 1.
8. 38 ÷ 34 = 38 × 43 = 12.
Flip 34 to get 43, then multiply: 38 × 43 = 1224. The 3s cancel and 1224 simplifies to 12.
9. The reciprocal of 6 written as a fraction is 16.
The whole number 6 equals 61, so flipping it gives 16 as the reciprocal.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
45 ÷ 25
→ 2
12
37 ÷ 914
→ 23
23
13 ÷ 29
→ 112
112
58 ÷ 54
→ 12
2
Correct matches: 45 ÷ 25 → 2; 37 ÷ 914 → 23; 13 ÷ 29 → 112; 58 ÷ 54 → 12.