Multiplying and Dividing Fractions — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. Convert 213 to an improper fraction: 73.
213: (2 × 3) + 1 = 7, over 3. So 213 = 73.
2. Convert 134 to an improper fraction: 74.
134: (1 × 4) + 3 = 7, over 4. So 134 = 74.
3. 112 × 23 = 32 × 23 = 1.
32 × 23 = 66 = 1. (Cross-cancel: 2s cancel and 3s cancel.)
4. 214 × 13 = 94 × 13 = 34.
94 × 13 = 912 = 34.
5. 312 ÷ 14 = 72 × 41 = 14.
72 × 41 = 282 = 14.
6. 125 × 57 = 75 × 57 = 1.
75 × 57 = 3535 = 1. (75 and 57 are reciprocals, so their product is always 1.)
7. 213 ÷ 12 = 73 × 21 = 423 as a mixed number.
73 × 21 = 143 = 423.
8. 114 × 225 = 54 × 125 = 3.
54 × 125 = 6020 = 3. (Cross-cancel: 5s → 1, 4 and 12 → 1 and 3. Result: 1×3=3.)
9. 412 ÷ 34 = 92 × 43 = 6.
92 × 43 = 366 = 6. (Cross-cancel: 9 and 3 → 3, 4 and 2 → 2. 3×2=6.)
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
113 × 34
→ 1
1
212 ÷ 56
→ 3
3
134 × 27
→ 12
5
313 ÷ 23
→ 5
12
1⅓×34=43×34=1; 2½÷56=52×65=3; 1¾×27=74×27=12; 3⅓÷23=103×32=5.