Multiplying and Dividing Fractions — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. Before multiplying 49 × 38, you can cancel the common factor 3 from 3 and 9.
Both 3 (numerator of the second fraction) and 9 (denominator of the first) are divisible by 3, so you can cross-cancel by dividing each by 3 before multiplying.
2. 49 × 38 simplified is 16.
Cross-cancel the 3 and 9 (both divide by 3) and the 4 and 8 (both divide by 4), leaving 13 × 12 = 16.
3. 712 × 47 = 13 after cross-cancelling the 7s.
The 7 in the numerator of 712 and the 7 in the denominator of 47 cancel, and 412 simplifies to 13.
4. 611 × 1118 = 13 after cancelling 11 and simplifying.
The 11s cancel each other, leaving 618, which simplifies to 13 when you divide both by 6.
5. 910 × 512 = 38 in simplest form.
Cross-cancel 5 and 10 (divide by 5) to get 92 × 112, then multiply: 924 simplifies to 38 by dividing both by 3.
6. 815 × 56 = 49 in simplest form.
Cross-cancel 5 and 15 (divide by 5) and 8 and 6 (divide by 2), giving 43 × 13 = 49.
7. Cross-cancellation works because dividing a numerator and a denominator by the same number does not change the value.
Dividing a numerator and a denominator by the same factor is like dividing by 1, so the overall value of the product stays the same.
8. 314 × 79 = 16 in simplest form.
Cross-cancel 7 and 14 (divide by 7) and 3 and 9 (divide by 3), leaving 12 × 13 = 16.
9. 1021 × 715 = 29 in simplest form.
Cross-cancel 7 and 21 (divide by 7) and 10 and 15 (divide by 5), leaving 23 × 13 = 29.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
310 × 59
→ 16
110
89 × 34
→ 23
112
512 × 625
→ 110
23
29 × 38
→ 112
16
Correct matches: 310 × 59 → 16; 89 × 34 → 23; 512 × 625 → 110; 29 × 38 → 112.