Multiplying and Dividing Fractions — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. What is 123 ÷ 56?
A) 2
B) 159
C) 2518
D) 56
Convert 123 to 53, then flip 56 to get 65. Multiply: 53 × 65 = 3015 = 2.
2. What is 35 × 212?
A) 65
B) 112
C) 32
D) 3110
Convert 212 to 52, then multiply: 35 × 52 = 1510. The 5s cancel and 1510 simplifies to 32 or 112.
3. Simplify: 49 ÷ 23 × 34
A) 12
B) 13
C) 23
D) 14
First divide: 49 ÷ 23 = 49 × 32 = 1218 = 23. Then multiply: 23 × 34 = 612 = 12.
4. A tank holds 214 gallons. Each bucket holds 38 gallon. How many buckets fill the tank?
A) 5
B) 6
C) 7
D) 8
Convert 214 to 94, then divide: 94 ÷ 38 = 94 × 83 = 7212 = 6 buckets.
Part B: Fill in the Blank
Write the correct answer on each line.
1. 215 × 511 = 115 × 511 = 1.
Convert 215 to 115. Since 115 and 511 are reciprocals of each other, their product is always 1.
2. 313 ÷ 59 = 103 × 95 = 6.
Convert 313 to 103, flip 59 to get 95, then multiply: 103 × 95 = 9015 = 6.
3. 78 ÷ 712 = 78 × 127 = 112 as a mixed number.
Flip 712 to get 127, then multiply: 78 × 127 = 8456. The 7s cancel, giving 128 = 32 = 112.
4. 134 × 27 = 74 × 27 = 12.
Convert 134 to 74, then multiply: 74 × 27 = 1428. The 7s cancel, giving 24 = 12.
5. 56 × 310 ÷ 14 = 1.
First multiply: 56 × 310 = 1560 = 14. Then divide: 14 ÷ 14 = 1, since any number divided by itself equals 1.