Unit 1 Advanced Worksheet

Fraction Operations - 20 Challenging Questions

Unit 1 Advanced Worksheet

Fraction Operations

Challenge yourself with advanced fraction operations.

Question 1: What is 5/6 × 3/10?

Answer: 0

5/6 × 3/10 = 15/60 = 1/4. Or cancel first: 5 and 10 share 5, 6 and 3 share 3.

Question 2: A garden is 3/5 of an acre. 2/3 of it is planted with vegetables. What fraction is vegetables?

Answer: 6/15 or 2/5 acre

2/3 of 3/5 means 2/3 × 3/5 = 6/15 = 2/5 acre is vegetables.

Question 3: What is 7/9 ÷ 2/3? ___

Answer: 21/18 or 7/6 or 1 1/6

7/9 ÷ 2/3 = 7/9 × 3/2 = 21/18 = 7/6 = 1 1/6.

Question 4: What is 1/4 × 1/4 × 1/4?

Answer: 0

Multiply across: 1×1×1=1, 4×4×4=64, so 1/64. This is (1/4)³.

Question 5: You walk 5/8 mile. Your friend walks 4/5 of that distance. How far does your friend walk?

Answer: 20/40 or 1/2 mile

4/5 of 5/8 means 4/5 × 5/8 = 20/40 = 1/2 mile.

Question 6: What is 3 3/5 × 1 2/3? ___

Answer: 6

Convert: 3 3/5 = 18/5 and 1 2/3 = 5/3. Then 18/5 × 5/3 = 90/15 = 6.

Question 7: When multiplying three fractions, you can multiply in any order.

Answer: True

True! Multiplication is commutative and associative.

Question 8: What is 6/7 ÷ 3/14?

Answer: 0

6/7 ÷ 3/14 = 6/7 × 14/3 = 84/21 = 4. The 7 and 14 cancel (×2).

Question 9: A pitcher holds 2 1/4 liters. You pour out 3/5 of it. How much is left?

Answer: 9/10 liter

Poured: 3/5 × 9/4 = 27/20. Left: 9/4 - 27/20 = 45/20 - 27/20 = 18/20 = 9/10 liter.

Question 10: What is 7 1/2 ÷ 2 1/2? ___

Answer: 3

Convert: 7 1/2 = 15/2 and 2 1/2 = 5/2. Then 15/2 ÷ 5/2 = 15/2 × 2/5 = 30/10 = 3.

Question 11: A board is 10 1/2 feet long. You need pieces that are 1 3/4 feet each. How many complete pieces?

Answer: 6 pieces

10 1/2 ÷ 1 3/4 = 21/2 ÷ 7/4 = 21/2 × 4/7 = 84/14 = 6 complete pieces.

Question 12: What is 9/10 × 5/6?

Answer: 0

9/10 × 5/6 = 45/60 = 3/4. Simplify by dividing both by 15.

Question 13: What is 2 2/5 × 3? ___

Answer: 7 1/5

Convert: 2 2/5 = 12/5. Then 12/5 × 3 = 36/5 = 7 1/5.

Question 14: A recipe serves 6 people and uses 2 2/3 cups rice. You want to serve 9 people. How much rice?

Answer: 4 cups

9÷6 = 1.5 times recipe. So 2 2/3 × 3/2 = 8/3 × 3/2 = 24/6 = 4 cups.

Question 15: 7/8 is greater than 5/6.

Answer: True

True! Convert: 7/8 = 21/24 and 5/6 = 20/24. Since 21 > 20, 7/8 > 5/6.

Question 16: What is 1 2/3 × 2 1/4?

Answer: 0

Convert: 1 2/3 = 5/3 and 2 1/4 = 9/4. Then 5/3 × 9/4 = 45/12 = 15/4 = 3 3/4.

Question 17: You have $30. You spend 2/5 on food and 1/3 of the remainder on entertainment. How much on entertainment?

Answer: $6

Food: 2/5 × 30 = $12. Remainder: 30 - 12 = $18. Entertainment: 1/3 × 18 = $6.

Question 18: What is 5/12 × 8/15? ___

Answer: 40/180 or 2/9

5/12 × 8/15 = 40/180 = 2/9. Or cancel first: 12 and 8 share 4, 5 and 15 share 5.

Question 19: A dress needs 2 3/8 yards fabric. You have 10 yards. How many complete dresses can you make?

Answer: 4 dresses

10 ÷ 2 3/8 = 10 ÷ 19/8 = 10 × 8/19 = 80/19 = 4 4/19. You can make 4 complete dresses.

Question 20: You read 2/5 of a book on Monday and 1/3 on Tuesday. What fraction remains?

Answer: 0

Read total: 2/5 + 1/3 = 6/15 + 5/15 = 11/15. Remaining: 1 - 11/15 = 4/15.

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