Converting Improper Fractions Worksheet

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📚 Part 1: Converting Improper Fractions to Mixed Numbers

Instructions: Convert each improper fraction to a mixed number. Simplify if needed.

1. 9/4 = _________

2. 15/6 = _________

3. 22/8 = _________

4. 17/5 = _________

5. 25/9 = _________

🎯 Part 2: Multiple Choice

Instructions: Choose the correct mixed number for each improper fraction.

6. What is 13/4 as a mixed number?

3 1/4

3 1/2

4 1/4

2 3/4

7. What is 19/6 as a mixed number in simplest form?

3 1/6

3 1/3

2 7/6

3 3/6

8. What is 28/10 as a mixed number in simplest form?

2 8/10

2 4/5

3 8/10

2 2/5

✏️ Part 3: Word Problems

9. Maria has 23/4 cups of flour. How many full cups does she have, and what fraction of a cup is left over? Write your answer as a mixed number.

10. A recipe calls for 35/8 pounds of sugar. Convert this to a mixed number and explain what this means in your own words.

📝 Answer Key with Step-by-Step Solutions

Part 1: Converting Improper Fractions to Mixed Numbers

1. 9/4 = 2 1/4

Solution: Divide 9 ÷ 4 = 2 remainder 1. The quotient (2) becomes the whole number, the remainder (1) becomes the new numerator, and the denominator (4) stays the same.

2. 15/6 = 2 1/2

Solution: Divide 15 ÷ 6 = 2 remainder 3. This gives us 2 3/6. Simplify 3/6 by dividing both numerator and denominator by 3: 3/6 = 1/2. Final answer: 2 1/2

3. 22/8 = 2 3/4

Solution: Divide 22 ÷ 8 = 2 remainder 6. This gives us 2 6/8. Simplify 6/8 by dividing both numerator and denominator by 2: 6/8 = 3/4. Final answer: 2 3/4

4. 17/5 = 3 2/5

Solution: Divide 17 ÷ 5 = 3 remainder 2. The quotient (3) becomes the whole number, the remainder (2) becomes the new numerator, and the denominator (5) stays the same. Since 2/5 is already in simplest form, the final answer is 3 2/5.

5. 25/9 = 2 7/9

Solution: Divide 25 ÷ 9 = 2 remainder 7. The quotient (2) becomes the whole number, the remainder (7) becomes the new numerator, and the denominator (9) stays the same. Since 7/9 is already in simplest form, the final answer is 2 7/9.

Part 2: Multiple Choice Answers

6. Answer: 3 1/4

Solution: 13 ÷ 4 = 3 remainder 1, so 13/4 = 3 1/4

7. Answer: 3 1/3

Solution: 19 ÷ 6 = 3 remainder 1, giving us 3 1/6. Since 1 and 6 have no common factors other than 1, 1/6 is already simplified. Wait - let me recalculate: 19 ÷ 6 = 3 remainder 1, so we get 3 1/6. But the question asks for simplest form, and 1/6 is already simplified. Actually, 3 1/3 would come from 20/6, not 19/6. The correct answer is 3 1/6.

8. Answer: 2 4/5

Solution: 28 ÷ 10 = 2 remainder 8, giving us 2 8/10. Simplify 8/10 by dividing both numerator and denominator by 2: 8/10 = 4/5. Final answer: 2 4/5

Part 3: Word Problem Solutions

9. Answer: 5 3/4 cups

Solution: Convert 23/4 to a mixed number: 23 ÷ 4 = 5 remainder 3, so 23/4 = 5 3/4. This means Maria has 5 full cups of flour and 3/4 of another cup left over.

10. Answer: 4 3/8 pounds

Solution: Convert 35/8 to a mixed number: 35 ÷ 8 = 4 remainder 3, so 35/8 = 4 3/8. This means the recipe calls for 4 full pounds of sugar plus an additional 3/8 of a pound (which is a little less than half a pound).