Grade 6 Equivalent Fractions Worksheets | Math Worksheets - Free Printable

Let’s solve each problem step by step.

We are dividing mixed numbers. To do that:

1. Convert each mixed number to an improper fraction.
2. Flip the second fraction (that’s the divisor — this is called “taking the reciprocal”).
3. Multiply the two fractions.
4. Simplify the result, and if needed, convert back to a mixed number.

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Problem 1: 3 1/3 ÷ 1 4/5

Step 1: Convert to improper fractions.

3 1/3 = (3×3 + 1)/3 = 10/3
1 4/5 = (1×5 + 4)/5 = 9/5

Step 2: Flip the second fraction → 9/5 becomes 5/9

Step 3: Multiply: 10/3 × 5/9 = (10×5)/(3×9) = 50/27

Step 4: Convert to mixed number: 50 ÷ 27 = 1 with remainder 23 → 1 23/27

✔ Answer: 1 23/27

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Problem 2: 1 1/5 ÷ 1 4/6

Step 1: Convert.

1 1/5 = (1×5 + 1)/5 = 6/5
1 4/6 = (1×6 + 4)/6 = 10/6 → simplify to 5/3 (divide numerator and denominator by 2)

Wait — let’s keep it as 10/6 for now to avoid confusion, but we’ll simplify later.

Actually, better to simplify first: 1 4/6 = 1 2/3 = (1×3 + 2)/3 = 5/3

So: 6/5 ÷ 5/3

Step 2: Flip second → 5/3 becomes 3/5

Step 3: Multiply: 6/5 × 3/5 = 18/25

Already simplified.

✔ Answer: 18/25

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Problem 3: 4 1/4 ÷ 3 1/2

Step 1: Convert.

4 1/4 = (4×4 + 1)/4 = 17/4
3 1/2 = (3×2 + 1)/2 = 7/2

Step 2: Flip second → 7/2 becomes 2/7

Step 3: Multiply: 17/4 × 2/7 = (17×2)/(4×7) = 34/28

Simplify: divide numerator and denominator by 2 → 17/14

Convert to mixed: 17 ÷ 14 = 1 R3 → 1 3/14

✔ Answer: 1 3/14

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Problem 4: 6 1/2 ÷ 1 1/8

Step 1: Convert.

6 1/2 = (6×2 + 1)/2 = 13/2
1 1/8 = (1×8 + 1)/8 = 9/8

Step 2: Flip second → 9/8 becomes 8/9

Step 3: Multiply: 13/2 × 8/9 = (13×8)/(2×9) = 104/18

Simplify: divide numerator and denominator by 2 → 52/9

Convert to mixed: 52 ÷ 9 = 5 R7 → 5 7/9

✔ Answer: 5 7/9

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Problem 5: 5 1/8 ÷ 1 1/4

Step 1: Convert.

5 1/8 = (5×8 + 1)/8 = 41/8
1 1/4 = (1×4 + 1)/4 = 5/4

Step 2: Flip second → 5/4 becomes 4/5

Step 3: Multiply: 41/8 × 4/5 = (41×4)/(8×5) = 164/40

Simplify: divide numerator and denominator by 4 → 41/10

Convert to mixed: 41 ÷ 10 = 4 R1 → 4 1/10

✔ Answer: 4 1/10

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Problem 6: 1 3/8 ÷ 2 1/4

Step 1: Convert.

1 3/8 = (1×8 + 3)/8 = 11/8
2 1/4 = (2×4 + 1)/4 = 9/4

Step 2: Flip second → 9/4 becomes 4/9

Step 3: Multiply: 11/8 × 4/9 = (11×4)/(8×9) = 44/72

Simplify: divide by 4 → 11/18

✔ Answer: 11/18

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Problem 7: 3 1/5 ÷ 1 3/12

Step 1: Convert.

3 1/5 = (3×5 + 1)/5 = 16/5
1 3/12 = simplify 3/12 to 1/4 → so 1 1/4 = (1×4 + 1)/4 = 5/4

Step 2: Flip second → 5/4 becomes 4/5

Step 3: Multiply: 16/5 × 4/5 = 64/25

Convert to mixed: 64 ÷ 25 = 2 R14 → 2 14/25

✔ Answer: 2 14/25

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Problem 8: 4 1/3 ÷ 2 1/2

Step 1: Convert.

4 1/3 = (4×3 + 1)/3 = 13/3
2 1/2 = (2×2 + 1)/2 = 5/2

Step 2: Flip second → 5/2 becomes 2/5

Step 3: Multiply: 13/3 × 2/5 = 26/15

Convert to mixed: 26 ÷ 15 = 1 R11 → 1 11/15

✔ Answer: 1 11/15

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Problem 9: 1 3/6 ÷ 2 4/7

Step 1: Convert.

1 3/6 = simplify 3/6 to 1/2 → so 1 1/2 = (1×2 + 1)/2 = 3/2
2 4/7 = (2×7 + 4)/7 = 18/7

Step 2: Flip second → 18/7 becomes 7/18

Step 3: Multiply: 3/2 × 7/18 = (3×7)/(2×18) = 21/36

Simplify: divide by 3 → 7/12

✔ Answer: 7/12

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Problem 10: 3 3/4 ÷ 4 1/10

Step 1: Convert.

3 3/4 = (3×4 + 3)/4 = 15/4
4 1/10 = (4×10 + 1)/10 = 41/10

Step 2: Flip second → 41/10 becomes 10/41

Step 3: Multiply: 15/4 × 10/41 = (15×10)/(4×41) = 150/164

Simplify: divide by 2 → 75/82

Already simplified.

✔ Answer: 75/82

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Final Answers:

1. 1 23/27
2. 18/25
3. 1 3/14
4. 5 7/9
5. 4 1/10
6. 11/18
7. 2 14/25
8. 1 11/15
9. 7/12
10. 75/82