Fraction Test: Mixed Operations Worksheet for 4th - 5th Grade ... - Free Printable

Let’s solve each problem step by step. We’ll go one at a time, carefully.

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1. 4/9 + 5/9 = ?
Same denominator → just add numerators:
4 + 5 = 9 → so 9/9 = 1

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2. 3/8 + 7/8 = ?
Add numerators: 3 + 7 = 10 → 10/8
Simplify: divide numerator and denominator by 2 → 5/4 or 1 1/4

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3. 6/7 + 1/7 = ?
6 + 1 = 7 → 7/7 = 1

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4. 9/10 - 1/10 = ?
Subtract numerators: 9 - 1 = 8 → 8/10
Simplify: divide by 2 → 4/5

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5. 1/3 + 1/3 = ?
1 + 1 = 2 → 2/3

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6. 6/9 + 2/9 = ?
6 + 2 = 8 → 8/9 (already simplified)

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7. 2/5 - 1/5 = ?
2 - 1 = 1 → 1/5

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8. 8/15 - 2/15 = ?
8 - 2 = 6 → 6/15
Simplify: divide by 3 → 2/5

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9. 3/4 - 1/4 = ?
3 - 1 = 2 → 2/4 → simplify to 1/2

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10. 5/6 - 1/6 = ?
5 - 1 = 4 → 4/6 → simplify to 2/3

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11. 12/13 - 1/13 = ?
12 - 1 = 11 → 11/13

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12. 3/4 × 1/5 = ?
Multiply straight across:
Numerator: 3 × 1 = 3
Denominator: 4 × 5 = 20 → 3/20

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13. 2/3 × 1/5 = ?
2 × 1 = 2
3 × 5 = 15 → 2/15

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14. 5/8 × 1/2 = ?
5 × 1 = 5
8 × 2 = 16 → 5/16

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15. 1/2 × 1/3 = ?
1 × 1 = 1
2 × 3 = 6 → 1/6

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16. 3/5 × 2/5 = ?
3 × 2 = 6
5 × 5 = 25 → 6/25

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17. 3/4 × 2/3 = ?
3 × 2 = 6
4 × 3 = 12 → 6/12 → simplify to 1/2

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18. 1/8 × 1/3 = ?
1 × 1 = 1
8 × 3 = 24 → 1/24

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Now the comparison problems — we need to compare fractions using <, >, or =

We can do this by finding common denominators or converting to decimals. Let’s use common denominators where possible.

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19. Compare 1/4 ___ 3/8

Convert 1/4 to eighths: 1/4 = 2/8
2/8 vs 3/8 → 2 < 3 → so 1/4 < 3/8

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20. Compare 2/5 ___ 2/5

They are the same → =

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21. Compare 7/8 ___ 7/9

When numerators are the same, the fraction with the smaller denominator is bigger.
8 < 9 → so 7/8 > 7/9 → >

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22. Compare 3/4 ___ 2/3

Find common denominator: 12
3/4 = 9/12
2/3 = 8/12
9 > 8 → so 3/4 > 2/3

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23. Compare 5/6 ___ 12/12

12/12 = 1
5/6 is less than 1 → so 5/6 < 12/12

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24. Compare 1/2 ___ 2/4

2/4 simplifies to 1/2 → so they are equal → =

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Final Answer:

1. 1
2. 5/4 or 1 1/4
3. 1
4. 4/5
5. 2/3
6. 8/9
7. 1/5
8. 2/5
9. 1/2
10. 2/3
11. 11/13
12. 3/20
13. 2/15
14. 5/16
15. 1/6
16. 6/25
17. 1/2
18. 1/24
19. <
20. =
21. >
22. >
23. <
24. =