Adding Fractions with Unlike Denominators - Math Worksheet

To solve these problems, we need to add fractions that have different bottom numbers (denominators). The key rule is: you can only add fractions if they have the same denominator.

Here’s how we do it step by step for each problem:

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Problem 1: 3/5 + 1/10

Step 1: Find a common denominator.
The denominators are 5 and 10. The smallest number both go into is 10.

Step 2: Change 3/5 so it has denominator 10.
Multiply top and bottom by 2 → 3×2 = 6, 5×2 = 10 → 6/10

Step 3: Now add: 6/10 + 1/10 = 7/10

✔ Answer: 7/10

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Problem 2: 1/4 + 1/2

Step 1: Common denominator? 4 works (since 2 goes into 4).

Step 2: Change 1/2 to fourths → multiply top and bottom by 2 → 2/4

Step 3: Add: 1/4 + 2/4 = 3/4

✔ Answer: 3/4

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Problem 3: 2/5 + 4/15

Step 1: Denominators 5 and 15 → LCM is 15.

Step 2: Change 2/5 to fifteenths → multiply by 3 → 6/15

Step 3: Add: 6/15 + 4/15 = 10/15

Step 4: Simplify! Divide top and bottom by 5 → 2/3

✔ Answer: 2/3

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Problem 4: 3/7 + 1/14

Step 1: Denominators 7 and 14 → LCM is 14.

Step 2: Change 3/7 → multiply by 2 → 6/14

Step 3: Add: 6/14 + 1/14 = 7/14

Step 4: Simplify → divide by 7 → 1/2

✔ Answer: 1/2

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Problem 5: 2/3 + 2/9

Step 1: Denominators 3 and 9 → LCM is 9.

Step 2: Change 2/3 → multiply by 3 → 6/9

Step 3: Add: 6/9 + 2/9 = 8/9

✔ Answer: 8/9

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Problem 6: 4/5 + 3/20

Step 1: Denominators 5 and 20 → LCM is 20.

Step 2: Change 4/5 → multiply by 4 → 16/20

Step 3: Add: 16/20 + 3/20 = 19/20

✔ Answer: 19/20

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Problem 7: 1/4 + 1/8

Step 1: Denominators 4 and 8 → LCM is 8.

Step 2: Change 1/4 → multiply by 2 → 2/8

Step 3: Add: 2/8 + 1/8 = 3/8

✔ Answer: 3/8

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Problem 8: 1/9 + 1/18

Step 1: Denominators 9 and 18 → LCM is 18.

Step 2: Change 1/9 → multiply by 2 → 2/18

Step 3: Add: 2/18 + 1/18 = 3/18

Step 4: Simplify → divide by 3 → 1/6

✔ Answer: 1/6

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Problem 9: 3/4 + 1/12

Step 1: Denominators 4 and 12 → LCM is 12.

Step 2: Change 3/4 → multiply by 3 → 9/12

Step 3: Add: 9/12 + 1/12 = 10/12

Step 4: Simplify → divide by 2 → 5/6

✔ Answer: 5/6

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Problem 10: 3/6 + 1/3

Step 1: First, simplify 3/6 → that’s 1/2. But let’s keep going with original to practice.

Denominators 6 and 3 → LCM is 6.

Step 2: Change 1/3 → multiply by 2 → 2/6

Step 3: Add: 3/6 + 2/6 = 5/6

✔ Answer: 5/6

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Final Answers:

1. 7/10
2. 3/4
3. 2/3
4. 1/2
5. 8/9
6. 19/20
7. 3/8
8. 1/6
9. 5/6
10. 5/6

Final Answer:
1. 7/10
2. 3/4
3. 2/3
4. 1/2
5. 8/9
6. 19/20
7. 3/8
8. 1/6
9. 5/6
10. 5/6