Math worksheet for practicing adding and subtracting fractions with unlike denominators.

Let’s solve each problem step by step. We’re adding and subtracting fractions with unlike denominators. That means the bottom numbers (denominators) are different, so we need to find a common denominator first — usually the least common multiple (LCM) of the two denominators.

We’ll go one by one:

---

1. 4/3 + 2/5

Denominators: 3 and 5 → LCM = 15
Convert:
4/3 = (4×5)/(3×5) = 20/15
2/5 = (2×3)/(5×3) = 6/15
Add: 20/15 + 6/15 = 26/15 → can’t simplify further → 26/15

---

2. 7/10 - 2/5

Denominators: 10 and 5 → LCM = 10
Convert:
7/10 stays same
2/5 = (2×2)/(5×2) = 4/10
Subtract: 7/10 - 4/10 = 3/10 → 3/10

---

3. 5/9 + 2/7

Denominators: 9 and 7 → LCM = 63
Convert:
5/9 = (5×7)/(9×7) = 35/63
2/7 = (2×9)/(7×9) = 18/63
Add: 35/63 + 18/63 = 53/63 → 53/63

---

4. 4/8 - 1/4

First, simplify 4/8 = 1/2
Now: 1/2 - 1/4
Denominators: 2 and 4 → LCM = 4
1/2 = 2/4
2/4 - 1/4 = 1/4 → 1/4

*(Alternatively, without simplifying first: 4/8 - 1/4 → LCM=8 → 4/8 - 2/8 = 2/8 = 1/4)*

---

5. 3/9 + 1/3

Simplify 3/9 = 1/3
So: 1/3 + 1/3 = 2/3 → 2/3

*(Or: 3/9 + 1/3 → LCM=9 → 3/9 + 3/9 = 6/9 = 2/3)*

---

6. 2/5 + 1/10

Denominators: 5 and 10 → LCM = 10
2/5 = 4/10
4/10 + 1/10 = 5/10 = 1/2 → 1/2

---

7. 4/5 + 9/10

Denominators: 5 and 10 → LCM = 10
4/5 = 8/10
8/10 + 9/10 = 17/10 → 17/10

---

8. 4/6 - 1/3

Simplify 4/6 = 2/3
2/3 - 1/3 = 1/3 → 1/3

*(Or: 4/6 - 1/3 → LCM=6 → 4/6 - 2/6 = 2/6 = 1/3)*

---

9. 3/12 + 2/4

Simplify: 3/12 = 1/4; 2/4 = 1/2
Now: 1/4 + 1/2 → LCM=4 → 1/4 + 2/4 = 3/4 → 3/4

*(Or: 3/12 + 2/4 → LCM=12 → 3/12 + 6/12 = 9/12 = 3/4)*

---

10. 5/12 - 1/6

Denominators: 12 and 6 → LCM = 12
1/6 = 2/12
5/12 - 2/12 = 3/12 = 1/4 → 1/4

---

11. 2/8 + 3/9

Simplify: 2/8 = 1/4; 3/9 = 1/3
Now: 1/4 + 1/3 → LCM=12
1/4 = 3/12; 1/3 = 4/12 → 3/12 + 4/12 = 7/12 → 7/12

*(Or: 2/8 + 3/9 → LCM=72? Too big. Better to simplify first. Or use LCM of 8 and 9 = 72:
2/8 = 18/72; 3/9 = 24/72 → 42/72 = 7/12 — same answer)*

---

12. 1/4 - 1/8

Denominators: 4 and 8 → LCM = 8
1/4 = 2/8
2/8 - 1/8 = 1/8 → 1/8

---

13. 6/7 + 2/6

Simplify 2/6 = 1/3
Now: 6/7 + 1/3 → LCM=21
6/7 = 18/21; 1/3 = 7/21 → 18/21 + 7/21 = 25/21 → 25/21

*(Or: 6/7 + 2/6 → LCM=42 → 36/42 + 14/42 = 50/42 = 25/21 — same)*

---

14. 1/3 - 1/7

Denominators: 3 and 7 → LCM = 21
1/3 = 7/21; 1/7 = 3/21
7/21 - 3/21 = 4/21 → 4/21

---

15. 7/8 + 4/5

Denominators: 8 and 5 → LCM = 40
7/8 = 35/40; 4/5 = 32/40
35/40 + 32/40 = 67/40 → 67/40

---

Final Answer:
1. 26/15
2. 3/10
3. 53/63
4. 1/4
5. 2/3
6. 1/2
7. 17/10
8. 1/3
9. 3/4
10. 1/4
11. 7/12
12. 1/8
13. 25/21
14. 4/21
15. 67/40