Math worksheet answer key for adding and subtracting mixed fractions, with solutions in lowest terms.

Let’s solve each problem step by step. We’ll convert mixed numbers to improper fractions, do the addition or subtraction, then simplify and convert back to a mixed number if needed.

---

Problem 1: 1 89 − 12⁄3

Convert to improper fractions:
- 1 8⁄9 = (9×1 + 8)/9 = 17⁄9
- 1 2⁄3 = (3×1 + 2)/3 = 5⁄3 → convert to ninths: 5⁄3 = 15⁄9

Now subtract:
17⁄9 − 15⁄9 = 2⁄9 ✔

---

Problem 2: 1 3⁄5 + 1 1⁄3

Convert:
- 1 3⁄5 = 8⁄5
- 1 1⁄3 = 4⁄3

Find common denominator (LCM of 5 and 3 is 15):
- 8⁄5 = 24⁄15
- 4⁄3 = 20⁄15

Add: 24⁄15 + 20⁄15 = 44⁄15
Convert to mixed: 44 ÷ 15 = 2 with remainder 14 → 2 1415 ✔

---

Problem 3: 4 3⁄5 − 2 4⁄7

Convert:
- 4 3⁄5 = 23⁄5
- 2 4⁄7 = 18⁄7

Common denominator (LCM of 5 and 7 is 35):
- 23⁄5 = 161⁄35
- 18⁄7 = 90⁄35

Subtract: 161⁄35 − 90⁄35 = 71⁄35
Convert: 71 ÷ 35 = 2 with remainder 1 → 2 1⁄35 ✔

---

Problem 4: 1 1⁄2 + 1 1⁄3

Convert:
- 1 1⁄2 = 3⁄2
- 1 1⁄3 = 4⁄3

Common denominator (6):
- 3⁄2 = 9⁄6
- 4⁄3 = 8⁄6

Add: 9⁄6 + 8⁄6 = 17⁄6
Convert: 17 ÷ 6 = 2 with remainder 5 → 2 5⁄6 ✔

---

Problem 5: 8 1⁄2 − 3 1⁄2

Same denominators — easy!
8 1⁄2 − 3 1⁄2 = (8−3) + (1⁄2−1⁄2) = 5 + 0 = 5 ✔

---

Problem 6: 5 3⁄4 − 1 2⁄3

Convert:
- 5 3⁄4 = 23⁄4
- 1 2⁄3 = 5⁄3

Common denominator (12):
- 23⁄4 = 69⁄12
- 5⁄3 = 20⁄12

Subtract: 69⁄12 − 20⁄12 = 49⁄12
Convert: 49 ÷ 12 = 4 with remainder 1 → 4 1⁄12 ✔

---

Problem 7: 3 1⁄2 + 1 1⁄8

Convert:
- 3 1⁄2 = 7⁄2
- 1 1⁄8 = 9⁄8

Common denominator (8):
- 7⁄2 = 28⁄8
- 9⁄8 stays same

Add: 28⁄8 + 9⁄8 = 37⁄8
Convert: 37 ÷ 8 = 4 with remainder 5 → 4 5⁄8 ✔

---

Problem 8: 2 1⁄11 + 1 1⁄2

Convert:
- 2 1⁄11 = 23⁄11
- 1 1⁄2 = 3⁄2

Common denominator (22):
- 23⁄11 = 46⁄22
- 3⁄2 = 33⁄22

Add: 46⁄22 + 33⁄22 = 79⁄22
Convert: 79 ÷ 22 = 3 with remainder 13 → 3 1322 ✔

---

Problem 9: 2 1⁄5 + 1 4⁄5

Same denominator:
2 1⁄5 + 1 4⁄5 = (2+1) + (1⁄5 + 4⁄5) = 3 + 5⁄5 = 3 + 1 = 4 ✔

---

Problem 10: 4 1⁄2 − 1 8⁄9

Convert:
- 4 1⁄2 = 9⁄2
- 1 8⁄9 = 17⁄9

Common denominator (18):
- 9⁄2 = 81⁄18
- 17⁄9 = 34⁄18

Subtract: 81⁄18 − 34⁄18 = 47⁄18
Convert: 47 ÷ 18 = 2 with remainder 11 → 2 11⁄18 ✔

---

Problem 11: 1 5⁄6 + 1 1⁄3

Convert:
- 1 5⁄6 = 11⁄6
- 1 1⁄3 = 4⁄3 = 8⁄6

Add: 11⁄6 + 8⁄6 = 19⁄6
Convert: 19 ÷ 6 = 3 with remainder 1 → 3 1⁄6 ✔

---

Problem 12: 1 6⁄7 − 1 1⁄2

Convert:
- 1 6⁄7 = 13⁄7
- 1 1⁄2 = 3⁄2

Common denominator (14):
- 13⁄7 = 26⁄14
- 3⁄2 = 21⁄14

Subtract: 26⁄14 − 21⁄14 = 5⁄14 ✔

---

Final Answer:

1. 2⁄9
2. 2 1415
3. 2 1⁄35
4. 2 5⁄6
5. 5
6. 4 1⁄12
7. 4 5⁄8
8. 3 1322
9. 4
10. 2 11⁄18
11. 3 1⁄6
12. 5⁄14