Grade 5 math worksheet for adding unlike fractions.

Let's solve each problem on the "Adding Unlike Fractions" worksheet step by step. The goal is to add fractions with different denominators by finding a common denominator, converting the fractions, and then adding.

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Problem 1:

$$
\frac{1}{4} + \frac{2}{9}
$$

- Find the least common denominator (LCD) of 4 and 9 → LCM(4, 9) = 36
- Convert:
$$
\frac{1}{4} = \frac{9}{36}, \quad \frac{2}{9} = \frac{8}{36}
$$
- Add:
$$
\frac{9}{36} + \frac{8}{36} = \frac{17}{36}
$$
✔ Answer: $\boxed{\frac{17}{36}}$

---

Problem 2:

$$
\frac{8}{12} + \frac{8}{11}
$$

- LCD of 12 and 11 → 132
- Convert:
$$
\frac{8}{12} = \frac{88}{132}, \quad \frac{8}{11} = \frac{96}{132}
$$
- Add:
$$
\frac{88}{132} + \frac{96}{132} = \frac{184}{132}
$$
- Simplify:
$$
\frac{184}{132} = \frac{46}{33} = 1\frac{13}{33}
$$
✔ Answer: $\boxed{1\frac{13}{33}}$

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Problem 3:

$$
\frac{2}{7} + \frac{8}{10}
$$

- Simplify $\frac{8}{10} = \frac{4}{5}$
- LCD of 7 and 5 → 35
- Convert:
$$
\frac{2}{7} = \frac{10}{35}, \quad \frac{4}{5} = \frac{28}{35}
$$
- Add:
$$
\frac{10}{35} + \frac{28}{35} = \frac{38}{35} = 1\frac{3}{35}
$$
✔ Answer: $\boxed{1\frac{3}{35}}$

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Problem 4:

$$
\frac{1}{6} + \frac{6}{11}
$$

- LCD of 6 and 11 → 66
- Convert:
$$
\frac{1}{6} = \frac{11}{66}, \quad \frac{6}{11} = \frac{36}{66}
$$
- Add:
$$
\frac{11}{66} + \frac{36}{66} = \frac{47}{66}
$$
✔ Answer: $\boxed{\frac{47}{66}}$

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Problem 5:

$$
\frac{5}{9} + \frac{1}{3}
$$

- LCD of 9 and 3 → 9
- Convert:
$$
\frac{1}{3} = \frac{3}{9}
$$
- Add:
$$
\frac{5}{9} + \frac{3}{9} = \frac{8}{9}
$$
✔ Answer: $\boxed{\frac{8}{9}}$

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Problem 6:

$$
\frac{9}{12} + \frac{2}{12}
$$

- Same denominator → just add numerators:
$$
\frac{9+2}{12} = \frac{11}{12}
$$
✔ Answer: $\boxed{\frac{11}{12}}$

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Problem 7:

$$
\frac{7}{7} + \frac{1}{4}
$$

- $\frac{7}{7} = 1$
- So: $1 + \frac{1}{4} = 1\frac{1}{4}$
✔ Answer: $\boxed{1\frac{1}{4}}$

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Problem 8:

$$
\frac{1}{4} + \frac{6}{9}
$$

- Simplify $\frac{6}{9} = \frac{2}{3}$
- LCD of 4 and 3 → 12
- Convert:
$$
\frac{1}{4} = \frac{3}{12}, \quad \frac{2}{3} = \frac{8}{12}
$$
- Add:
$$
\frac{3}{12} + \frac{8}{12} = \frac{11}{12}
$$
✔ Answer: $\boxed{\frac{11}{12}}$

---

Problem 9:

$$
\frac{4}{10} + \frac{4}{5}
$$

- Simplify $\frac{4}{10} = \frac{2}{5}$
- Now: $\frac{2}{5} + \frac{4}{5} = \frac{6}{5} = 1\frac{1}{5}$
✔ Answer: $\boxed{1\frac{1}{5}}$

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Problem 10:

$$
\frac{1}{2} + \frac{8}{11}
$$

- LCD of 2 and 11 → 22
- Convert:
$$
\frac{1}{2} = \frac{11}{22}, \quad \frac{8}{11} = \frac{16}{22}
$$
- Add:
$$
\frac{11}{22} + \frac{16}{22} = \frac{27}{22} = 1\frac{5}{22}
$$
✔ Answer: $\boxed{1\frac{5}{22}}$

---

Problem 11:

$$
\frac{1}{11} + \frac{2}{12}
$$

- Simplify $\frac{2}{12} = \frac{1}{6}$
- LCD of 11 and 6 → 66
- Convert:
$$
\frac{1}{11} = \frac{6}{66}, \quad \frac{1}{6} = \frac{11}{66}
$$
- Add:
$$
\frac{6}{66} + \frac{11}{66} = \frac{17}{66}
$$
✔ Answer: $\boxed{\frac{17}{66}}$

---

Problem 12:

$$
\frac{2}{12} + \frac{2}{4}
$$

- Simplify:
$\frac{2}{12} = \frac{1}{6}$, $\frac{2}{4} = \frac{1}{2}$
- LCD of 6 and 2 → 6
- Convert:
$$
\frac{1}{6} + \frac{3}{6} = \frac{4}{6} = \frac{2}{3}
$$
✔ Answer: $\boxed{\frac{2}{3}}$

---

Problem 13:

$$
\frac{3}{8} + \frac{3}{8}
$$

- Same denominator:
$$
\frac{3+3}{8} = \frac{6}{8} = \frac{3}{4}
$$
✔ Answer: $\boxed{\frac{3}{4}}$

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Problem 14:

$$
\frac{6}{8} + \frac{1}{2}
$$

- Simplify $\frac{6}{8} = \frac{3}{4}$
- $\frac{1}{2} = \frac{2}{4}$
- Add:
$$
\frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1\frac{1}{4}
$$
✔ Answer: $\boxed{1\frac{1}{4}}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $\frac{17}{36}$ |
| 2 | $1\frac{13}{33}$ |
| 3 | $1\frac{3}{35}$ |
| 4 | $\frac{47}{66}$ |
| 5 | $\frac{8}{9}$ |
| 6 | $\frac{11}{12}$ |
| 7 | $1\frac{1}{4}$ |
| 8 | $\frac{11}{12}$ |
| 9 | $1\frac{1}{5}$ |
| 10 | $1\frac{5}{22}$ |
| 11 | $\frac{17}{66}$ |
| 12 | $\frac{2}{3}$ |
| 13 | $\frac{3}{4}$ |
| 14 | $1\frac{1}{4}$ |

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🔍 Key Steps Recap:

1. Find the LCD (Least Common Denominator)
2. Convert fractions to equivalent fractions with the LCD
3. Add the numerators
4. Simplify if needed (reduce or convert to mixed number)

Let me know if you'd like this as a printable PDF or want explanations for any specific step!