Adding Mixed Fractions With Unlike Denominators - Math Practice Worksheet

Let's solve each of these mixed fraction addition problems step by step. The key is to:

1. Convert mixed numbers to improper fractions.
2. Find a common denominator for the fractions.
3. Add the fractions.
4. Convert back to a mixed number if needed.

---

Problem 1:

$$
1\frac{1}{4} + 1\frac{2}{3}
$$

Step 1: Convert to improper fractions:
- $1\frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4}$
- $1\frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}$

Step 2: Find common denominator: LCM of 4 and 3 is 12.

Convert:
- $\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}$
- $\frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12}$

Step 3: Add:
$$
\frac{15}{12} + \frac{20}{12} = \frac{35}{12}
$$

Step 4: Convert to mixed number:
$$
\frac{35}{12} = 2\frac{11}{12}
$$

✔ Answer: $2\frac{11}{12}$

---

Problem 2:

$$
2\frac{3}{8} + 1\frac{1}{2}
$$

Step 1: Convert:
- $2\frac{3}{8} = \frac{8 \times 2 + 3}{8} = \frac{19}{8}$
- $1\frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}$

Step 2: Common denominator: LCM of 8 and 2 is 8.

Convert:
- $\frac{3}{2} = \frac{3 \times 4}{2 \times 4} = \frac{12}{8}$

Step 3: Add:
$$
\frac{19}{8} + \frac{12}{8} = \frac{31}{8}
$$

Step 4: Convert:
$$
\frac{31}{8} = 3\frac{7}{8}
$$

✔ Answer: $3\frac{7}{8}$

---

Problem 3:

$$
2\frac{3}{8} + 2\frac{3}{4}
$$

Step 1: Convert:
- $2\frac{3}{8} = \frac{19}{8}$
- $2\frac{3}{4} = \frac{4 \times 2 + 3}{4} = \frac{11}{4}$

Step 2: Common denominator: LCM of 8 and 4 is 8.

Convert:
- $\frac{11}{4} = \frac{11 \times 2}{4 \times 2} = \frac{22}{8}$

Step 3: Add:
$$
\frac{19}{8} + \frac{22}{8} = \frac{41}{8}
$$

Step 4: Convert:
$$
\frac{41}{8} = 5\frac{1}{8}
$$

✔ Answer: $5\frac{1}{8}$

---

Problem 4:

$$
2\frac{3}{5} + 1\frac{2}{3}
$$

Step 1: Convert:
- $2\frac{3}{5} = \frac{5 \times 2 + 3}{5} = \frac{13}{5}$
- $1\frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3}$

Step 2: Common denominator: LCM of 5 and 3 is 15.

Convert:
- $\frac{13}{5} = \frac{13 \times 3}{5 \times 3} = \frac{39}{15}$
- $\frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15}$

Step 3: Add:
$$
\frac{39}{15} + \frac{25}{15} = \frac{64}{15}
$$

Step 4: Convert:
$$
\frac{64}{15} = 4\frac{4}{15}
$$

✔ Answer: $4\frac{4}{15}$

---

Problem 5:

$$
2\frac{2}{3} + 1\frac{3}{4}
$$

Step 1: Convert:
- $2\frac{2}{3} = \frac{3 \times 2 + 2}{3} = \frac{8}{3}$
- $1\frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}$

Step 2: Common denominator: LCM of 3 and 4 is 12.

Convert:
- $\frac{8}{3} = \frac{8 \times 4}{3 \times 4} = \frac{32}{12}$
- $\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}$

Step 3: Add:
$$
\frac{32}{12} + \frac{21}{12} = \frac{53}{12}
$$

Step 4: Convert:
$$
\frac{53}{12} = 4\frac{5}{12}
$$

✔ Answer: $4\frac{5}{12}$

---

Problem 6:

$$
1\frac{3}{7} + \frac{1}{2}
$$

Note: One is a mixed number, one is a proper fraction.

Step 1: Convert:
- $1\frac{3}{7} = \frac{7 \times 1 + 3}{7} = \frac{10}{7}$

Step 2: Common denominator: LCM of 7 and 2 is 14.

Convert:
- $\frac{10}{7} = \frac{10 \times 2}{7 \times 2} = \frac{20}{14}$
- $\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}$

Step 3: Add:
$$
\frac{20}{14} + \frac{7}{14} = \frac{27}{14}
$$

Step 4: Convert:
$$
\frac{27}{14} = 1\frac{13}{14}
$$

✔ Answer: $1\frac{13}{14}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| $1\frac{1}{4} + 1\frac{2}{3}$ | $2\frac{11}{12}$ |
| $2\frac{3}{8} + 1\frac{1}{2}$ | $3\frac{7}{8}$ |
| $2\frac{3}{8} + 2\frac{3}{4}$ | $5\frac{1}{8}$ |
| $2\frac{3}{5} + 1\frac{2}{3}$ | $4\frac{4}{15}$ |
| $2\frac{2}{3} + 1\frac{3}{4}$ | $4\frac{5}{12}$ |
| $1\frac{3}{7} + \frac{1}{2}$ | $1\frac{13}{14}$ |

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