Comprehensive math worksheet featuring 12 problems on adding and subtracting fractions, complete with an answer key on the right side.

You’ve uploaded a worksheet titled “Adding & Subtracting Fractions” with 12 problems and an answer key on the right. The goal is to solve each problem correctly and explain the solution process, even though the worksheet already shows answers (some of which are incorrect or incomplete).

Let’s go through each problem one by one, solve it properly, and explain the steps — including finding common denominators, converting mixed numbers to improper fractions, adding/subtracting, simplifying, and converting back to mixed numbers if needed.

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🔢 Problem 1:

$\frac{1}{2} + \frac{4}{5}$

✔ Step-by-step:
- Find LCD of 2 and 5 → 10
- Convert: $\frac{1}{2} = \frac{5}{10}, \quad \frac{4}{5} = \frac{8}{10}$
- Add: $\frac{5}{10} + \frac{8}{10} = \frac{13}{10}$
- Convert to mixed number: $1\frac{3}{10}$

✔ Answer: $\boxed{1\frac{3}{10}}$ ✔️ (Matches answer key)

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🔢 Problem 2:

$\frac{23}{6} + 3\frac{3}{10}$

✔ Step-by-step:
- Convert mixed number: $3\frac{3}{10} = \frac{33}{10}$
- LCD of 6 and 10 → 30
- Convert: $\frac{23}{6} = \frac{115}{30}, \quad \frac{33}{10} = \frac{99}{30}$
- Add: $\frac{115 + 99}{30} = \frac{214}{30}$
- Simplify: Divide numerator and denominator by 2 → $\frac{107}{15}$
- Convert to mixed number: $7\frac{2}{15}$

✔ Answer: $\boxed{7\frac{2}{15}}$ ✔️ (Answer key says $7\frac{4}{30}$ — that’s not simplified! Correct simplified form is $7\frac{2}{15}$)

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🔢 Problem 3:

$\frac{20}{8} - \frac{12}{10}$

✔ Step-by-step:
- Simplify fractions first:
- $\frac{20}{8} = \frac{5}{2}$
- $\frac{12}{10} = \frac{6}{5}$
- LCD of 2 and 5 → 10
- Convert: $\frac{5}{2} = \frac{25}{10}, \quad \frac{6}{5} = \frac{12}{10}$
- Subtract: $\frac{25 - 12}{10} = \frac{13}{10} = 1\frac{3}{10}$

✔ Answer: $\boxed{1\frac{3}{10}}$ ✔️ (Answer key says $1\frac{12}{40}$ — that’s equivalent but not simplified! $1\frac{3}{10}$ is correct.)

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🔢 Problem 4:

$1\frac{7}{10} + \frac{7}{4}$

✔ Step-by-step:
- Convert mixed number: $1\frac{7}{10} = \frac{17}{10}$
- LCD of 10 and 4 → 20
- Convert: $\frac{17}{10} = \frac{34}{20}, \quad \frac{7}{4} = \frac{35}{20}$
- Add: $\frac{34 + 35}{20} = \frac{69}{20}$
- Convert to mixed number: $3\frac{9}{20}$

✔ Answer: $\boxed{3\frac{9}{20}}$ ✔️ (Matches answer key)

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🔢 Problem 5:

$1\frac{1}{4} - \frac{12}{10}$

✔ Step-by-step:
- Convert mixed number: $1\frac{1}{4} = \frac{5}{4}$
- Simplify $\frac{12}{10} = \frac{6}{5}$
- LCD of 4 and 5 → 20
- Convert: $\frac{5}{4} = \frac{25}{20}, \quad \frac{6}{5} = \frac{24}{20}$
- Subtract: $\frac{25 - 24}{20} = \frac{1}{20}$

✔ Answer: $\boxed{\frac{1}{20}}$ ✔️ (Matches answer key)

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🔢 Problem 6:

$\frac{8}{5} + \frac{19}{12}$

✔ Step-by-step:
- LCD of 5 and 12 → 60
- Convert: $\frac{8}{5} = \frac{96}{60}, \quad \frac{19}{12} = \frac{95}{60}$
- Add: $\frac{96 + 95}{60} = \frac{191}{60}$
- Convert to mixed number: $3\frac{11}{60}$

✔ Answer: $\boxed{3\frac{11}{60}}$ ✔️ (Matches answer key)

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🔢 Problem 7:

$1\frac{3}{8} - 1\frac{1}{10}$

✔ Step-by-step:
- Convert both to improper fractions:
- $1\frac{3}{8} = \frac{11}{8}$
- $1\frac{1}{10} = \frac{11}{10}$
- LCD of 8 and 10 → 40
- Convert: $\frac{11}{8} = \frac{55}{40}, \quad \frac{11}{10} = \frac{44}{40}$
- Subtract: $\frac{55 - 44}{40} = \frac{11}{40}$

✔ Answer: $\boxed{\frac{11}{40}}$ ✔️ (Matches answer key)

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🔢 Problem 8:

$\frac{8}{5} + \frac{11}{6}$

✔ Step-by-step:
- LCD of 5 and 6 → 30
- Convert: $\frac{8}{5} = \frac{48}{30}, \quad \frac{11}{6} = \frac{55}{30}$
- Add: $\frac{48 + 55}{30} = \frac{103}{30}$
- Convert to mixed number: $3\frac{13}{30}$

✔ Answer: $\boxed{3\frac{13}{30}}$ ✔️ (Matches answer key)

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🔢 Problem 9:

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

✔ Step-by-step:
- LCD of 6 and 2 → 6
- Convert: $\frac{1}{2} = \frac{3}{6}$
- Add: $\frac{1}{6} + \frac{3}{6} = \frac{4}{6} = \frac{2}{3}$

✔ Answer: $\boxed{\frac{2}{3}}$ ✔️ (Answer key says $4/6 = 2/3$ — correct!)

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🔢 Problem 10:

$3\frac{1}{2} + \frac{13}{5}$

✔ Step-by-step:
- Convert mixed number: $3\frac{1}{2} = \frac{7}{2}$
- LCD of 2 and 5 → 10
- Convert: $\frac{7}{2} = \frac{35}{10}, \quad \frac{13}{5} = \frac{26}{10}$
- Add: $\frac{35 + 26}{10} = \frac{61}{10} = 6\frac{1}{10}$

✔ Answer: $\boxed{6\frac{1}{10}}$ ✔️ (Matches answer key)

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🔢 Problem 11:

$\frac{11}{4} + 2\frac{9}{10}$

✔ Step-by-step:
- Convert mixed number: $2\frac{9}{10} = \frac{29}{10}$
- LCD of 4 and 10 → 20
- Convert: $\frac{11}{4} = \frac{55}{20}, \quad \frac{29}{10} = \frac{58}{20}$
- Add: $\frac{55 + 58}{20} = \frac{113}{20} = 5\frac{13}{20}$

✔ Answer: $\boxed{5\frac{13}{20}}$ ✔️ (Matches answer key)

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🔢 Problem 12:

$2\frac{1}{10} + 1\frac{4}{8}$

✔ Step-by-step:
- Simplify $\frac{4}{8} = \frac{1}{2}$
- Convert mixed numbers:
- $2\frac{1}{10} = \frac{21}{10}$
- $1\frac{1}{2} = \frac{3}{2}$
- LCD of 10 and 2 → 10
- Convert: $\frac{3}{2} = \frac{15}{10}$
- Add: $\frac{21 + 15}{10} = \frac{36}{10} = \frac{18}{5} = 3\frac{3}{5}$

✔ Answer: $\boxed{3\frac{3}{5}}$ ✔️ (Answer key says $3\frac{24}{40} = 3\frac{3}{5}$ — correct, but should simplify to lowest terms.)

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## ✔ Final Summary:

All problems were solved correctly. Some answers in the provided key were not fully simplified (e.g., Problem 2: $7\frac{4}{30}$ → should be $7\frac{2}{15}$; Problem 3: $1\frac{12}{40}$ → should be $1\frac{3}{10}$). Always reduce fractions to lowest terms!

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## 📌 Key Concepts Used:
- Find Least Common Denominator (LCD) to add/subtract fractions.
- Convert mixed numbers to improper fractions before operating.
- Simplify results by dividing numerator and denominator by GCF.
- Convert back to mixed numbers if needed.

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