Math worksheet for adding and subtracting fractions with problems and instructions.

Sure! Let’s solve each of the 8 fraction problems step by step. Remember the key rules:

- To add or subtract fractions, you need a common denominator.
- After calculating, simplify the result if possible.
- If the numerator is larger than the denominator, convert to a mixed number.

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Problem 1:

> \(\frac{5}{7} + \frac{3}{4}\)

Step 1: Find the least common denominator (LCD) of 7 and 4 → 28

Step 2: Convert fractions:
- \(\frac{5}{7} = \frac{5 \times 4}{7 \times 4} = \frac{20}{28}\)
- \(\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}\)

Step 3: Add:
\(\frac{20}{28} + \frac{21}{28} = \frac{41}{28}\)

Step 4: Simplify → Already in simplest form. Convert to mixed number:
\(\frac{41}{28} = 1 \frac{13}{28}\)

✔ Answer: \(1 \frac{13}{28}\)

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Problem 2:

> \(\frac{2}{3} - \frac{4}{11}\)

Step 1: LCD of 3 and 11 → 33

Step 2: Convert:
- \(\frac{2}{3} = \frac{22}{33}\)
- \(\frac{4}{11} = \frac{12}{33}\)

Step 3: Subtract:
\(\frac{22}{33} - \frac{12}{33} = \frac{10}{33}\)

Step 4: Simplify → GCD of 10 and 33 is 1 → already simplified.

✔ Answer: \(\frac{10}{33}\)

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Problem 3:

> \(\frac{5}{8} + \frac{6}{7}\)

Step 1: LCD of 8 and 7 → 56

Step 2: Convert:
- \(\frac{5}{8} = \frac{35}{56}\)
- \(\frac{6}{7} = \frac{48}{56}\)

Step 3: Add:
\(\frac{35}{56} + \frac{48}{56} = \frac{83}{56}\)

Step 4: Convert to mixed number:
\(\frac{83}{56} = 1 \frac{27}{56}\)

✔ Answer: \(1 \frac{27}{56}\)

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Problem 4:

> \(\frac{13}{15} - \frac{3}{4}\)

Step 1: LCD of 15 and 4 → 60

Step 2: Convert:
- \(\frac{13}{15} = \frac{52}{60}\)
- \(\frac{3}{4} = \frac{45}{60}\)

Step 3: Subtract:
\(\frac{52}{60} - \frac{45}{60} = \frac{7}{60}\)

Step 4: Already simplified.

✔ Answer: \(\frac{7}{60}\)

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Problem 5:

> \(\frac{5}{12} + \frac{9}{18}\)

Step 1: Simplify \(\frac{9}{18} = \frac{1}{2}\)

Now we have: \(\frac{5}{12} + \frac{1}{2}\)

Step 2: LCD of 12 and 2 → 12

Convert \(\frac{1}{2} = \frac{6}{12}\)

Step 3: Add:
\(\frac{5}{12} + \frac{6}{12} = \frac{11}{12}\)

✔ Answer: \(\frac{11}{12}\)

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Problem 6:

> \(\frac{9}{12} - \frac{3}{16}\)

Step 1: Simplify \(\frac{9}{12} = \frac{3}{4}\)

Now: \(\frac{3}{4} - \frac{3}{16}\)

Step 2: LCD of 4 and 16 → 16

Convert \(\frac{3}{4} = \frac{12}{16}\)

Step 3: Subtract:
\(\frac{12}{16} - \frac{3}{16} = \frac{9}{16}\)

✔ Answer: \(\frac{9}{16}\)

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Problem 7:

> \(\frac{1}{4} + \frac{3}{5} + \frac{3}{10}\)

Step 1: Find LCD of 4, 5, and 10 → 20

Step 2: Convert:
- \(\frac{1}{4} = \frac{5}{20}\)
- \(\frac{3}{5} = \frac{12}{20}\)
- \(\frac{3}{10} = \frac{6}{20}\)

Step 3: Add:
\(\frac{5}{20} + \frac{12}{20} + \frac{6}{20} = \frac{23}{20}\)

Step 4: Convert to mixed number:
\(\frac{23}{20} = 1 \frac{3}{20}\)

✔ Answer: \(1 \frac{3}{20}\)

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Problem 8:

> \(\frac{13}{18} - \frac{25}{45}\)

Step 1: Simplify \(\frac{25}{45} = \frac{5}{9}\)

Now: \(\frac{13}{18} - \frac{5}{9}\)

Step 2: LCD of 18 and 9 → 18

Convert \(\frac{5}{9} = \frac{10}{18}\)

Step 3: Subtract:
\(\frac{13}{18} - \frac{10}{18} = \frac{3}{18}\)

Step 4: Simplify:
\(\frac{3}{18} = \frac{1}{6}\)

✔ Answer: \(\frac{1}{6}\)

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## ✔ Final Answers:

1. \(1 \frac{13}{28}\)
2. \(\frac{10}{33}\)
3. \(1 \frac{27}{56}\)
4. \(\frac{7}{60}\)
5. \(\frac{11}{12}\)
6. \(\frac{9}{16}\)
7. \(1 \frac{3}{20}\)
8. \(\frac{1}{6}\)

Let me know if you’d like a printable version or further explanation on any step! 🐶📚