Adding Subtracting Multiplying and Dividing Fractions Worksheets ... - Free Printable

Here is the step-by-step solution to all 12 fraction problems on the worksheet. Each problem involves adding, subtracting, multiplying, or dividing fractions. I’ll show the work and simplify each answer to lowest terms.

---

Problem 1:

$\frac{17}{3} + \frac{3}{17}$

- Find LCD of 3 and 17 → $3 \times 17 = 51$
- Convert:
- $\frac{17}{3} = \frac{17 \times 17}{3 \times 17} = \frac{289}{51}$
- $\frac{3}{17} = \frac{3 \times 3}{17 \times 3} = \frac{9}{51}$
- Add: $\frac{289 + 9}{51} = \frac{298}{51}$
- Simplify? 298 and 51 have no common factors → $\boxed{\frac{298}{51}}$ (or mixed number: $5\frac{43}{51}$)

---

Problem 2:

$\frac{7}{2} + \frac{11}{13}$

- LCD of 2 and 13 → 26
- Convert:
- $\frac{7}{2} = \frac{7 \times 13}{2 \times 13} = \frac{91}{26}$
- $\frac{11}{13} = \frac{11 \times 2}{13 \times 2} = \frac{22}{26}$
- Add: $\frac{91 + 22}{26} = \frac{113}{26}$
- Simplify? 113 is prime, doesn’t divide 26 → $\boxed{\frac{113}{26}}$ (or $4\frac{9}{26}$)

---

Problem 3:

$\frac{3}{2} + \frac{20}{3}$

- LCD of 2 and 3 → 6
- Convert:
- $\frac{3}{2} = \frac{9}{6}$
- $\frac{20}{3} = \frac{40}{6}$
- Add: $\frac{9 + 40}{6} = \frac{49}{6}$
- Simplify? No → $\boxed{\frac{49}{6}}$ (or $8\frac{1}{6}$)

---

Problem 4:

$\frac{13}{14} - \frac{12}{22}$

- First, simplify $\frac{12}{22} = \frac{6}{11}$
- Now: $\frac{13}{14} - \frac{6}{11}$
- LCD of 14 and 11 → 154
- Convert:
- $\frac{13}{14} = \frac{13 \times 11}{14 \times 11} = \frac{143}{154}$
- $\frac{6}{11} = \frac{6 \times 14}{11 \times 14} = \frac{84}{154}$
- Subtract: $\frac{143 - 84}{154} = \frac{59}{154}$
- Simplify? 59 is prime, doesn’t divide 154 → $\boxed{\frac{59}{154}}$

---

Problem 5:

$\frac{9}{10} - \frac{3}{15}$

- Simplify $\frac{3}{15} = \frac{1}{5}$
- Now: $\frac{9}{10} - \frac{1}{5}$
- LCD of 10 and 5 → 10
- Convert: $\frac{1}{5} = \frac{2}{10}$
- Subtract: $\frac{9 - 2}{10} = \frac{7}{10}$
- Already simplified → $\boxed{\frac{7}{10}}$

---

Problem 6:

$\frac{18}{19} - \frac{5}{6}$

- LCD of 19 and 6 → 114
- Convert:
- $\frac{18}{19} = \frac{18 \times 6}{19 \times 6} = \frac{108}{114}$
- $\frac{5}{6} = \frac{5 \times 19}{6 \times 19} = \frac{95}{114}$
- Subtract: $\frac{108 - 95}{114} = \frac{13}{114}$
- Simplify? 13 is prime, doesn’t divide 114 → $\boxed{\frac{13}{114}}$

---

Problem 7:

$\frac{12}{15} \times \frac{6}{20}$

- Simplify first:
- $\frac{12}{15} = \frac{4}{5}$
- $\frac{6}{20} = \frac{3}{10}$
- Multiply: $\frac{4}{5} \times \frac{3}{10} = \frac{12}{50}$
- Simplify: $\frac{12}{50} = \frac{6}{25}$
→ $\boxed{\frac{6}{25}}$

*(Alternative: multiply first: $\frac{12 \times 6}{15 \times 20} = \frac{72}{300} = \frac{6}{25}$)*

---

Problem 8:

$\frac{23}{18} \times \frac{16}{21}$

- Multiply numerators and denominators:
- $\frac{23 \times 16}{18 \times 21} = \frac{368}{378}$
- Simplify:
- Divide numerator and denominator by 2: $\frac{184}{189}$
- Check for more simplification: 184 and 189 — GCF is 1 → $\boxed{\frac{184}{189}}$

---

Problem 9:

$\frac{9}{14} \times \frac{22}{24}$

- Simplify $\frac{22}{24} = \frac{11}{12}$
- Now: $\frac{9}{14} \times \frac{11}{12} = \frac{99}{168}$
- Simplify: divide numerator and denominator by 3 → $\frac{33}{56}$
→ $\boxed{\frac{33}{56}}$

---

Problem 10:

$\frac{26}{52} \div \frac{12}{13}$

- Simplify $\frac{26}{52} = \frac{1}{2}$
- Dividing fractions: multiply by reciprocal → $\frac{1}{2} \times \frac{13}{12} = \frac{13}{24}$
→ $\boxed{\frac{13}{24}}$

---

Problem 11:

$\frac{5}{96} \div \frac{3}{64}$

- Multiply by reciprocal: $\frac{5}{96} \times \frac{64}{3}$
- Simplify before multiplying:
- 64 and 96 → both divisible by 32: $64 ÷ 32 = 2$, $96 ÷ 32 = 3$
- So: $\frac{5}{3} \times \frac{2}{3} = \frac{10}{9}$
→ $\boxed{\frac{10}{9}}$ (or $1\frac{1}{9}$)

---

Problem 12:

$\frac{27}{21} \div \frac{44}{14}$

- Simplify both fractions:
- $\frac{27}{21} = \frac{9}{7}$
- $\frac{44}{14} = \frac{22}{7}$
- Now: $\frac{9}{7} \div \frac{22}{7} = \frac{9}{7} \times \frac{7}{22}$
- Cancel 7s: $\frac{9}{1} \times \frac{1}{22} = \frac{9}{22}$
→ $\boxed{\frac{9}{22}}$

---

## ✔ Final Answers:

1. $\boxed{\frac{298}{51}}$
2. $\boxed{\frac{113}{26}}$
3. $\boxed{\frac{49}{6}}$
4. $\boxed{\frac{59}{154}}$
5. $\boxed{\frac{7}{10}}$
6. $\boxed{\frac{13}{114}}$
7. $\boxed{\frac{6}{25}}$
8. $\boxed{\frac{184}{189}}$
9. $\boxed{\frac{33}{56}}$
10. $\boxed{\frac{13}{24}}$
11. $\boxed{\frac{10}{9}}$
12. $\boxed{\frac{9}{22}}$

Let me know if you’d like these as mixed numbers or decimals too!