Adding Subtracting Multiplying And Dividing Worksheet - Free Printable

Let's solve each problem step by step. The problems involve adding, subtracting, multiplying, and dividing fractions. We'll go through each one systematically.

---

Problem 1: $\frac{17}{3} + \frac{3}{17}$

To add these fractions, we need a common denominator. The least common denominator (LCD) of 3 and 17 is $3 \times 17 = 51$.

\[
\frac{17}{3} = \frac{17 \times 17}{3 \times 17} = \frac{289}{51}
\]
\[
\frac{3}{17} = \frac{3 \times 3}{17 \times 3} = \frac{9}{51}
\]

Now add the fractions:

\[
\frac{289}{51} + \frac{9}{51} = \frac{289 + 9}{51} = \frac{298}{51}
\]

So, the answer is:

\[
\boxed{\frac{298}{51}}
\]

---

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

The LCD of 2 and 13 is $2 \times 13 = 26$.

\[
\frac{7}{2} = \frac{7 \times 13}{2 \times 13} = \frac{91}{26}
\]
\[
\frac{11}{13} = \frac{11 \times 2}{13 \times 2} = \frac{22}{26}
\]

Now add the fractions:

\[
\frac{91}{26} + \frac{22}{26} = \frac{91 + 22}{26} = \frac{113}{26}
\]

So, the answer is:

\[
\boxed{\frac{113}{26}}
\]

---

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

The LCD of 2 and 3 is $2 \times 3 = 6$.

\[
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}
\]
\[
\frac{20}{3} = \frac{20 \times 2}{3 \times 2} = \frac{40}{6}
\]

Now add the fractions:

\[
\frac{9}{6} + \frac{40}{6} = \frac{9 + 40}{6} = \frac{49}{6}
\]

So, the answer is:

\[
\boxed{\frac{49}{6}}
\]

---

Problem 4: $\frac{13}{14} - \frac{12}{22}$

First, simplify $\frac{12}{22}$:

\[
\frac{12}{22} = \frac{6}{11}
\]

The LCD of 14 and 11 is $14 \times 11 = 154$.

\[
\frac{13}{14} = \frac{13 \times 11}{14 \times 11} = \frac{143}{154}
\]
\[
\frac{6}{11} = \frac{6 \times 14}{11 \times 14} = \frac{84}{154}
\]

Now subtract the fractions:

\[
\frac{143}{154} - \frac{84}{154} = \frac{143 - 84}{154} = \frac{59}{154}
\]

So, the answer is:

\[
\boxed{\frac{59}{154}}
\]

---

Problem 5: $\frac{9}{10} - \frac{3}{15}$

First, simplify $\frac{3}{15}$:

\[
\frac{3}{15} = \frac{1}{5}
\]

The LCD of 10 and 5 is 10.

\[
\frac{9}{10} = \frac{9}{10}
\]
\[
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
\]

Now subtract the fractions:

\[
\frac{9}{10} - \frac{2}{10} = \frac{9 - 2}{10} = \frac{7}{10}
\]

So, the answer is:

\[
\boxed{\frac{7}{10}}
\]

---

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

The LCD of 19 and 6 is $19 \times 6 = 114$.

\[
\frac{18}{19} = \frac{18 \times 6}{19 \times 6} = \frac{108}{114}
\]
\[
\frac{5}{6} = \frac{5 \times 19}{6 \times 19} = \frac{95}{114}
\]

Now subtract the fractions:

\[
\frac{108}{114} - \frac{95}{114} = \frac{108 - 95}{114} = \frac{13}{114}
\]

So, the answer is:

\[
\boxed{\frac{13}{114}}
\]

---

Problem 7: $\frac{12}{15} \times \frac{6}{20}$

First, simplify the fractions:

\[
\frac{12}{15} = \frac{4}{5}, \quad \frac{6}{20} = \frac{3}{10}
\]

Now multiply the fractions:

\[
\frac{4}{5} \times \frac{3}{10} = \frac{4 \times 3}{5 \times 10} = \frac{12}{50}
\]

Simplify $\frac{12}{50}$:

\[
\frac{12}{50} = \frac{6}{25}
\]

So, the answer is:

\[
\boxed{\frac{6}{25}}
\]

---

Problem 8: $\frac{23}{18} \times \frac{16}{21}$

Multiply the fractions:

\[
\frac{23}{18} \times \frac{16}{21} = \frac{23 \times 16}{18 \times 21} = \frac{368}{378}
\]

Simplify $\frac{368}{378}$ by finding the greatest common divisor (GCD) of 368 and 378, which is 2:

\[
\frac{368}{378} = \frac{184}{189}
\]

So, the answer is:

\[
\boxed{\frac{184}{189}}
\]

---

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

First, simplify $\frac{22}{24}$:

\[
\frac{22}{24} = \frac{11}{12}
\]

Now multiply the fractions:

\[
\frac{9}{14} \times \frac{11}{12} = \frac{9 \times 11}{14 \times 12} = \frac{99}{168}
\]

Simplify $\frac{99}{168}$ by finding the GCD of 99 and 168, which is 3:

\[
\frac{99}{168} = \frac{33}{56}
\]

So, the answer is:

\[
\boxed{\frac{33}{56}}
\]

---

Problem 10: $\frac{26}{52} \div \frac{12}{13}$

First, simplify $\frac{26}{52}$:

\[
\frac{26}{52} = \frac{1}{2}
\]

Now divide the fractions by multiplying by the reciprocal of $\frac{12}{13}$:

\[
\frac{1}{2} \div \frac{12}{13} = \frac{1}{2} \times \frac{13}{12} = \frac{1 \times 13}{2 \times 12} = \frac{13}{24}
\]

So, the answer is:

\[
\boxed{\frac{13}{24}}
\]

---

Problem 11: $\frac{5}{96} \div \frac{3}{64}$

Divide the fractions by multiplying by the reciprocal of $\frac{3}{64}$:

\[
\frac{5}{96} \div \frac{3}{64} = \frac{5}{96} \times \frac{64}{3} = \frac{5 \times 64}{96 \times 3} = \frac{320}{288}
\]

Simplify $\frac{320}{288}$ by finding the GCD of 320 and 288, which is 32:

\[
\frac{320}{288} = \frac{10}{9}
\]

So, the answer is:

\[
\boxed{\frac{10}{9}}
\]

---

Problem 12: $\frac{27}{21} \div \frac{44}{14}$

First, simplify $\frac{27}{21}$ and $\frac{44}{14}$:

\[
\frac{27}{21} = \frac{9}{7}, \quad \frac{44}{14} = \frac{22}{7}
\]

Now divide the fractions by multiplying by the reciprocal of $\frac{22}{7}$:

\[
\frac{9}{7} \div \frac{22}{7} = \frac{9}{7} \times \frac{7}{22} = \frac{9 \times 7}{7 \times 22} = \frac{9}{22}
\]

So, the answer is:

\[
\boxed{\frac{9}{22}}
\]

---

Final Answers:

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