Math worksheet for practicing addition of fractions and finding their reciprocals.

To solve the problem, we need to:

1. Add the fractions given in each pair.
2. Find the reciprocal of the resulting sum.

Step-by-Step Solution:

#### 1) $\frac{3}{4} + \frac{2}{10}$
- Simplify $\frac{2}{10}$ to $\frac{1}{5}$.
- Find a common denominator for $\frac{3}{4}$ and $\frac{1}{5}$, which is $20$.
- Convert the fractions:
$$
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}, \quad \frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}
$$
- Add the fractions:
$$
\frac{15}{20} + \frac{4}{20} = \frac{19}{20}
$$
- The reciprocal of $\frac{19}{20}$ is $\frac{20}{19}$.
- Answer: $\frac{19}{20}$, $\frac{20}{19}$

#### 2) $\frac{1}{5} + \frac{7}{10}$
- Find a common denominator for $\frac{1}{5}$ and $\frac{7}{10}$, which is $10$.
- Convert the fractions:
$$
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}, \quad \frac{7}{10} = \frac{7}{10}
$$
- Add the fractions:
$$
\frac{2}{10} + \frac{7}{10} = \frac{9}{10}
$$
- The reciprocal of $\frac{9}{10}$ is $\frac{10}{9}$.
- Answer: $\frac{9}{10}$, $\frac{10}{9}$

#### 3) $\frac{4}{9} + \frac{3}{12}$
- Simplify $\frac{3}{12}$ to $\frac{1}{4}$.
- Find a common denominator for $\frac{4}{9}$ and $\frac{1}{4}$, which is $36$.
- Convert the fractions:
$$
\frac{4}{9} = \frac{4 \times 4}{9 \times 4} = \frac{16}{36}, \quad \frac{1}{4} = \frac{1 \times 9}{4 \times 9} = \frac{9}{36}
$$
- Add the fractions:
$$
\frac{16}{36} + \frac{9}{36} = \frac{25}{36}
$$
- The reciprocal of $\frac{25}{36}$ is $\frac{36}{25}$.
- Answer: $\frac{25}{36}$, $\frac{36}{25}$

#### 4) $\frac{5}{12} + \frac{4}{9}$
- Find a common denominator for $\frac{5}{12}$ and $\frac{4}{9}$, which is $36$.
- Convert the fractions:
$$
\frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}, \quad \frac{4}{9} = \frac{4 \times 4}{9 \times 4} = \frac{16}{36}
$$
- Add the fractions:
$$
\frac{15}{36} + \frac{16}{36} = \frac{31}{36}
$$
- The reciprocal of $\frac{31}{36}$ is $\frac{36}{31}$.
- Answer: $\frac{31}{36}$, $\frac{36}{31}$

#### 5) $\frac{2}{7} + \frac{1}{14}$
- Find a common denominator for $\frac{2}{7}$ and $\frac{1}{14}$, which is $14$.
- Convert the fractions:
$$
\frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14}, \quad \frac{1}{14} = \frac{1}{14}
$$
- Add the fractions:
$$
\frac{4}{14} + \frac{1}{14} = \frac{5}{14}
$$
- The reciprocal of $\frac{5}{14}$ is $\frac{14}{5}$.
- Answer: $\frac{5}{14}$, $\frac{14}{5}$

#### 6) $\frac{4}{12} + \frac{3}{8}$
- Simplify $\frac{4}{12}$ to $\frac{1}{3}$.
- Find a common denominator for $\frac{1}{3}$ and $\frac{3}{8}$, which is $24$.
- Convert the fractions:
$$
\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}, \quad \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
$$
- Add the fractions:
$$
\frac{8}{24} + \frac{9}{24} = \frac{17}{24}
$$
- The reciprocal of $\frac{17}{24}$ is $\frac{24}{17}$.
- Answer: $\frac{17}{24}$, $\frac{24}{17}$

#### 7) $\frac{8}{12} + \frac{4}{15}$
- Simplify $\frac{8}{12}$ to $\frac{2}{3}$.
- Find a common denominator for $\frac{2}{3}$ and $\frac{4}{15}$, which is $15$.
- Convert the fractions:
$$
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}, \quad \frac{4}{15} = \frac{4}{15}
$$
- Add the fractions:
$$
\frac{10}{15} + \frac{4}{15} = \frac{14}{15}
$$
- The reciprocal of $\frac{14}{15}$ is $\frac{15}{14}$.
- Answer: $\frac{14}{15}$, $\frac{15}{14}$

#### 8) $\frac{1}{3} + \frac{2}{15}$
- Find a common denominator for $\frac{1}{3}$ and $\frac{2}{15}$, which is $15$.
- Convert the fractions:
$$
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}, \quad \frac{2}{15} = \frac{2}{15}
$$
- Add the fractions:
$$
\frac{5}{15} + \frac{2}{15} = \frac{7}{15}
$$
- The reciprocal of $\frac{7}{15}$ is $\frac{15}{7}$.
- Answer: $\frac{7}{15}$, $\frac{15}{7}$

#### 9) $\frac{3}{5} + \frac{2}{10}$
- Simplify $\frac{2}{10}$ to $\frac{1}{5}$.
- Find a common denominator for $\frac{3}{5}$ and $\frac{1}{5}$, which is $5$.
- Convert the fractions:
$$
\frac{3}{5} = \frac{3}{5}, \quad \frac{1}{5} = \frac{1}{5}
$$
- Add the fractions:
$$
\frac{3}{5} + \frac{1}{5} = \frac{4}{5}
$$
- The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$.
- Answer: $\frac{4}{5}$, $\frac{5}{4}$

#### 10) $\frac{1}{6} + \frac{3}{4}$
- Find a common denominator for $\frac{1}{6}$ and $\frac{3}{4}$, which is $12$.
- Convert the fractions:
$$
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}, \quad \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
$$
- Add the fractions:
$$
\frac{2}{12} + \frac{9}{12} = \frac{11}{12}
$$
- The reciprocal of $\frac{11}{12}$ is $\frac{12}{11}$.
- Answer: $\frac{11}{12}$, $\frac{12}{11}$

#### 11) $\frac{1}{12} + \frac{3}{5}$
- Find a common denominator for $\frac{1}{12}$ and $\frac{3}{5}$, which is $60$.
- Convert the fractions:
$$
\frac{1}{12} = \frac{1 \times 5}{12 \times 5} = \frac{5}{60}, \quad \frac{3}{5} = \frac{3 \times 12}{5 \times 12} = \frac{36}{60}
$$
- Add the fractions:
$$
\frac{5}{60} + \frac{36}{60} = \frac{41}{60}
$$
- The reciprocal of $\frac{41}{60}$ is $\frac{60}{41}$.
- Answer: $\frac{41}{60}$, $\frac{60}{41}$

#### 12) $\frac{2}{5} + \frac{3}{10}$
- Find a common denominator for $\frac{2}{5}$ and $\frac{3}{10}$, which is $10$.
- Convert the fractions:
$$
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}, \quad \frac{3}{10} = \frac{3}{10}
$$
- Add the fractions:
$$
\frac{4}{10} + \frac{3}{10} = \frac{7}{10}
$$
- The reciprocal of $\frac{7}{10}$ is $\frac{10}{7}$.
- Answer: $\frac{7}{10}$, $\frac{10}{7}$

#### 13) $\frac{5}{8} + \frac{2}{10}$
- Simplify $\frac{2}{10}$ to $\frac{1}{5}$.
- Find a common denominator for $\frac{5}{8}$ and $\frac{1}{5}$, which is $40$.
- Convert the fractions:
$$
\frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40}, \quad \frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40}
$$
- Add the fractions:
$$
\frac{25}{40} + \frac{8}{40} = \frac{33}{40}
$$
- The reciprocal of $\frac{33}{40}$ is $\frac{40}{33}$.
- Answer: $\frac{33}{40}$, $\frac{40}{33}$

#### 14) $\frac{4}{7} + \frac{3}{9}$
- Simplify $\frac{3}{9}$ to $\frac{1}{3}$.
- Find a common denominator for $\frac{4}{7}$ and $\frac{1}{3}$, which is $21$.
- Convert the fractions:
$$
\frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21}, \quad \frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}
$$
- Add the fractions:
$$
\frac{12}{21} + \frac{7}{21} = \frac{19}{21}
$$
- The reciprocal of $\frac{19}{21}$ is $\frac{21}{19}$.
- Answer: $\frac{19}{21}$, $\frac{21}{19}$

#### 15) $\frac{4}{10} + \frac{2}{5}$
- Simplify $\frac{4}{10}$ to $\frac{2}{5}$.
- Find a common denominator for $\frac{2}{5}$ and $\frac{2}{5}$, which is $5$.
- Convert the fractions:
$$
\frac{2}{5} = \frac{2}{5}, \quad \frac{2}{5} = \frac{2}{5}
$$
- Add the fractions:
$$
\frac{2}{5} + \frac{2}{5} = \frac{4}{5}
$$
- The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$.
- Answer: $\frac{4}{5}$, $\frac{5}{4}$

#### 16) $\frac{3}{5} + \frac{2}{15}$
- Find a common denominator for $\frac{3}{5}$ and $\frac{2}{15}$, which is $15$.
- Convert the fractions:
$$
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}, \quad \frac{2}{15} = \frac{2}{15}
$$
- Add the fractions:
$$
\frac{9}{15} + \frac{2}{15} = \frac{11}{15}
$$
- The reciprocal of $\frac{11}{15}$ is $\frac{15}{11}$.
- Answer: $\frac{11}{15}$, $\frac{15}{11}$

Final Answer:

$$
\boxed{
\begin{array}{ll}
1) & \frac{19}{20}, \frac{20}{19} \\
2) & \frac{9}{10}, \frac{10}{9} \\
3) & \frac{25}{36}, \frac{36}{25} \\
4) & \frac{31}{36}, \frac{36}{31} \\
5) & \frac{5}{14}, \frac{14}{5} \\
6) & \frac{17}{24}, \frac{24}{17} \\
7) & \frac{14}{15}, \frac{15}{14} \\
8) & \frac{7}{15}, \frac{15}{7} \\
9) & \frac{4}{5}, \frac{5}{4} \\
10) & \frac{11}{12}, \frac{12}{11} \\
11) & \frac{41}{60}, \frac{60}{41} \\
12) & \frac{7}{10}, \frac{10}{7} \\
13) & \frac{33}{40}, \frac{40}{33} \\
14) & \frac{19}{21}, \frac{21}{19} \\
15) & \frac{4}{5}, \frac{5}{4} \\
16) & \frac{11}{15}, \frac{15}{11} \\
\end{array}
}
$$