Adding Fractions Worksheets - Free Printable

To solve the problems on the "Adding Fractions Sheet 6," we need to add the fractions, simplify the results if necessary, and convert any improper fractions to mixed numbers. Let's go through each problem step by step.

Problem 1: $\frac{3}{4} + \frac{1}{3}$

1. Find the least common denominator (LCD) of 4 and 3, which is 12.
2. Convert each fraction to have the denominator of 12:
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}, \quad \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
\]
3. Add the fractions:
\[
\frac{9}{12} + \frac{4}{12} = \frac{13}{12}
\]
4. Convert the improper fraction to a mixed number:
\[
\frac{13}{12} = 1 \frac{1}{12}
\]

Answer: $\boxed{1 \frac{1}{12}}$

Problem 2: $\frac{5}{7} + \frac{1}{2}$

1. Find the LCD of 7 and 2, which is 14.
2. Convert each fraction:
\[
\frac{5}{7} = \frac{5 \times 2}{7 \times 2} = \frac{10}{14}, \quad \frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}
\]
3. Add the fractions:
\[
\frac{10}{14} + \frac{7}{14} = \frac{17}{14}
\]
4. Convert to a mixed number:
\[
\frac{17}{14} = 1 \frac{3}{14}
\]

Answer: $\boxed{1 \frac{3}{14}}$

Problem 3: $\frac{2}{5} + \frac{2}{3}$

1. Find the LCD of 5 and 3, which is 15.
2. Convert each fraction:
\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}, \quad \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\]
3. Add the fractions:
\[
\frac{6}{15} + \frac{10}{15} = \frac{16}{15}
\]
4. Convert to a mixed number:
\[
\frac{16}{15} = 1 \frac{1}{15}
\]

Answer: $\boxed{1 \frac{1}{15}}$

Problem 4: $\frac{1}{2} + \frac{11}{12}$

1. Find the LCD of 2 and 12, which is 12.
2. Convert each fraction:
\[
\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}, \quad \frac{11}{12} = \frac{11}{12}
\]
3. Add the fractions:
\[
\frac{6}{12} + \frac{11}{12} = \frac{17}{12}
\]
4. Convert to a mixed number:
\[
\frac{17}{12} = 1 \frac{5}{12}
\]

Answer: $\boxed{1 \frac{5}{12}}$

Problem 5: $\frac{4}{11} + \frac{9}{11}$

1. The denominators are the same, so add the numerators directly:
\[
\frac{4}{11} + \frac{9}{11} = \frac{4 + 9}{11} = \frac{13}{11}
\]
2. Convert to a mixed number:
\[
\frac{13}{11} = 1 \frac{2}{11}
\]

Answer: $\boxed{1 \frac{2}{11}}$

Problem 6: $\frac{3}{8} + \frac{4}{5}$

1. Find the LCD of 8 and 5, which is 40.
2. Convert each fraction:
\[
\frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40}, \quad \frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40}
\]
3. Add the fractions:
\[
\frac{15}{40} + \frac{32}{40} = \frac{47}{40}
\]
4. Convert to a mixed number:
\[
\frac{47}{40} = 1 \frac{7}{40}
\]

Answer: $\boxed{1 \frac{7}{40}}$

Problem 7: $\frac{5}{7} + \frac{3}{4}$

1. Find the LCD of 7 and 4, which is 28.
2. Convert each fraction:
\[
\frac{5}{7} = \frac{5 \times 4}{7 \times 4} = \frac{20}{28}, \quad \frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}
\]
3. Add the fractions:
\[
\frac{20}{28} + \frac{21}{28} = \frac{41}{28}
\]
4. Convert to a mixed number:
\[
\frac{41}{28} = 1 \frac{13}{28}
\]

Answer: $\boxed{1 \frac{13}{28}}$

Problem 8: $\frac{5}{8} + \frac{1}{2}$

1. Find the LCD of 8 and 2, which is 8.
2. Convert each fraction:
\[
\frac{5}{8} = \frac{5}{8}, \quad \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
\]
3. Add the fractions:
\[
\frac{5}{8} + \frac{4}{8} = \frac{9}{8}
\]
4. Convert to a mixed number:
\[
\frac{9}{8} = 1 \frac{1}{8}
\]

Answer: $\boxed{1 \frac{1}{8}}$

Problem 9: $\frac{6}{11} + \frac{5}{6}$

1. Find the LCD of 11 and 6, which is 66.
2. Convert each fraction:
\[
\frac{6}{11} = \frac{6 \times 6}{11 \times 6} = \frac{36}{66}, \quad \frac{5}{6} = \frac{5 \times 11}{6 \times 11} = \frac{55}{66}
\]
3. Add the fractions:
\[
\frac{36}{66} + \frac{55}{66} = \frac{91}{66}
\]
4. Convert to a mixed number:
\[
\frac{91}{66} = 1 \frac{25}{66}
\]

Answer: $\boxed{1 \frac{25}{66}}$

Problem 10: $\frac{7}{10} + \frac{3}{4}$

1. Find the LCD of 10 and 4, which is 20.
2. Convert each fraction:
\[
\frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{14}{20}, \quad \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
\]
3. Add the fractions:
\[
\frac{14}{20} + \frac{15}{20} = \frac{29}{20}
\]
4. Convert to a mixed number:
\[
\frac{29}{20} = 1 \frac{9}{20}
\]

Answer: $\boxed{1 \frac{9}{20}}$

Problem 11: $\frac{2}{7} + \frac{3}{5}$

1. Find the LCD of 7 and 5, which is 35.
2. Convert each fraction:
\[
\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}, \quad \frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}
\]
3. Add the fractions:
\[
\frac{10}{35} + \frac{21}{35} = \frac{31}{35}
\]

Answer: $\boxed{\frac{31}{35}}$

Problem 12: $\frac{3}{8} + \frac{2}{9}$

1. Find the LCD of 8 and 9, which is 72.
2. Convert each fraction:
\[
\frac{3}{8} = \frac{3 \times 9}{8 \times 9} = \frac{27}{72}, \quad \frac{2}{9} = \frac{2 \times 8}{9 \times 8} = \frac{16}{72}
\]
3. Add the fractions:
\[
\frac{27}{72} + \frac{16}{72} = \frac{43}{72}
\]

Answer: $\boxed{\frac{43}{72}}$

Problem 13: $\frac{5}{9} + \frac{3}{4}$

1. Find the LCD of 9 and 4, which is 36.
2. Convert each fraction:
\[
\frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}, \quad \frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36}
\]
3. Add the fractions:
\[
\frac{20}{36} + \frac{27}{36} = \frac{47}{36}
\]
4. Convert to a mixed number:
\[
\frac{47}{36} = 1 \frac{11}{36}
\]

Answer: $\boxed{1 \frac{11}{36}}$

Problem 14: $\frac{3}{7} + \frac{9}{10}$

1. Find the LCD of 7 and 10, which is 70.
2. Convert each fraction:
\[
\frac{3}{7} = \frac{3 \times 10}{7 \times 10} = \frac{30}{70}, \quad \frac{9}{10} = \frac{9 \times 7}{10 \times 7} = \frac{63}{70}
\]
3. Add the fractions:
\[
\frac{30}{70} + \frac{63}{70} = \frac{93}{70}
\]
4. Convert to a mixed number:
\[
\frac{93}{70} = 1 \frac{23}{70}
\]

Answer: $\boxed{1 \frac{23}{70}}$

Problem 15: $\frac{4}{9} + \frac{13}{18}$

1. Find the LCD of 9 and 18, which is 18.
2. Convert each fraction:
\[
\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}, \quad \frac{13}{18} = \frac{13}{18}
\]
3. Add the fractions:
\[
\frac{8}{18} + \frac{13}{18} = \frac{21}{18}
\]
4. Simplify the fraction:
\[
\frac{21}{18} = \frac{7}{6}
\]
5. Convert to a mixed number:
\[
\frac{7}{6} = 1 \frac{1}{6}
\]

Answer: $\boxed{1 \frac{1}{6}}$

Problem 16: $\frac{5}{6} + \frac{3}{11}$

1. Find the LCD of 6 and 11, which is 66.
2. Convert each fraction:
\[
\frac{5}{6} = \frac{5 \times 11}{6 \times 11} = \frac{55}{66}, \quad \frac{3}{11} = \frac{3 \times 6}{11 \times 6} = \frac{18}{66}
\]
3. Add the fractions:
\[
\frac{55}{66} + \frac{18}{66} = \frac{73}{66}
\]
4. Convert to a mixed number:
\[
\frac{73}{66} = 1 \frac{7}{66}
\]

Answer: $\boxed{1 \frac{7}{66}}$

Problem 17: $\frac{7}{12} + \frac{4}{5}$

1. Find the LCD of 12 and 5, which is 60.
2. Convert each fraction:
\[
\frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}, \quad \frac{4}{5} = \frac{4 \times 12}{5 \times 12} = \frac{48}{60}
\]
3. Add the fractions:
\[
\frac{35}{60} + \frac{48}{60} = \frac{83}{60}
\]
4. Convert to a mixed number:
\[
\frac{83}{60} = 1 \frac{23}{60}
\]

Answer: $\boxed{1 \frac{23}{60}}$

Problem 18: $\frac{3}{8} + \frac{4}{9}$

1. Find the LCD of 8 and 9, which is 72.
2. Convert each fraction:
\[
\frac{3}{8} = \frac{3 \times 9}{8 \times 9} = \frac{27}{72}, \quad \frac{4}{9} = \frac{4 \times 8}{9 \times 8} = \frac{32}{72}
\]
3. Add the fractions:
\[
\frac{27}{72} + \frac{32}{72} = \frac{59}{72}
\]

Answer: $\boxed{\frac{59}{72}}$

Problem 19: $\frac{17}{20} + \frac{3}{5}$

1. Find the LCD of 20 and 5, which is 20.
2. Convert each fraction:
\[
\frac{17}{20} = \frac{17}{20}, \quad \frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}
\]
3. Add the fractions:
\[
\frac{17}{20} + \frac{12}{20} = \frac{29}{20}
\]
4. Convert to a mixed number:
\[
\frac{29}{20} = 1 \frac{9}{20}
\]

Answer: $\boxed{1 \frac{9}{20}}$

Problem 20: $\frac{7}{8} + \frac{6}{7}$

1. Find the LCD of 8 and 7, which is 56.
2. Convert each fraction:
\[
\frac{7}{8} = \frac{7 \times 7}{8 \times 7} = \frac{49}{56}, \quad \frac{6}{7} = \frac{6 \times 8}{7 \times 8} = \frac{48}{56}
\]
3. Add the fractions:
\[
\frac{49}{56} + \frac{48}{56} = \frac{97}{56}
\]
4. Convert to a mixed number:
\[
\frac{97}{56} = 1 \frac{41}{56}
\]

Answer: $\boxed{1 \frac{41}{56}}$

Final Answer:

\[
\boxed{
\begin{array}{ll}
1) & 1 \frac{1}{12} \\
2) & 1 \frac{3}{14} \\
3) & 1 \frac{1}{15} \\
4) & 1 \frac{5}{12} \\
5) & 1 \frac{2}{11} \\
6) & 1 \frac{7}{40} \\
7) & 1 \frac{13}{28} \\
8) & 1 \frac{1}{8} \\
9) & 1 \frac{25}{66} \\
10) & 1 \frac{9}{20} \\
11) & \frac{31}{35} \\
12) & \frac{43}{72} \\
13) & 1 \frac{11}{36} \\
14) & 1 \frac{23}{70} \\
15) & 1 \frac{1}{6} \\
16) & 1 \frac{7}{66} \\
17) & 1 \frac{23}{60} \\
18) & \frac{59}{72} \\
19) & 1 \frac{9}{20} \\
20) & 1 \frac{41}{56} \\
\end{array}
}
\]