Question

3\frac{4}{5}+4\frac{2}{3}=\
2\frac{2}{7}+3\frac{5}{6}=\
2\frac{4}{7}+3\frac{2}{3}=\
3\frac{1}{6}+2\frac{1}{5}=\

Explanation:

First problem: \( 3\frac{4}{5} + 4\frac{2}{3} \)

Step1: Convert mixed numbers to improper fractions

\( 3\frac{4}{5} = \frac{3\times5 + 4}{5} = \frac{19}{5} \)
\( 4\frac{2}{3} = \frac{4\times3 + 2}{3} = \frac{14}{3} \)

Step2: Find a common denominator (15) and add

\( \frac{19}{5} = \frac{19\times3}{5\times3} = \frac{57}{15} \)
\( \frac{14}{3} = \frac{14\times5}{3\times5} = \frac{70}{15} \)
\( \frac{57}{15} + \frac{70}{15} = \frac{57 + 70}{15} = \frac{127}{15} \)

Step3: Convert back to mixed number

\( \frac{127}{15} = 8\frac{7}{15} \)

Step1: Convert mixed numbers to improper fractions

\( 2\frac{2}{7} = \frac{2\times7 + 2}{7} = \frac{16}{7} \)
\( 3\frac{5}{6} = \frac{3\times6 + 5}{6} = \frac{23}{6} \)

Step2: Find a common denominator (42) and add

\( \frac{16}{7} = \frac{16\times6}{7\times6} = \frac{96}{42} \)
\( \frac{23}{6} = \frac{23\times7}{6\times7} = \frac{161}{42} \)
\( \frac{96}{42} + \frac{161}{42} = \frac{96 + 161}{42} = \frac{257}{42} \)

Step3: Convert back to mixed number

\( \frac{257}{42} = 6\frac{5}{42} \)

Step1: Convert mixed numbers to improper fractions

\( 2\frac{4}{7} = \frac{2\times7 + 4}{7} = \frac{18}{7} \)
\( 3\frac{2}{3} = \frac{3\times3 + 2}{3} = \frac{11}{3} \)

Step2: Find a common denominator (21) and add

\( \frac{18}{7} = \frac{18\times3}{7\times3} = \frac{54}{21} \)
\( \frac{11}{3} = \frac{11\times7}{3\times7} = \frac{77}{21} \)
\( \frac{54}{21} + \frac{77}{21} = \frac{54 + 77}{21} = \frac{131}{21} \)

Step3: Convert back to mixed number

\( \frac{131}{21} = 6\frac{5}{21} \)

Answer:

\( 8\frac{7}{15} \)

Second problem: \( 2\frac{2}{7} + 3\frac{5}{6} \)