Question

name
write the correct answer for each sentence.
$6\frac{1}{2} + 4\frac{2}{3} =$
$3\frac{1}{6} + 2\frac{3}{5} =$
$6\frac{3}{7} + 1\frac{2}{5} =$
$3\frac{4}{5} + 4\frac{1}{3} =$
$1\frac{3}{4} + 6\frac{6}{7} =$
$3\frac{4}{5} + 4\frac{2}{3} =$
$2\frac{2}{7} + 3\frac{5}{6} =$
$2\frac{4}{7} + 3\frac{2}{3} =$
$3\frac{1}{6} + 2\frac{1}{5} =$

Explanation:

1. \( 6\frac{1}{2} + 4\frac{2}{3} \)

Step1: Convert mixed numbers to improper fractions

\( 6\frac{1}{2}=\frac{6\times2 + 1}{2}=\frac{13}{2} \), \( 4\frac{2}{3}=\frac{4\times3+2}{3}=\frac{14}{3} \)

Step2: Find a common denominator (6) and add

\( \frac{13}{2}=\frac{13\times3}{2\times3}=\frac{39}{6} \), \( \frac{14}{3}=\frac{14\times2}{3\times2}=\frac{28}{6} \)
\( \frac{39}{6}+\frac{28}{6}=\frac{39 + 28}{6}=\frac{67}{6}=11\frac{1}{6} \)

Step1: Convert to improper fractions

\( 3\frac{1}{6}=\frac{3\times6 + 1}{6}=\frac{19}{6} \), \( 2\frac{3}{5}=\frac{2\times5+3}{5}=\frac{13}{5} \)

Step2: Common denominator (30) and add

\( \frac{19}{6}=\frac{19\times5}{6\times5}=\frac{95}{30} \), \( \frac{13}{5}=\frac{13\times6}{5\times6}=\frac{78}{30} \)
\( \frac{95}{30}+\frac{78}{30}=\frac{95 + 78}{30}=\frac{173}{30}=5\frac{23}{30} \)

Step1: Convert to improper fractions

\( 6\frac{3}{7}=\frac{6\times7+3}{7}=\frac{45}{7} \), \( 1\frac{2}{5}=\frac{1\times5 + 2}{5}=\frac{7}{5} \)

Step2: Common denominator (35) and add

\( \frac{45}{7}=\frac{45\times5}{7\times5}=\frac{225}{35} \), \( \frac{7}{5}=\frac{7\times7}{5\times7}=\frac{49}{35} \)
\( \frac{225}{35}+\frac{49}{35}=\frac{225 + 49}{35}=\frac{274}{35}=7\frac{29}{35} \)

Answer:

\( 11\frac{1}{6} \)

2. \( 3\frac{1}{6}+2\frac{3}{5} \)