To multiply mixed numbers, first write them as fractions. Then multiply and write the answer in lowest terms.
Example 1: $1 \ \frac{3}{7} \ \ x \ \ 6 \ \frac{1}{3}$
= $\frac{10}{7} \ x \ \frac{19}{3}$
Since we can not use the cancellation method, then
= $\frac{10 \ x \ 19}{7 \ x \ 3}$
= $\frac{190}{21}$ or $9 \ \frac{1}{21}$
Example 2: $8 \ \frac{1}{3} \ \ x \ \ 4\frac{1}{5}$
= $\frac{25}{3} \ x \ \frac{21}{5}$
Using cancellation method,
= $\frac{5}{1} \ x \ \frac{7}{1}$
= $35$
Sometimes using the distributive property of multiplication is helpful!
Example 3: $2 \ x \ (\frac{2}{3} \ + \ \frac{1}{5})$
= $(2 \ x \ \frac{2}{3}) \ + \ ( 2 \ x \ \frac{1}{5})$
= $(\frac{2}{1} \ x \ \frac{2}{3}) \ + \ ( \frac{2}{1} \ x \ \frac{1}{5})$
= $\frac{4}{3} \ + \ \frac{2}{5}$ using the LCD which is 15,
= $\frac{4}{3} \ (\frac{5}{5}) \ + \ \frac{2}{5} \ (\frac{3}{3}) $
= $\frac{20}{15} \ + \ \frac{6}{15}$
= $\frac{26}{15}$ or $1\frac{11}{15}$
Example 4: $3 \ x \ 4\frac{2}{5}$
= $3 \ x \ (4 \ + \ \frac{2}{5})$
= $(3 \ x \ 4) \ + \ (\frac{3}{1}) \ x \ (\frac{2}{5})$
= $12 \ + \ \frac{6}{5}$
= $12 \ + \ 1 \ \frac{1}{5}$
= $13 \ + \ \frac{1}{5}$
= $13 \ \frac{1}{5}$
