Solve [4/15div20/30]+[7/20div14/35]

$$[ \frac { 4 } { 15 } \div \frac { 20 } { 30 } ] + [ \frac { 7 } { 20 } \div \frac { 14 } { 35 } ]$$

Evaluate

$$\frac{51}{40}=1.275$$

Solution Steps

Divide \frac{4}{15} by \frac{20}{30} by multiplying \frac{4}{15} by the reciprocal of \frac{20}{30}.

$$\frac{4\times 30}{15\times 20}+\frac{\frac{7}{20}}{\frac{14}{35}}$$

Cancel out 4\times 15 in both numerator and denominator.

$$\frac{2}{5}+\frac{\frac{7}{20}}{\frac{14}{35}}$$

Divide \frac{7}{20} by \frac{14}{35} by multiplying \frac{7}{20} by the reciprocal of \frac{14}{35}.

$$\frac{2}{5}+\frac{7\times 35}{20\times 14}$$

Cancel out 5\times 7 in both numerator and denominator.

$$\frac{2}{5}+\frac{7}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{2}{5}+\frac{7}{8}$$

Least common multiple of 5 and 8 is 40. Convert \frac{2}{5} and \frac{7}{8} to fractions with denominator 40.

$$\frac{16}{40}+\frac{35}{40}$$

Since \frac{16}{40} and \frac{35}{40} have the same denominator, add them by adding their numerators.

$$\frac{16+35}{40}$$

Add 16 and 35 to get 51.

$$\frac{51}{40}$$

Factor

$$\frac{3 \cdot 17}{2 ^ {3} \cdot 5} = 1\frac{11}{40} = 1.275$$