Solve (1/4)+4/5+2/5:(2/3)

$$( \frac { 1 } { 4 } ) + \frac { 4 } { 5 } + \frac { 2 } { 5 } : ( \frac { 2 } { 3 } )$$

Evaluate

$$\frac{33}{20}=1.65$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{4}{5} to fractions with denominator 20.

$$\frac{5}{20}+\frac{16}{20}+\frac{\frac{2}{5}}{\frac{2}{3}}$$

Since \frac{5}{20} and \frac{16}{20} have the same denominator, add them by adding their numerators.

$$\frac{5+16}{20}+\frac{\frac{2}{5}}{\frac{2}{3}}$$

Add 5 and 16 to get 21.

$$\frac{21}{20}+\frac{\frac{2}{5}}{\frac{2}{3}}$$

Divide \frac{2}{5} by \frac{2}{3} by multiplying \frac{2}{5} by the reciprocal of \frac{2}{3}.

$$\frac{21}{20}+\frac{2}{5}\times \frac{3}{2}$$

Multiply \frac{2}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21}{20}+\frac{2\times 3}{5\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{21}{20}+\frac{3}{5}$$

Least common multiple of 20 and 5 is 20. Convert \frac{21}{20} and \frac{3}{5} to fractions with denominator 20.

$$\frac{21}{20}+\frac{12}{20}$$

Since \frac{21}{20} and \frac{12}{20} have the same denominator, add them by adding their numerators.

$$\frac{21+12}{20}$$

Add 21 and 12 to get 33.

$$\frac{33}{20}$$

Factor

$$\frac{3 \cdot 11}{2 ^ {2} \cdot 5} = 1\frac{13}{20} = 1.65$$