Solve 2/5+3/4div3/20-2/3

$$\frac{ 2 }{ 5 } + \frac{ 3 }{ 4 } \div \frac{ 3 }{ 20 } - \frac{ 2 }{ 3 }$$

Evaluate

$$\frac{71}{15}\approx 4.733333333$$

Solution Steps

Divide \frac{3}{4} by \frac{3}{20} by multiplying \frac{3}{4} by the reciprocal of \frac{3}{20}.

$$\frac{2}{5}+\frac{3}{4}\times \frac{20}{3}-\frac{2}{3}$$

Multiply \frac{3}{4} times \frac{20}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}+\frac{3\times 20}{4\times 3}-\frac{2}{3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2}{5}+\frac{20}{4}-\frac{2}{3}$$

Divide 20 by 4 to get 5.

$$\frac{2}{5}+5-\frac{2}{3}$$

Convert 5 to fraction \frac{25}{5}.

$$\frac{2}{5}+\frac{25}{5}-\frac{2}{3}$$

Since \frac{2}{5} and \frac{25}{5} have the same denominator, add them by adding their numerators.

$$\frac{2+25}{5}-\frac{2}{3}$$

Add 2 and 25 to get 27.

$$\frac{27}{5}-\frac{2}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{27}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{81}{15}-\frac{10}{15}$$

Since \frac{81}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81-10}{15}$$

Subtract 10 from 81 to get 71.

$$\frac{71}{15}$$

Factor

$$\frac{71}{3 \cdot 5} = 4\frac{11}{15} = 4.733333333333333$$