Solve 31/5-2/3/2frac{4{5}}

$$\frac { 3 \frac { 1 } { 5 } - \frac { 2 } { 3 } } { 2 \frac { 4 } { 5 } }$$

Evaluate

$$\frac{19}{21}\approx 0.904761905$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{\frac{15+1}{5}-\frac{2}{3}}{\frac{2\times 5+4}{5}}$$

Add 15 and 1 to get 16.

$$\frac{\frac{16}{5}-\frac{2}{3}}{\frac{2\times 5+4}{5}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{16}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{\frac{48}{15}-\frac{10}{15}}{\frac{2\times 5+4}{5}}$$

Since \frac{48}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{48-10}{15}}{\frac{2\times 5+4}{5}}$$

Subtract 10 from 48 to get 38.

$$\frac{\frac{38}{15}}{\frac{2\times 5+4}{5}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{38}{15}}{\frac{10+4}{5}}$$

Add 10 and 4 to get 14.

$$\frac{\frac{38}{15}}{\frac{14}{5}}$$

Divide \frac{38}{15} by \frac{14}{5} by multiplying \frac{38}{15} by the reciprocal of \frac{14}{5}.

$$\frac{38}{15}\times \frac{5}{14}$$

Multiply \frac{38}{15} times \frac{5}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{38\times 5}{15\times 14}$$

Do the multiplications in the fraction \frac{38\times 5}{15\times 14}.

$$\frac{190}{210}$$

Reduce the fraction \frac{190}{210} to lowest terms by extracting and canceling out 10.

$$\frac{19}{21}$$

Factor

$$\frac{19}{3 \cdot 7} = 0.9047619047619048$$