Solve 5/2-4/4/frac{2{5}+1/4}

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

Evaluate

$$\frac{30}{13}\approx 2.307692308$$

Solution Steps

Divide 4 by 4 to get 1.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{5}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 5 to get 3.

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

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{\frac{3}{2}}{\frac{8}{20}+\frac{5}{20}}$$

Since \frac{8}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{2}}{\frac{8+5}{20}}$$

Add 8 and 5 to get 13.

$$\frac{\frac{3}{2}}{\frac{13}{20}}$$

Divide \frac{3}{2} by \frac{13}{20} by multiplying \frac{3}{2} by the reciprocal of \frac{13}{20}.

$$\frac{3}{2}\times \frac{20}{13}$$

Multiply \frac{3}{2} times \frac{20}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 20}{2\times 13}$$

Do the multiplications in the fraction \frac{3\times 20}{2\times 13}.

$$\frac{60}{26}$$

Reduce the fraction \frac{60}{26} to lowest terms by extracting and canceling out 2.

$$\frac{30}{13}$$

Factor

$$\frac{2 \cdot 3 \cdot 5}{13} = 2\frac{4}{13} = 2.3076923076923075$$