Solve 5/25/8-(1/2div3/4*frac{1}{4})

$$\frac { 5 } { 2 } \frac { 5 } { 8 } - ( \frac { 1 } { 2 } \div \frac { 3 } { 4 } \times \frac { 1 } { 4 } )$$

Evaluate

$$\frac{67}{48}\approx 1.395833333$$

Solution Steps

Multiply \frac{5}{2} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 5}{2\times 8}-\frac{\frac{1}{2}}{\frac{3}{4}}\times \frac{1}{4}$$

Do the multiplications in the fraction \frac{5\times 5}{2\times 8}.

$$\frac{25}{16}-\frac{\frac{1}{2}}{\frac{3}{4}}\times \frac{1}{4}$$

Divide \frac{1}{2} by \frac{3}{4} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{4}.

$$\frac{25}{16}-\frac{1}{2}\times \frac{4}{3}\times \frac{1}{4}$$

Multiply \frac{1}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25}{16}-\frac{1\times 4}{2\times 3}\times \frac{1}{4}$$

Do the multiplications in the fraction \frac{1\times 4}{2\times 3}.

$$\frac{25}{16}-\frac{4}{6}\times \frac{1}{4}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{25}{16}-\frac{2}{3}\times \frac{1}{4}$$

Multiply \frac{2}{3} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25}{16}-\frac{2\times 1}{3\times 4}$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 4}.

$$\frac{25}{16}-\frac{2}{12}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{25}{16}-\frac{1}{6}$$

Least common multiple of 16 and 6 is 48. Convert \frac{25}{16} and \frac{1}{6} to fractions with denominator 48.

$$\frac{75}{48}-\frac{8}{48}$$

Since \frac{75}{48} and \frac{8}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-8}{48}$$

Subtract 8 from 75 to get 67.

$$\frac{67}{48}$$

Factor

$$\frac{67}{2 ^ {4} \cdot 3} = 1\frac{19}{48} = 1.3958333333333333$$