Solve 3/4*7/2/frac{7{5}-5/4}

$$\frac { \frac { 3 } { 4 } \times \frac { 7 } { 2 } } { \frac { 7 } { 5 } - \frac { 5 } { 4 } }$$

Evaluate

$$\frac{35}{2}=17.5$$

Solution Steps

Multiply \frac{3}{4} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 7}{4\times 2}}{\frac{7}{5}-\frac{5}{4}}$$

Do the multiplications in the fraction \frac{3\times 7}{4\times 2}.

$$\frac{\frac{21}{8}}{\frac{7}{5}-\frac{5}{4}}$$

Least common multiple of 5 and 4 is 20. Convert \frac{7}{5} and \frac{5}{4} to fractions with denominator 20.

$$\frac{\frac{21}{8}}{\frac{28}{20}-\frac{25}{20}}$$

Since \frac{28}{20} and \frac{25}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21}{8}}{\frac{28-25}{20}}$$

Subtract 25 from 28 to get 3.

$$\frac{\frac{21}{8}}{\frac{3}{20}}$$

Divide \frac{21}{8} by \frac{3}{20} by multiplying \frac{21}{8} by the reciprocal of \frac{3}{20}.

$$\frac{21}{8}\times \frac{20}{3}$$

Multiply \frac{21}{8} times \frac{20}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 20}{8\times 3}$$

Do the multiplications in the fraction \frac{21\times 20}{8\times 3}.

$$\frac{420}{24}$$

Reduce the fraction \frac{420}{24} to lowest terms by extracting and canceling out 12.

$$\frac{35}{2}$$

Factor

$$\frac{5 \cdot 7}{2} = 17\frac{1}{2} = 17.5$$