Solve (9/5-3/4):(7/20+1/4)=

$$( \frac { 9 } { 5 } - \frac { 3 } { 4 } ) : ( \frac { 7 } { 20 } + \frac { 1 } { 4 } ) =$$

Evaluate

$$\frac{7}{4}=1.75$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{9}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{\frac{36}{20}-\frac{15}{20}}{\frac{7}{20}+\frac{1}{4}}$$

Since \frac{36}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{36-15}{20}}{\frac{7}{20}+\frac{1}{4}}$$

Subtract 15 from 36 to get 21.

$$\frac{\frac{21}{20}}{\frac{7}{20}+\frac{1}{4}}$$

Least common multiple of 20 and 4 is 20. Convert \frac{7}{20} and \frac{1}{4} to fractions with denominator 20.

$$\frac{\frac{21}{20}}{\frac{7}{20}+\frac{5}{20}}$$

Since \frac{7}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{21}{20}}{\frac{7+5}{20}}$$

Add 7 and 5 to get 12.

$$\frac{\frac{21}{20}}{\frac{12}{20}}$$

Reduce the fraction \frac{12}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{21}{20}}{\frac{3}{5}}$$

Divide \frac{21}{20} by \frac{3}{5} by multiplying \frac{21}{20} by the reciprocal of \frac{3}{5}.

$$\frac{21}{20}\times \frac{5}{3}$$

Multiply \frac{21}{20} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 5}{20\times 3}$$

Do the multiplications in the fraction \frac{21\times 5}{20\times 3}.

$$\frac{105}{60}$$

Reduce the fraction \frac{105}{60} to lowest terms by extracting and canceling out 15.

$$\frac{7}{4}$$

Factor

$$\frac{7}{2 ^ {2}} = 1\frac{3}{4} = 1.75$$