Solve 9/10(3/4-1/5)-3/8(frac{5}{3}-frac{1}{2})=

$$\frac { 9 } { 10 } ( \frac { 3 } { 4 } - \frac { 1 } { 5 } ) - \frac { 3 } { 8 } ( \frac { 5 } { 3 } - \frac { 1 } { 2 } ) =$$

Evaluate

$$\frac{23}{400}=0.0575$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{9}{10}\left(\frac{15}{20}-\frac{4}{20}\right)-\frac{3}{8}\left(\frac{5}{3}-\frac{1}{2}\right)$$

Since \frac{15}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{10}\times \frac{15-4}{20}-\frac{3}{8}\left(\frac{5}{3}-\frac{1}{2}\right)$$

Subtract 4 from 15 to get 11.

$$\frac{9}{10}\times \frac{11}{20}-\frac{3}{8}\left(\frac{5}{3}-\frac{1}{2}\right)$$

Multiply \frac{9}{10} times \frac{11}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 11}{10\times 20}-\frac{3}{8}\left(\frac{5}{3}-\frac{1}{2}\right)$$

Do the multiplications in the fraction \frac{9\times 11}{10\times 20}.

$$\frac{99}{200}-\frac{3}{8}\left(\frac{5}{3}-\frac{1}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{99}{200}-\frac{3}{8}\left(\frac{10}{6}-\frac{3}{6}\right)$$

Since \frac{10}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{99}{200}-\frac{3}{8}\times \frac{10-3}{6}$$

Subtract 3 from 10 to get 7.

$$\frac{99}{200}-\frac{3}{8}\times \frac{7}{6}$$

Multiply \frac{3}{8} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{99}{200}-\frac{3\times 7}{8\times 6}$$

Do the multiplications in the fraction \frac{3\times 7}{8\times 6}.

$$\frac{99}{200}-\frac{21}{48}$$

Reduce the fraction \frac{21}{48} to lowest terms by extracting and canceling out 3.

$$\frac{99}{200}-\frac{7}{16}$$

Least common multiple of 200 and 16 is 400. Convert \frac{99}{200} and \frac{7}{16} to fractions with denominator 400.

$$\frac{198}{400}-\frac{175}{400}$$

Since \frac{198}{400} and \frac{175}{400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{198-175}{400}$$

Subtract 175 from 198 to get 23.

$$\frac{23}{400}$$

Factor

$$\frac{23}{2 ^ {4} \cdot 5 ^ {2}} = 0.0575$$