Solve (3/4-3/16)*(2/9+1/3)quad25*frac{23}{24}quad[frac{1}{2}-(frac{3}{4}-frac{3}{5})]divfrac{7}{10}

$$( \frac { 3 } { 4 } - \frac { 3 } { 16 } ) \times ( \frac { 2 } { 9 } + \frac { 1 } { 3 } ) \quad 25 \times \frac { 23 } { 24 } \quad [ \frac { 1 } { 2 } - ( \frac { 3 } { 4 } - \frac { 3 } { 5 } ) ] \div \frac { 7 } { 10 }$$

Evaluate

$$\frac{2875}{768}\approx 3.743489583$$

Solution Steps

Least common multiple of 4 and 16 is 16. Convert \frac{3}{4} and \frac{3}{16} to fractions with denominator 16.

$$\frac{\left(\frac{12}{16}-\frac{3}{16}\right)\left(\frac{2}{9}+\frac{1}{3}\right)\times 25\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Since \frac{12}{16} and \frac{3}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12-3}{16}\left(\frac{2}{9}+\frac{1}{3}\right)\times 25\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Subtract 3 from 12 to get 9.

$$\frac{\frac{9}{16}\left(\frac{2}{9}+\frac{1}{3}\right)\times 25\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{2}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{\frac{9}{16}\left(\frac{2}{9}+\frac{3}{9}\right)\times 25\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Since \frac{2}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9}{16}\times \frac{2+3}{9}\times 25\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Add 2 and 3 to get 5.

$$\frac{\frac{9}{16}\times \frac{5}{9}\times 25\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Multiply \frac{9}{16} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\times 5}{16\times 9}\times 25\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Cancel out 9 in both numerator and denominator.

$$\frac{\frac{5}{16}\times 25\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Express \frac{5}{16}\times 25 as a single fraction.

$$\frac{\frac{5\times 25}{16}\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Multiply 5 and 25 to get 125.

$$\frac{\frac{125}{16}\times \frac{23}{24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Multiply \frac{125}{16} times \frac{23}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{125\times 23}{16\times 24}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

Do the multiplications in the fraction \frac{125\times 23}{16\times 24}.

$$\frac{\frac{2875}{384}\left(\frac{1}{2}-\left(\frac{3}{4}-\frac{3}{5}\right)\right)}{\frac{7}{10}}$$

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

$$\frac{\frac{2875}{384}\left(\frac{1}{2}-\left(\frac{15}{20}-\frac{12}{20}\right)\right)}{\frac{7}{10}}$$

Since \frac{15}{20} and \frac{12}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2875}{384}\left(\frac{1}{2}-\frac{15-12}{20}\right)}{\frac{7}{10}}$$

Subtract 12 from 15 to get 3.

$$\frac{\frac{2875}{384}\left(\frac{1}{2}-\frac{3}{20}\right)}{\frac{7}{10}}$$

Least common multiple of 2 and 20 is 20. Convert \frac{1}{2} and \frac{3}{20} to fractions with denominator 20.

$$\frac{\frac{2875}{384}\left(\frac{10}{20}-\frac{3}{20}\right)}{\frac{7}{10}}$$

Since \frac{10}{20} and \frac{3}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2875}{384}\times \frac{10-3}{20}}{\frac{7}{10}}$$

Subtract 3 from 10 to get 7.

$$\frac{\frac{2875}{384}\times \frac{7}{20}}{\frac{7}{10}}$$

Multiply \frac{2875}{384} times \frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2875\times 7}{384\times 20}}{\frac{7}{10}}$$

Do the multiplications in the fraction \frac{2875\times 7}{384\times 20}.

$$\frac{\frac{20125}{7680}}{\frac{7}{10}}$$

Reduce the fraction \frac{20125}{7680} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{4025}{1536}}{\frac{7}{10}}$$

Divide \frac{4025}{1536} by \frac{7}{10} by multiplying \frac{4025}{1536} by the reciprocal of \frac{7}{10}.

$$\frac{4025}{1536}\times \frac{10}{7}$$

Multiply \frac{4025}{1536} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4025\times 10}{1536\times 7}$$

Do the multiplications in the fraction \frac{4025\times 10}{1536\times 7}.

$$\frac{40250}{10752}$$

Reduce the fraction \frac{40250}{10752} to lowest terms by extracting and canceling out 14.

$$\frac{2875}{768}$$

Factor

$$\frac{5 ^ {3} \cdot 23}{2 ^ {8} \cdot 3} = 3\frac{571}{768} = 3.7434895833333335$$