Solve 9/4-21/8:(-3/8+6/5-frac{25}{12})=

$$\frac { 9 } { 4 } - \frac { 21 } { 8 } : ( - \frac { 3 } { 8 } + \frac { 6 } { 5 } - \frac { 25 } { 12 } ) =$$

Evaluate

$$\frac{2619}{604}\approx 4.336092715$$

Solution Steps

Least common multiple of 8 and 5 is 40. Convert -\frac{3}{8} and \frac{6}{5} to fractions with denominator 40.

$$\frac{9}{4}-\frac{\frac{21}{8}}{-\frac{15}{40}+\frac{48}{40}-\frac{25}{12}}$$

Since -\frac{15}{40} and \frac{48}{40} have the same denominator, add them by adding their numerators.

$$\frac{9}{4}-\frac{\frac{21}{8}}{\frac{-15+48}{40}-\frac{25}{12}}$$

Add -15 and 48 to get 33.

$$\frac{9}{4}-\frac{\frac{21}{8}}{\frac{33}{40}-\frac{25}{12}}$$

Least common multiple of 40 and 12 is 120. Convert \frac{33}{40} and \frac{25}{12} to fractions with denominator 120.

$$\frac{9}{4}-\frac{\frac{21}{8}}{\frac{99}{120}-\frac{250}{120}}$$

Since \frac{99}{120} and \frac{250}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{4}-\frac{\frac{21}{8}}{\frac{99-250}{120}}$$

Subtract 250 from 99 to get -151.

$$\frac{9}{4}-\frac{\frac{21}{8}}{-\frac{151}{120}}$$

Divide \frac{21}{8} by -\frac{151}{120} by multiplying \frac{21}{8} by the reciprocal of -\frac{151}{120}.

$$\frac{9}{4}-\frac{21}{8}\left(-\frac{120}{151}\right)$$

Multiply \frac{21}{8} times -\frac{120}{151} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{4}-\frac{21\left(-120\right)}{8\times 151}$$

Do the multiplications in the fraction \frac{21\left(-120\right)}{8\times 151}.

$$\frac{9}{4}-\frac{-2520}{1208}$$

Reduce the fraction \frac{-2520}{1208} to lowest terms by extracting and canceling out 8.

$$\frac{9}{4}-\left(-\frac{315}{151}\right)$$

The opposite of -\frac{315}{151} is \frac{315}{151}.

$$\frac{9}{4}+\frac{315}{151}$$

Least common multiple of 4 and 151 is 604. Convert \frac{9}{4} and \frac{315}{151} to fractions with denominator 604.

$$\frac{1359}{604}+\frac{1260}{604}$$

Since \frac{1359}{604} and \frac{1260}{604} have the same denominator, add them by adding their numerators.

$$\frac{1359+1260}{604}$$

Add 1359 and 1260 to get 2619.

$$\frac{2619}{604}$$

Factor

$$\frac{3 ^ {3} \cdot 97}{2 ^ {2} \cdot 151} = 4\frac{203}{604} = 4.336092715231788$$