Solve 7/4-[(-9/4+5/6):(-7/10*frac{10}{2})]

$$\frac { 7 } { 4 } - [ ( - \frac { 9 } { 4 } + \frac { 5 } { 6 } ) : ( \frac { - 7 } { 10 } \times \frac { 10 } { 2 } ) ]$$

Evaluate

$$\frac{113}{84}\approx 1.345238095$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert -\frac{9}{4} and \frac{5}{6} to fractions with denominator 12.

$$\frac{7}{4}-\frac{-\frac{27}{12}+\frac{10}{12}}{\frac{-7}{10}\times \frac{10}{2}}$$

Since -\frac{27}{12} and \frac{10}{12} have the same denominator, add them by adding their numerators.

$$\frac{7}{4}-\frac{\frac{-27+10}{12}}{\frac{-7}{10}\times \frac{10}{2}}$$

Add -27 and 10 to get -17.

$$\frac{7}{4}-\frac{-\frac{17}{12}}{\frac{-7}{10}\times \frac{10}{2}}$$

Fraction \frac{-7}{10} can be rewritten as -\frac{7}{10} by extracting the negative sign.

$$\frac{7}{4}-\frac{-\frac{17}{12}}{-\frac{7}{10}\times \frac{10}{2}}$$

Divide 10 by 2 to get 5.

$$\frac{7}{4}-\frac{-\frac{17}{12}}{-\frac{7}{10}\times 5}$$

Express -\frac{7}{10}\times 5 as a single fraction.

$$\frac{7}{4}-\frac{-\frac{17}{12}}{\frac{-7\times 5}{10}}$$

Multiply -7 and 5 to get -35.

$$\frac{7}{4}-\frac{-\frac{17}{12}}{\frac{-35}{10}}$$

Reduce the fraction \frac{-35}{10} to lowest terms by extracting and canceling out 5.

$$\frac{7}{4}-\frac{-\frac{17}{12}}{-\frac{7}{2}}$$

Divide -\frac{17}{12} by -\frac{7}{2} by multiplying -\frac{17}{12} by the reciprocal of -\frac{7}{2}.

$$\frac{7}{4}-\left(-\frac{17}{12}\left(-\frac{2}{7}\right)\right)$$

Multiply -\frac{17}{12} times -\frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{4}-\frac{-17\left(-2\right)}{12\times 7}$$

Do the multiplications in the fraction \frac{-17\left(-2\right)}{12\times 7}.

$$\frac{7}{4}-\frac{34}{84}$$

Reduce the fraction \frac{34}{84} to lowest terms by extracting and canceling out 2.

$$\frac{7}{4}-\frac{17}{42}$$

Least common multiple of 4 and 42 is 84. Convert \frac{7}{4} and \frac{17}{42} to fractions with denominator 84.

$$\frac{147}{84}-\frac{34}{84}$$

Since \frac{147}{84} and \frac{34}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{147-34}{84}$$

Subtract 34 from 147 to get 113.

$$\frac{113}{84}$$

Factor

$$\frac{113}{2 ^ {2} \cdot 3 \cdot 7} = 1\frac{29}{84} = 1.3452380952380953$$