Solve 3+2/7[1-21/4:(3/5-2-7/2)]

$$3 + \frac { 2 } { 7 } [ 1 - \frac { 21 } { 4 } : ( \frac { 3 } { 5 } - 2 - \frac { 7 } { 2 } ) ]$$

Evaluate

$$\frac{176}{49}\approx 3.591836735$$

Solution Steps

Convert 2 to fraction \frac{10}{5}.

$$3+\frac{2}{7}\left(1-\frac{\frac{21}{4}}{\frac{3}{5}-\frac{10}{5}-\frac{7}{2}}\right)$$

Since \frac{3}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$3+\frac{2}{7}\left(1-\frac{\frac{21}{4}}{\frac{3-10}{5}-\frac{7}{2}}\right)$$

Subtract 10 from 3 to get -7.

$$3+\frac{2}{7}\left(1-\frac{\frac{21}{4}}{-\frac{7}{5}-\frac{7}{2}}\right)$$

Least common multiple of 5 and 2 is 10. Convert -\frac{7}{5} and \frac{7}{2} to fractions with denominator 10.

$$3+\frac{2}{7}\left(1-\frac{\frac{21}{4}}{-\frac{14}{10}-\frac{35}{10}}\right)$$

Since -\frac{14}{10} and \frac{35}{10} have the same denominator, subtract them by subtracting their numerators.

$$3+\frac{2}{7}\left(1-\frac{\frac{21}{4}}{\frac{-14-35}{10}}\right)$$

Subtract 35 from -14 to get -49.

$$3+\frac{2}{7}\left(1-\frac{\frac{21}{4}}{-\frac{49}{10}}\right)$$

Divide \frac{21}{4} by -\frac{49}{10} by multiplying \frac{21}{4} by the reciprocal of -\frac{49}{10}.

$$3+\frac{2}{7}\left(1-\frac{21}{4}\left(-\frac{10}{49}\right)\right)$$

Multiply \frac{21}{4} times -\frac{10}{49} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{2}{7}\left(1-\frac{21\left(-10\right)}{4\times 49}\right)$$

Do the multiplications in the fraction \frac{21\left(-10\right)}{4\times 49}.

$$3+\frac{2}{7}\left(1-\frac{-210}{196}\right)$$

Reduce the fraction \frac{-210}{196} to lowest terms by extracting and canceling out 14.

$$3+\frac{2}{7}\left(1-\left(-\frac{15}{14}\right)\right)$$

The opposite of -\frac{15}{14} is \frac{15}{14}.

$$3+\frac{2}{7}\left(1+\frac{15}{14}\right)$$

Convert 1 to fraction \frac{14}{14}.

$$3+\frac{2}{7}\left(\frac{14}{14}+\frac{15}{14}\right)$$

Since \frac{14}{14} and \frac{15}{14} have the same denominator, add them by adding their numerators.

$$3+\frac{2}{7}\times \frac{14+15}{14}$$

Add 14 and 15 to get 29.

$$3+\frac{2}{7}\times \frac{29}{14}$$

Multiply \frac{2}{7} times \frac{29}{14} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{2\times 29}{7\times 14}$$

Do the multiplications in the fraction \frac{2\times 29}{7\times 14}.

$$3+\frac{58}{98}$$

Reduce the fraction \frac{58}{98} to lowest terms by extracting and canceling out 2.

$$3+\frac{29}{49}$$

Convert 3 to fraction \frac{147}{49}.

$$\frac{147}{49}+\frac{29}{49}$$

Since \frac{147}{49} and \frac{29}{49} have the same denominator, add them by adding their numerators.

$$\frac{147+29}{49}$$

Add 147 and 29 to get 176.

$$\frac{176}{49}$$

Factor

$$\frac{2 ^ {4} \cdot 11}{7 ^ {2}} = 3\frac{29}{49} = 3.5918367346938775$$