Solve 5-[3/4+{21/2-(1/2+1/6-frac{1}{7})}]=?

$$5 - [ \frac { 3 } { 4 } + \{ 2 \frac { 1 } { 2 } - ( \frac { 1 } { 2 } + \frac { 1 } { 6 } - \frac { 1 } { 7 } ) \} ] = ?$$

Evaluate

$$\frac{191}{84}\approx 2.273809524$$

Solution Steps

Multiply 2 and 2 to get 4.

$$5-\left(\frac{3}{4}+\frac{4+1}{2}-\left(\frac{1}{2}+\frac{1}{6}-\frac{1}{7}\right)\right)$$

Add 4 and 1 to get 5.

$$5-\left(\frac{3}{4}+\frac{5}{2}-\left(\frac{1}{2}+\frac{1}{6}-\frac{1}{7}\right)\right)$$

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

$$5-\left(\frac{3}{4}+\frac{5}{2}-\left(\frac{3}{6}+\frac{1}{6}-\frac{1}{7}\right)\right)$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$5-\left(\frac{3}{4}+\frac{5}{2}-\left(\frac{3+1}{6}-\frac{1}{7}\right)\right)$$

Add 3 and 1 to get 4.

$$5-\left(\frac{3}{4}+\frac{5}{2}-\left(\frac{4}{6}-\frac{1}{7}\right)\right)$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 3 and 7 is 21. Convert \frac{2}{3} and \frac{1}{7} to fractions with denominator 21.

$$5-\left(\frac{3}{4}+\frac{5}{2}-\left(\frac{14}{21}-\frac{3}{21}\right)\right)$$

Since \frac{14}{21} and \frac{3}{21} have the same denominator, subtract them by subtracting their numerators.

$$5-\left(\frac{3}{4}+\frac{5}{2}-\frac{14-3}{21}\right)$$

Subtract 3 from 14 to get 11.

$$5-\left(\frac{3}{4}+\frac{5}{2}-\frac{11}{21}\right)$$

Least common multiple of 2 and 21 is 42. Convert \frac{5}{2} and \frac{11}{21} to fractions with denominator 42.

$$5-\left(\frac{3}{4}+\frac{105}{42}-\frac{22}{42}\right)$$

Since \frac{105}{42} and \frac{22}{42} have the same denominator, subtract them by subtracting their numerators.

$$5-\left(\frac{3}{4}+\frac{105-22}{42}\right)$$

Subtract 22 from 105 to get 83.

$$5-\left(\frac{3}{4}+\frac{83}{42}\right)$$

Least common multiple of 4 and 42 is 84. Convert \frac{3}{4} and \frac{83}{42} to fractions with denominator 84.

$$5-\left(\frac{63}{84}+\frac{166}{84}\right)$$

Since \frac{63}{84} and \frac{166}{84} have the same denominator, add them by adding their numerators.

$$5-\frac{63+166}{84}$$

Add 63 and 166 to get 229.

$$5-\frac{229}{84}$$

Convert 5 to fraction \frac{420}{84}.

$$\frac{420}{84}-\frac{229}{84}$$

Since \frac{420}{84} and \frac{229}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{420-229}{84}$$

Subtract 229 from 420 to get 191.

$$\frac{191}{84}$$

Factor

$$\frac{191}{2 ^ {2} \cdot 3 \cdot 7} = 2\frac{23}{84} = 2.2738095238095237$$