Solve 21/4-1/15[21/8-(11/4-frac{1}{6})]

$$2 \frac { 1 } { 4 } - \frac { 1 } { 15 } [ 2 \frac { 1 } { 8 } - ( 1 \frac { 1 } { 4 } - \frac { 1 } { 6 } ) ]$$

Evaluate

$$\frac{157}{72}\approx 2.180555556$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8+1}{4}-\frac{1}{15}\left(\frac{2\times 8+1}{8}-\left(\frac{1\times 4+1}{4}-\frac{1}{6}\right)\right)$$

Add 8 and 1 to get 9.

$$\frac{9}{4}-\frac{1}{15}\left(\frac{2\times 8+1}{8}-\left(\frac{1\times 4+1}{4}-\frac{1}{6}\right)\right)$$

Multiply 2 and 8 to get 16.

$$\frac{9}{4}-\frac{1}{15}\left(\frac{16+1}{8}-\left(\frac{1\times 4+1}{4}-\frac{1}{6}\right)\right)$$

Add 16 and 1 to get 17.

$$\frac{9}{4}-\frac{1}{15}\left(\frac{17}{8}-\left(\frac{1\times 4+1}{4}-\frac{1}{6}\right)\right)$$

Multiply 1 and 4 to get 4.

$$\frac{9}{4}-\frac{1}{15}\left(\frac{17}{8}-\left(\frac{4+1}{4}-\frac{1}{6}\right)\right)$$

Add 4 and 1 to get 5.

$$\frac{9}{4}-\frac{1}{15}\left(\frac{17}{8}-\left(\frac{5}{4}-\frac{1}{6}\right)\right)$$

Least common multiple of 4 and 6 is 12. Convert \frac{5}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{9}{4}-\frac{1}{15}\left(\frac{17}{8}-\left(\frac{15}{12}-\frac{2}{12}\right)\right)$$

Since \frac{15}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{4}-\frac{1}{15}\left(\frac{17}{8}-\frac{15-2}{12}\right)$$

Subtract 2 from 15 to get 13.

$$\frac{9}{4}-\frac{1}{15}\left(\frac{17}{8}-\frac{13}{12}\right)$$

Least common multiple of 8 and 12 is 24. Convert \frac{17}{8} and \frac{13}{12} to fractions with denominator 24.

$$\frac{9}{4}-\frac{1}{15}\left(\frac{51}{24}-\frac{26}{24}\right)$$

Since \frac{51}{24} and \frac{26}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{4}-\frac{1}{15}\times \frac{51-26}{24}$$

Subtract 26 from 51 to get 25.

$$\frac{9}{4}-\frac{1}{15}\times \frac{25}{24}$$

Multiply \frac{1}{15} times \frac{25}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{4}-\frac{1\times 25}{15\times 24}$$

Do the multiplications in the fraction \frac{1\times 25}{15\times 24}.

$$\frac{9}{4}-\frac{25}{360}$$

Reduce the fraction \frac{25}{360} to lowest terms by extracting and canceling out 5.

$$\frac{9}{4}-\frac{5}{72}$$

Least common multiple of 4 and 72 is 72. Convert \frac{9}{4} and \frac{5}{72} to fractions with denominator 72.

$$\frac{162}{72}-\frac{5}{72}$$

Since \frac{162}{72} and \frac{5}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{162-5}{72}$$

Subtract 5 from 162 to get 157.

$$\frac{157}{72}$$

Factor

$$\frac{157}{2 ^ {3} \cdot 3 ^ {2}} = 2\frac{13}{72} = 2.1805555555555554$$