Solve 41/10[21/2-{5/6-(2/5+frac{3}{10}-frac{4}{15})}]

$$4 \frac { 1 } { 10 } [ 2 \frac { 1 } { 2 } - \{ \frac { 5 } { 6 } - ( \frac { 2 } { 5 } + \frac { 3 } { 10 } - \frac { 4 } { 15 } ) \} ]$$

Evaluate

$$\frac{861}{100}=8.61$$

Solution Steps

Multiply 4 and 10 to get 40.

$$\frac{40+1}{10}\left(\frac{2\times 2+1}{2}-\left(\frac{5}{6}-\left(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\right)\right)\right)$$

Add 40 and 1 to get 41.

$$\frac{41}{10}\left(\frac{2\times 2+1}{2}-\left(\frac{5}{6}-\left(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\right)\right)\right)$$

Multiply 2 and 2 to get 4.

$$\frac{41}{10}\left(\frac{4+1}{2}-\left(\frac{5}{6}-\left(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\right)\right)\right)$$

Add 4 and 1 to get 5.

$$\frac{41}{10}\left(\frac{5}{2}-\left(\frac{5}{6}-\left(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\right)\right)\right)$$

Least common multiple of 5 and 10 is 10. Convert \frac{2}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{41}{10}\left(\frac{5}{2}-\left(\frac{5}{6}-\left(\frac{4}{10}+\frac{3}{10}-\frac{4}{15}\right)\right)\right)$$

Since \frac{4}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{41}{10}\left(\frac{5}{2}-\left(\frac{5}{6}-\left(\frac{4+3}{10}-\frac{4}{15}\right)\right)\right)$$

Add 4 and 3 to get 7.

$$\frac{41}{10}\left(\frac{5}{2}-\left(\frac{5}{6}-\left(\frac{7}{10}-\frac{4}{15}\right)\right)\right)$$

Least common multiple of 10 and 15 is 30. Convert \frac{7}{10} and \frac{4}{15} to fractions with denominator 30.

$$\frac{41}{10}\left(\frac{5}{2}-\left(\frac{5}{6}-\left(\frac{21}{30}-\frac{8}{30}\right)\right)\right)$$

Since \frac{21}{30} and \frac{8}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41}{10}\left(\frac{5}{2}-\left(\frac{5}{6}-\frac{21-8}{30}\right)\right)$$

Subtract 8 from 21 to get 13.

$$\frac{41}{10}\left(\frac{5}{2}-\left(\frac{5}{6}-\frac{13}{30}\right)\right)$$

Least common multiple of 6 and 30 is 30. Convert \frac{5}{6} and \frac{13}{30} to fractions with denominator 30.

$$\frac{41}{10}\left(\frac{5}{2}-\left(\frac{25}{30}-\frac{13}{30}\right)\right)$$

Since \frac{25}{30} and \frac{13}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41}{10}\left(\frac{5}{2}-\frac{25-13}{30}\right)$$

Subtract 13 from 25 to get 12.

$$\frac{41}{10}\left(\frac{5}{2}-\frac{12}{30}\right)$$

Reduce the fraction \frac{12}{30} to lowest terms by extracting and canceling out 6.

$$\frac{41}{10}\left(\frac{5}{2}-\frac{2}{5}\right)$$

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

$$\frac{41}{10}\left(\frac{25}{10}-\frac{4}{10}\right)$$

Since \frac{25}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41}{10}\times \frac{25-4}{10}$$

Subtract 4 from 25 to get 21.

$$\frac{41}{10}\times \frac{21}{10}$$

Multiply \frac{41}{10} times \frac{21}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41\times 21}{10\times 10}$$

Do the multiplications in the fraction \frac{41\times 21}{10\times 10}.

$$\frac{861}{100}$$

Factor

$$\frac{3 \cdot 7 \cdot 41}{2 ^ {2} \cdot 5 ^ {2}} = 8\frac{61}{100} = 8.61$$