Solve [22/3*{21/4div(11/8+21/4-1frac{1}{2})}]-1frac{2}{3}-frac{2}{5}

$$[ 2 \frac { 2 } { 3 } \times \{ 2 \frac { 1 } { 4 } \div ( 1 \frac { 1 } { 8 } + 2 \frac { 1 } { 4 } - 1 \frac { 1 } { 2 } ) \} ] - 1 \frac { 2 } { 3 } - \frac { 2 } { 5 }$$

Evaluate

$$\frac{17}{15}\approx 1.133333333$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6+2}{3}\times \frac{\frac{2\times 4+1}{4}}{\frac{1\times 8+1}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Add 6 and 2 to get 8.

$$\frac{8}{3}\times \frac{\frac{2\times 4+1}{4}}{\frac{1\times 8+1}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Multiply 2 and 4 to get 8.

$$\frac{8}{3}\times \frac{\frac{8+1}{4}}{\frac{1\times 8+1}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Add 8 and 1 to get 9.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{1\times 8+1}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Multiply 1 and 8 to get 8.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{8+1}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Add 8 and 1 to get 9.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Multiply 2 and 4 to get 8.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9}{8}+\frac{8+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Add 8 and 1 to get 9.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9}{8}+\frac{9}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Least common multiple of 8 and 4 is 8. Convert \frac{9}{8} and \frac{9}{4} to fractions with denominator 8.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9}{8}+\frac{18}{8}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Since \frac{9}{8} and \frac{18}{8} have the same denominator, add them by adding their numerators.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9+18}{8}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Add 9 and 18 to get 27.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27}{8}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Multiply 1 and 2 to get 2.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27}{8}-\frac{2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Add 2 and 1 to get 3.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27}{8}-\frac{3}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Least common multiple of 8 and 2 is 8. Convert \frac{27}{8} and \frac{3}{2} to fractions with denominator 8.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27}{8}-\frac{12}{8}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Since \frac{27}{8} and \frac{12}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27-12}{8}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Subtract 12 from 27 to get 15.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{15}{8}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Divide \frac{9}{4} by \frac{15}{8} by multiplying \frac{9}{4} by the reciprocal of \frac{15}{8}.

$$\frac{8}{3}\times \frac{9}{4}\times \frac{8}{15}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Multiply \frac{9}{4} times \frac{8}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{3}\times \frac{9\times 8}{4\times 15}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Do the multiplications in the fraction \frac{9\times 8}{4\times 15}.

$$\frac{8}{3}\times \frac{72}{60}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Reduce the fraction \frac{72}{60} to lowest terms by extracting and canceling out 12.

$$\frac{8}{3}\times \frac{6}{5}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Multiply \frac{8}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 6}{3\times 5}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Do the multiplications in the fraction \frac{8\times 6}{3\times 5}.

$$\frac{48}{15}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Reduce the fraction \frac{48}{15} to lowest terms by extracting and canceling out 3.

$$\frac{16}{5}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Multiply 1 and 3 to get 3.

$$\frac{16}{5}-\frac{3+2}{3}-\frac{2}{5}$$

Add 3 and 2 to get 5.

$$\frac{16}{5}-\frac{5}{3}-\frac{2}{5}$$

Least common multiple of 5 and 3 is 15. Convert \frac{16}{5} and \frac{5}{3} to fractions with denominator 15.

$$\frac{48}{15}-\frac{25}{15}-\frac{2}{5}$$

Since \frac{48}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48-25}{15}-\frac{2}{5}$$

Subtract 25 from 48 to get 23.

$$\frac{23}{15}-\frac{2}{5}$$

Least common multiple of 15 and 5 is 15. Convert \frac{23}{15} and \frac{2}{5} to fractions with denominator 15.

$$\frac{23}{15}-\frac{6}{15}$$

Since \frac{23}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23-6}{15}$$

Subtract 6 from 23 to get 17.

$$\frac{17}{15}$$

Factor

$$\frac{17}{3 \cdot 5} = 1\frac{2}{15} = 1.1333333333333333$$