Solve (2-11/5)*31/3+11/8

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

Evaluate

$$\frac{91}{24}\approx 3.791666667$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\left(2-\frac{5+1}{5}\right)\times \frac{3\times 3+1}{3}+\frac{1\times 8+1}{8}$$

Add 5 and 1 to get 6.

$$\left(2-\frac{6}{5}\right)\times \frac{3\times 3+1}{3}+\frac{1\times 8+1}{8}$$

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

$$\left(\frac{10}{5}-\frac{6}{5}\right)\times \frac{3\times 3+1}{3}+\frac{1\times 8+1}{8}$$

Since \frac{10}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-6}{5}\times \frac{3\times 3+1}{3}+\frac{1\times 8+1}{8}$$

Subtract 6 from 10 to get 4.

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

Multiply 3 and 3 to get 9.

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

Add 9 and 1 to get 10.

$$\frac{4}{5}\times \frac{10}{3}+\frac{1\times 8+1}{8}$$

Multiply \frac{4}{5} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 10}{5\times 3}+\frac{1\times 8+1}{8}$$

Do the multiplications in the fraction \frac{4\times 10}{5\times 3}.

$$\frac{40}{15}+\frac{1\times 8+1}{8}$$

Reduce the fraction \frac{40}{15} to lowest terms by extracting and canceling out 5.

$$\frac{8}{3}+\frac{1\times 8+1}{8}$$

Multiply 1 and 8 to get 8.

$$\frac{8}{3}+\frac{8+1}{8}$$

Add 8 and 1 to get 9.

$$\frac{8}{3}+\frac{9}{8}$$

Least common multiple of 3 and 8 is 24. Convert \frac{8}{3} and \frac{9}{8} to fractions with denominator 24.

$$\frac{64}{24}+\frac{27}{24}$$

Since \frac{64}{24} and \frac{27}{24} have the same denominator, add them by adding their numerators.

$$\frac{64+27}{24}$$

Add 64 and 27 to get 91.

$$\frac{91}{24}$$

Factor

$$\frac{7 \cdot 13}{2 ^ {3} \cdot 3} = 3\frac{19}{24} = 3.7916666666666665$$