Solve 27/8+11/5/8-2frac{1{4}}

$$\frac { 2 \frac { 7 } { 8 } + 1 \frac { 1 } { 5 } } { 8 - 2 \frac { 1 } { 4 } }$$

Evaluate

$$\frac{163}{230}\approx 0.708695652$$

Solution Steps

Multiply 2 and 8 to get 16.

$$\frac{\frac{16+7}{8}+\frac{1\times 5+1}{5}}{8-\frac{2\times 4+1}{4}}$$

Add 16 and 7 to get 23.

$$\frac{\frac{23}{8}+\frac{1\times 5+1}{5}}{8-\frac{2\times 4+1}{4}}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{23}{8}+\frac{5+1}{5}}{8-\frac{2\times 4+1}{4}}$$

Add 5 and 1 to get 6.

$$\frac{\frac{23}{8}+\frac{6}{5}}{8-\frac{2\times 4+1}{4}}$$

Least common multiple of 8 and 5 is 40. Convert \frac{23}{8} and \frac{6}{5} to fractions with denominator 40.

$$\frac{\frac{115}{40}+\frac{48}{40}}{8-\frac{2\times 4+1}{4}}$$

Since \frac{115}{40} and \frac{48}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{115+48}{40}}{8-\frac{2\times 4+1}{4}}$$

Add 115 and 48 to get 163.

$$\frac{\frac{163}{40}}{8-\frac{2\times 4+1}{4}}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{163}{40}}{8-\frac{8+1}{4}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{163}{40}}{8-\frac{9}{4}}$$

Convert 8 to fraction \frac{32}{4}.

$$\frac{\frac{163}{40}}{\frac{32}{4}-\frac{9}{4}}$$

Since \frac{32}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{163}{40}}{\frac{32-9}{4}}$$

Subtract 9 from 32 to get 23.

$$\frac{\frac{163}{40}}{\frac{23}{4}}$$

Divide \frac{163}{40} by \frac{23}{4} by multiplying \frac{163}{40} by the reciprocal of \frac{23}{4}.

$$\frac{163}{40}\times \frac{4}{23}$$

Multiply \frac{163}{40} times \frac{4}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{163\times 4}{40\times 23}$$

Do the multiplications in the fraction \frac{163\times 4}{40\times 23}.

$$\frac{652}{920}$$

Reduce the fraction \frac{652}{920} to lowest terms by extracting and canceling out 4.

$$\frac{163}{230}$$

Factor

$$\frac{163}{2 \cdot 5 \cdot 23} = 0.7086956521739131$$