Solve 2/5+5-2(2/8+1/6)

$$\frac{ 2 }{ 5 } +5-2( \frac{ 2 }{ 8 } + \frac{ 1 }{ 6 } )$$

Evaluate

$$\frac{137}{30}\approx 4.566666667$$

Solution Steps

Convert 5 to fraction \frac{25}{5}.

$$\frac{2}{5}+\frac{25}{5}-2\left(\frac{2}{8}+\frac{1}{6}\right)$$

Since \frac{2}{5} and \frac{25}{5} have the same denominator, add them by adding their numerators.

$$\frac{2+25}{5}-2\left(\frac{2}{8}+\frac{1}{6}\right)$$

Add 2 and 25 to get 27.

$$\frac{27}{5}-2\left(\frac{2}{8}+\frac{1}{6}\right)$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{27}{5}-2\left(\frac{1}{4}+\frac{1}{6}\right)$$

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

$$\frac{27}{5}-2\left(\frac{3}{12}+\frac{2}{12}\right)$$

Since \frac{3}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{27}{5}-2\times \frac{3+2}{12}$$

Add 3 and 2 to get 5.

$$\frac{27}{5}-2\times \frac{5}{12}$$

Express 2\times \frac{5}{12} as a single fraction.

$$\frac{27}{5}-\frac{2\times 5}{12}$$

Multiply 2 and 5 to get 10.

$$\frac{27}{5}-\frac{10}{12}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$\frac{27}{5}-\frac{5}{6}$$

Least common multiple of 5 and 6 is 30. Convert \frac{27}{5} and \frac{5}{6} to fractions with denominator 30.

$$\frac{162}{30}-\frac{25}{30}$$

Since \frac{162}{30} and \frac{25}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{162-25}{30}$$

Subtract 25 from 162 to get 137.

$$\frac{137}{30}$$

Factor

$$\frac{137}{2 \cdot 3 \cdot 5} = 4\frac{17}{30} = 4.566666666666666$$