Solve 8[2/3+1/4-2/5]=

$$8 [ \frac { 2 } { 3 } + \frac { 1 } { 4 } - \frac { 2 } { 5 } ] =$$

Evaluate

$$\frac{62}{15}\approx 4.133333333$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$8\left(\frac{8}{12}+\frac{3}{12}-\frac{2}{5}\right)$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$8\left(\frac{8+3}{12}-\frac{2}{5}\right)$$

Add 8 and 3 to get 11.

$$8\left(\frac{11}{12}-\frac{2}{5}\right)$$

Least common multiple of 12 and 5 is 60. Convert \frac{11}{12} and \frac{2}{5} to fractions with denominator 60.

$$8\left(\frac{55}{60}-\frac{24}{60}\right)$$

Since \frac{55}{60} and \frac{24}{60} have the same denominator, subtract them by subtracting their numerators.

$$8\times \frac{55-24}{60}$$

Subtract 24 from 55 to get 31.

$$8\times \frac{31}{60}$$

Express 8\times \frac{31}{60} as a single fraction.

$$\frac{8\times 31}{60}$$

Multiply 8 and 31 to get 248.

$$\frac{248}{60}$$

Reduce the fraction \frac{248}{60} to lowest terms by extracting and canceling out 4.

$$\frac{62}{15}$$

Factor

$$\frac{2 \cdot 31}{3 \cdot 5} = 4\frac{2}{15} = 4.133333333333334$$