Solve 8left(1/3+1/4-2/5+1/3right)

$$8 \left( \frac{ 1 }{ 3 } + \frac{ 1 }{ 4 } - \frac{ 2 }{ 5 } + \frac{ 1 }{ 3 } \right)$$

Evaluate

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

Solution Steps

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

$$8\left(\frac{4}{12}+\frac{3}{12}-\frac{2}{5}+\frac{1}{3}\right)$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$8\left(\frac{4+3}{12}-\frac{2}{5}+\frac{1}{3}\right)$$

Add 4 and 3 to get 7.

$$8\left(\frac{7}{12}-\frac{2}{5}+\frac{1}{3}\right)$$

Least common multiple of 12 and 5 is 60. Convert \frac{7}{12} and \frac{2}{5} to fractions with denominator 60.

$$8\left(\frac{35}{60}-\frac{24}{60}+\frac{1}{3}\right)$$

Since \frac{35}{60} and \frac{24}{60} have the same denominator, subtract them by subtracting their numerators.

$$8\left(\frac{35-24}{60}+\frac{1}{3}\right)$$

Subtract 24 from 35 to get 11.

$$8\left(\frac{11}{60}+\frac{1}{3}\right)$$

Least common multiple of 60 and 3 is 60. Convert \frac{11}{60} and \frac{1}{3} to fractions with denominator 60.

$$8\left(\frac{11}{60}+\frac{20}{60}\right)$$

Since \frac{11}{60} and \frac{20}{60} have the same denominator, add them by adding their numerators.

$$8\times \frac{11+20}{60}$$

Add 11 and 20 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

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