Solve left(4/3-2/51/3right)1/4+frac{1}{2}

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

Evaluate

$$\frac{4}{5}=0.8$$

Solution Steps

Multiply \frac{2}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 1}{5\times 3}.

$$\left(\frac{4}{3}-\frac{2}{15}\right)\times \frac{1}{4}+\frac{1}{2}$$

Least common multiple of 3 and 15 is 15. Convert \frac{4}{3} and \frac{2}{15} to fractions with denominator 15.

$$\left(\frac{20}{15}-\frac{2}{15}\right)\times \frac{1}{4}+\frac{1}{2}$$

Since \frac{20}{15} and \frac{2}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-2}{15}\times \frac{1}{4}+\frac{1}{2}$$

Subtract 2 from 20 to get 18.

$$\frac{18}{15}\times \frac{1}{4}+\frac{1}{2}$$

Reduce the fraction \frac{18}{15} to lowest terms by extracting and canceling out 3.

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

Multiply \frac{6}{5} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{6\times 1}{5\times 4}.

$$\frac{6}{20}+\frac{1}{2}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{3}{10}+\frac{1}{2}$$

Least common multiple of 10 and 2 is 10. Convert \frac{3}{10} and \frac{1}{2} to fractions with denominator 10.

$$\frac{3}{10}+\frac{5}{10}$$

Since \frac{3}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{3+5}{10}$$

Add 3 and 5 to get 8.

$$\frac{8}{10}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}$$

Factor

$$\frac{2 ^ {2}}{5} = 0.8$$