Solve (3/1+1/5)-2/3*(3/5-frac{1}{10})

$$( \frac{ 3 }{ 1 } + \frac{ 1 }{ 5 } )- \frac{ 2 }{ 3 } \times ( \frac{ 3 }{ 5 } - \frac{ 1 }{ 10 } )$$

Evaluate

$$\frac{43}{15}\approx 2.866666667$$

Solution Steps

Anything divided by one gives itself.

$$3+\frac{1}{5}-\frac{2}{3}\left(\frac{3}{5}-\frac{1}{10}\right)$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{15}{5}+\frac{1}{5}-\frac{2}{3}\left(\frac{3}{5}-\frac{1}{10}\right)$$

Since \frac{15}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{15+1}{5}-\frac{2}{3}\left(\frac{3}{5}-\frac{1}{10}\right)$$

Add 15 and 1 to get 16.

$$\frac{16}{5}-\frac{2}{3}\left(\frac{3}{5}-\frac{1}{10}\right)$$

Least common multiple of 5 and 10 is 10. Convert \frac{3}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{16}{5}-\frac{2}{3}\left(\frac{6}{10}-\frac{1}{10}\right)$$

Since \frac{6}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16}{5}-\frac{2}{3}\times \frac{6-1}{10}$$

Subtract 1 from 6 to get 5.

$$\frac{16}{5}-\frac{2}{3}\times \frac{5}{10}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{16}{5}-\frac{2}{3}\times \frac{1}{2}$$

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

$$\frac{16}{5}-\frac{2\times 1}{3\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{16}{5}-\frac{1}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{16}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{48}{15}-\frac{5}{15}$$

Since \frac{48}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48-5}{15}$$

Subtract 5 from 48 to get 43.

$$\frac{43}{15}$$

Factor

$$\frac{43}{3 \cdot 5} = 2\frac{13}{15} = 2.8666666666666667$$