Solve 12/3left(34/5-3/5+1/2-frac{1}{3}right)

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

Evaluate

$$\frac{101}{18}\approx 5.611111111$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Multiply 3 and 5 to get 15.

$$\frac{5}{3}\left(\frac{15+4}{5}-\frac{3}{5}+\frac{1}{2}-\frac{1}{3}\right)$$

Add 15 and 4 to get 19.

$$\frac{5}{3}\left(\frac{19}{5}-\frac{3}{5}+\frac{1}{2}-\frac{1}{3}\right)$$

Since \frac{19}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}\left(\frac{19-3}{5}+\frac{1}{2}-\frac{1}{3}\right)$$

Subtract 3 from 19 to get 16.

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

Least common multiple of 5 and 2 is 10. Convert \frac{16}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{5}{3}\left(\frac{32}{10}+\frac{5}{10}-\frac{1}{3}\right)$$

Since \frac{32}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{5}{3}\left(\frac{32+5}{10}-\frac{1}{3}\right)$$

Add 32 and 5 to get 37.

$$\frac{5}{3}\left(\frac{37}{10}-\frac{1}{3}\right)$$

Least common multiple of 10 and 3 is 30. Convert \frac{37}{10} and \frac{1}{3} to fractions with denominator 30.

$$\frac{5}{3}\left(\frac{111}{30}-\frac{10}{30}\right)$$

Since \frac{111}{30} and \frac{10}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}\times \frac{111-10}{30}$$

Subtract 10 from 111 to get 101.

$$\frac{5}{3}\times \frac{101}{30}$$

Multiply \frac{5}{3} times \frac{101}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 101}{3\times 30}$$

Do the multiplications in the fraction \frac{5\times 101}{3\times 30}.

$$\frac{505}{90}$$

Reduce the fraction \frac{505}{90} to lowest terms by extracting and canceling out 5.

$$\frac{101}{18}$$

Factor

$$\frac{101}{2 \cdot 3 ^ {2}} = 5\frac{11}{18} = 5.611111111111111$$