Solve (11/6+10/23)-(3/23-5/6)

$$( 1 \frac { 1 } { 6 } + \frac{ 10 }{ 23 } )-( \frac{ 3 }{ 23 } - \frac{ 5 }{ 6 } )$$

Evaluate

$$\frac{53}{23}\approx 2.304347826$$

Solution Steps

Multiply 1 and 6 to get 6.

$$\frac{6+1}{6}+\frac{10}{23}-\left(\frac{3}{23}-\frac{5}{6}\right)$$

Add 6 and 1 to get 7.

$$\frac{7}{6}+\frac{10}{23}-\left(\frac{3}{23}-\frac{5}{6}\right)$$

Least common multiple of 6 and 23 is 138. Convert \frac{7}{6} and \frac{10}{23} to fractions with denominator 138.

$$\frac{161}{138}+\frac{60}{138}-\left(\frac{3}{23}-\frac{5}{6}\right)$$

Since \frac{161}{138} and \frac{60}{138} have the same denominator, add them by adding their numerators.

$$\frac{161+60}{138}-\left(\frac{3}{23}-\frac{5}{6}\right)$$

Add 161 and 60 to get 221.

$$\frac{221}{138}-\left(\frac{3}{23}-\frac{5}{6}\right)$$

Least common multiple of 23 and 6 is 138. Convert \frac{3}{23} and \frac{5}{6} to fractions with denominator 138.

$$\frac{221}{138}-\left(\frac{18}{138}-\frac{115}{138}\right)$$

Since \frac{18}{138} and \frac{115}{138} have the same denominator, subtract them by subtracting their numerators.

$$\frac{221}{138}-\frac{18-115}{138}$$

Subtract 115 from 18 to get -97.

$$\frac{221}{138}-\left(-\frac{97}{138}\right)$$

The opposite of -\frac{97}{138} is \frac{97}{138}.

$$\frac{221}{138}+\frac{97}{138}$$

Since \frac{221}{138} and \frac{97}{138} have the same denominator, add them by adding their numerators.

$$\frac{221+97}{138}$$

Add 221 and 97 to get 318.

$$\frac{318}{138}$$

Reduce the fraction \frac{318}{138} to lowest terms by extracting and canceling out 6.

$$\frac{53}{23}$$

Factor

$$\frac{53}{23} = 2\frac{7}{23} = 2.3043478260869565$$