Solve 1/3quadtext{(11)}quad5/6-(1/2-1/3)

$$\frac { 1 } { 3 } \quad \text { (11) } \quad \frac { 5 } { 6 } - ( \frac { 1 } { 2 } - \frac { 1 } { 3 } )$$

Evaluate

$$\frac{26}{9}\approx 2.888888889$$

Solution Steps

Multiply \frac{1}{3} and 11 to get \frac{11}{3}.

$$\frac{11}{3}\times \frac{5}{6}-\left(\frac{1}{2}-\frac{1}{3}\right)$$

Multiply \frac{11}{3} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 5}{3\times 6}-\left(\frac{1}{2}-\frac{1}{3}\right)$$

Do the multiplications in the fraction \frac{11\times 5}{3\times 6}.

$$\frac{55}{18}-\left(\frac{1}{2}-\frac{1}{3}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{55}{18}-\left(\frac{3}{6}-\frac{2}{6}\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55}{18}-\frac{3-2}{6}$$

Subtract 2 from 3 to get 1.

$$\frac{55}{18}-\frac{1}{6}$$

Least common multiple of 18 and 6 is 18. Convert \frac{55}{18} and \frac{1}{6} to fractions with denominator 18.

$$\frac{55}{18}-\frac{3}{18}$$

Since \frac{55}{18} and \frac{3}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-3}{18}$$

Subtract 3 from 55 to get 52.

$$\frac{52}{18}$$

Reduce the fraction \frac{52}{18} to lowest terms by extracting and canceling out 2.

$$\frac{26}{9}$$

Factor

$$\frac{2 \cdot 13}{3 ^ {2}} = 2\frac{8}{9} = 2.888888888888889$$