Solve 51/2text{of}(2/3-3/5)+1/2divfrac{5}{11}

$$5 \frac { 1 } { 2 } \text { of } ( \frac { 2 } { 3 } - \frac { 3 } { 5 } ) + \frac { 1 } { 2 } \div \frac { 5 } { 11 }$$

Evaluate

$$\frac{22}{15}\approx 1.466666667$$

Solution Steps

Multiply 5 and 2 to get 10.

$$\frac{10+1}{2}\left(\frac{2}{3}-\frac{3}{5}\right)+\frac{\frac{1}{2}}{\frac{5}{11}}$$

Add 10 and 1 to get 11.

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

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{11}{2}\left(\frac{10}{15}-\frac{9}{15}\right)+\frac{\frac{1}{2}}{\frac{5}{11}}$$

Since \frac{10}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{2}\times \frac{10-9}{15}+\frac{\frac{1}{2}}{\frac{5}{11}}$$

Subtract 9 from 10 to get 1.

$$\frac{11}{2}\times \frac{1}{15}+\frac{\frac{1}{2}}{\frac{5}{11}}$$

Multiply \frac{11}{2} times \frac{1}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 1}{2\times 15}+\frac{\frac{1}{2}}{\frac{5}{11}}$$

Do the multiplications in the fraction \frac{11\times 1}{2\times 15}.

$$\frac{11}{30}+\frac{\frac{1}{2}}{\frac{5}{11}}$$

Divide \frac{1}{2} by \frac{5}{11} by multiplying \frac{1}{2} by the reciprocal of \frac{5}{11}.

$$\frac{11}{30}+\frac{1}{2}\times \frac{11}{5}$$

Multiply \frac{1}{2} times \frac{11}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{30}+\frac{1\times 11}{2\times 5}$$

Do the multiplications in the fraction \frac{1\times 11}{2\times 5}.

$$\frac{11}{30}+\frac{11}{10}$$

Least common multiple of 30 and 10 is 30. Convert \frac{11}{30} and \frac{11}{10} to fractions with denominator 30.

$$\frac{11}{30}+\frac{33}{30}$$

Since \frac{11}{30} and \frac{33}{30} have the same denominator, add them by adding their numerators.

$$\frac{11+33}{30}$$

Add 11 and 33 to get 44.

$$\frac{44}{30}$$

Reduce the fraction \frac{44}{30} to lowest terms by extracting and canceling out 2.

$$\frac{22}{15}$$

Factor

$$\frac{2 \cdot 11}{3 \cdot 5} = 1\frac{7}{15} = 1.4666666666666666$$