Solve 1/3(3/2+3/5-2/2)quad52

$$\frac { 1 } { 3 } ( \frac { 3 } { 2 } + \frac { 3 } { 5 } - \frac { 2 } { 2 } ) \quad 52$$

Evaluate

$$\frac{286}{15}\approx 19.066666667$$

Solution Steps

Divide 2 by 2 to get 1.

$$\frac{1}{3}\left(\frac{3}{2}+\frac{3}{5}-1\right)\times 52$$

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{3}{5} to fractions with denominator 10.

$$\frac{1}{3}\left(\frac{15}{10}+\frac{6}{10}-1\right)\times 52$$

Since \frac{15}{10} and \frac{6}{10} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}\left(\frac{15+6}{10}-1\right)\times 52$$

Add 15 and 6 to get 21.

$$\frac{1}{3}\left(\frac{21}{10}-1\right)\times 52$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{1}{3}\left(\frac{21}{10}-\frac{10}{10}\right)\times 52$$

Since \frac{21}{10} and \frac{10}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{21-10}{10}\times 52$$

Subtract 10 from 21 to get 11.

$$\frac{1}{3}\times \frac{11}{10}\times 52$$

Multiply \frac{1}{3} times \frac{11}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 11}{3\times 10}\times 52$$

Do the multiplications in the fraction \frac{1\times 11}{3\times 10}.

$$\frac{11}{30}\times 52$$

Express \frac{11}{30}\times 52 as a single fraction.

$$\frac{11\times 52}{30}$$

Multiply 11 and 52 to get 572.

$$\frac{572}{30}$$

Reduce the fraction \frac{572}{30} to lowest terms by extracting and canceling out 2.

$$\frac{286}{15}$$

Factor

$$\frac{2 \cdot 11 \cdot 13}{3 \cdot 5} = 19\frac{1}{15} = 19.066666666666666$$