Solve 6/10+(2/9+15/90-25/90):frac{3}{9}

$$\frac { 6 } { 10 } + ( \frac { 2 } { 9 } + \frac { 15 } { 90 } - \frac { 25 } { 90 } ) : \frac { 3 } { 9 }$$

Evaluate

$$\frac{14}{15}\approx 0.933333333$$

Solution Steps

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{5}+\frac{\frac{2}{9}+\frac{15}{90}-\frac{25}{90}}{\frac{3}{9}}$$

Reduce the fraction \frac{15}{90} to lowest terms by extracting and canceling out 15.

$$\frac{3}{5}+\frac{\frac{2}{9}+\frac{1}{6}-\frac{25}{90}}{\frac{3}{9}}$$

Least common multiple of 9 and 6 is 18. Convert \frac{2}{9} and \frac{1}{6} to fractions with denominator 18.

$$\frac{3}{5}+\frac{\frac{4}{18}+\frac{3}{18}-\frac{25}{90}}{\frac{3}{9}}$$

Since \frac{4}{18} and \frac{3}{18} have the same denominator, add them by adding their numerators.

$$\frac{3}{5}+\frac{\frac{4+3}{18}-\frac{25}{90}}{\frac{3}{9}}$$

Add 4 and 3 to get 7.

$$\frac{3}{5}+\frac{\frac{7}{18}-\frac{25}{90}}{\frac{3}{9}}$$

Reduce the fraction \frac{25}{90} to lowest terms by extracting and canceling out 5.

$$\frac{3}{5}+\frac{\frac{7}{18}-\frac{5}{18}}{\frac{3}{9}}$$

Since \frac{7}{18} and \frac{5}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{5}+\frac{\frac{7-5}{18}}{\frac{3}{9}}$$

Subtract 5 from 7 to get 2.

$$\frac{3}{5}+\frac{\frac{2}{18}}{\frac{3}{9}}$$

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

$$\frac{3}{5}+\frac{\frac{1}{9}}{\frac{3}{9}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{3}{5}+\frac{\frac{1}{9}}{\frac{1}{3}}$$

Divide \frac{1}{9} by \frac{1}{3} by multiplying \frac{1}{9} by the reciprocal of \frac{1}{3}.

$$\frac{3}{5}+\frac{1}{9}\times 3$$

Multiply \frac{1}{9} and 3 to get \frac{3}{9}.

$$\frac{3}{5}+\frac{3}{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{3}{5}+\frac{1}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{9}{15}+\frac{5}{15}$$

Since \frac{9}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{9+5}{15}$$

Add 9 and 5 to get 14.

$$\frac{14}{15}$$

Factor

$$\frac{2 \cdot 7}{3 \cdot 5} = 0.9333333333333333$$