Solve 21/3*2/5-6/5:18/25-frac{10}{25}=

$$2 \frac { 1 } { 3 } \cdot \frac { 2 } { 5 } - \frac { 6 } { 5 } : \frac { 18 } { 25 } - \frac { 10 } { 25 } =$$

Evaluate

$$-\frac{17}{15}\approx -1.133333333$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6+1}{3}\times \frac{2}{5}-\frac{\frac{6}{5}}{\frac{18}{25}}-\frac{10}{25}$$

Add 6 and 1 to get 7.

$$\frac{7}{3}\times \frac{2}{5}-\frac{\frac{6}{5}}{\frac{18}{25}}-\frac{10}{25}$$

Multiply \frac{7}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 2}{3\times 5}-\frac{\frac{6}{5}}{\frac{18}{25}}-\frac{10}{25}$$

Do the multiplications in the fraction \frac{7\times 2}{3\times 5}.

$$\frac{14}{15}-\frac{\frac{6}{5}}{\frac{18}{25}}-\frac{10}{25}$$

Divide \frac{6}{5} by \frac{18}{25} by multiplying \frac{6}{5} by the reciprocal of \frac{18}{25}.

$$\frac{14}{15}-\frac{6}{5}\times \frac{25}{18}-\frac{10}{25}$$

Multiply \frac{6}{5} times \frac{25}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14}{15}-\frac{6\times 25}{5\times 18}-\frac{10}{25}$$

Do the multiplications in the fraction \frac{6\times 25}{5\times 18}.

$$\frac{14}{15}-\frac{150}{90}-\frac{10}{25}$$

Reduce the fraction \frac{150}{90} to lowest terms by extracting and canceling out 30.

$$\frac{14}{15}-\frac{5}{3}-\frac{10}{25}$$

Least common multiple of 15 and 3 is 15. Convert \frac{14}{15} and \frac{5}{3} to fractions with denominator 15.

$$\frac{14}{15}-\frac{25}{15}-\frac{10}{25}$$

Since \frac{14}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-25}{15}-\frac{10}{25}$$

Subtract 25 from 14 to get -11.

$$-\frac{11}{15}-\frac{10}{25}$$

Reduce the fraction \frac{10}{25} to lowest terms by extracting and canceling out 5.

$$-\frac{11}{15}-\frac{2}{5}$$

Least common multiple of 15 and 5 is 15. Convert -\frac{11}{15} and \frac{2}{5} to fractions with denominator 15.

$$-\frac{11}{15}-\frac{6}{15}$$

Since -\frac{11}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-6}{15}$$

Subtract 6 from -11 to get -17.

$$-\frac{17}{15}$$

Factor

$$-\frac{17}{15} = -1\frac{2}{15} = -1.1333333333333333$$