Solve (3/2*10/9-14/5*2/7-frac{1}{6})

$$( \frac { 3 } { 2 } \cdot \frac { 10 } { 9 } - \frac { 14 } { 5 } \cdot \frac { 2 } { 7 } - \frac { 1 } { 6 } )$$

Evaluate

$$\frac{7}{10}=0.7$$

Solution Steps

Multiply \frac{3}{2} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 10}{2\times 9}-\frac{14}{5}\times \frac{2}{7}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{3\times 10}{2\times 9}.

$$\frac{30}{18}-\frac{14}{5}\times \frac{2}{7}-\frac{1}{6}$$

Reduce the fraction \frac{30}{18} to lowest terms by extracting and canceling out 6.

$$\frac{5}{3}-\frac{14}{5}\times \frac{2}{7}-\frac{1}{6}$$

Multiply \frac{14}{5} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{3}-\frac{14\times 2}{5\times 7}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{14\times 2}{5\times 7}.

$$\frac{5}{3}-\frac{28}{35}-\frac{1}{6}$$

Reduce the fraction \frac{28}{35} to lowest terms by extracting and canceling out 7.

$$\frac{5}{3}-\frac{4}{5}-\frac{1}{6}$$

Least common multiple of 3 and 5 is 15. Convert \frac{5}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{25}{15}-\frac{12}{15}-\frac{1}{6}$$

Since \frac{25}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-12}{15}-\frac{1}{6}$$

Subtract 12 from 25 to get 13.

$$\frac{13}{15}-\frac{1}{6}$$

Least common multiple of 15 and 6 is 30. Convert \frac{13}{15} and \frac{1}{6} to fractions with denominator 30.

$$\frac{26}{30}-\frac{5}{30}$$

Since \frac{26}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{26-5}{30}$$

Subtract 5 from 26 to get 21.

$$\frac{21}{30}$$

Reduce the fraction \frac{21}{30} to lowest terms by extracting and canceling out 3.

$$\frac{7}{10}$$

Factor

$$\frac{7}{2 \cdot 5} = 0.7$$