Solve (1-1/6*2/5)div7/9

$$( 1 - \frac { 1 } { 6 } \times \frac { 2 } { 5 } ) \div \frac { 7 } { 9 }$$

Evaluate

$$\frac{6}{5}=1.2$$

Solution Steps

Multiply \frac{1}{6} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 2}{6\times 5}.

$$\frac{1-\frac{2}{30}}{\frac{7}{9}}$$

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

$$\frac{1-\frac{1}{15}}{\frac{7}{9}}$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{\frac{15}{15}-\frac{1}{15}}{\frac{7}{9}}$$

Since \frac{15}{15} and \frac{1}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-1}{15}}{\frac{7}{9}}$$

Subtract 1 from 15 to get 14.

$$\frac{\frac{14}{15}}{\frac{7}{9}}$$

Divide \frac{14}{15} by \frac{7}{9} by multiplying \frac{14}{15} by the reciprocal of \frac{7}{9}.

$$\frac{14}{15}\times \frac{9}{7}$$

Multiply \frac{14}{15} times \frac{9}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14\times 9}{15\times 7}$$

Do the multiplications in the fraction \frac{14\times 9}{15\times 7}.

$$\frac{126}{105}$$

Reduce the fraction \frac{126}{105} to lowest terms by extracting and canceling out 21.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$