Solve (1-1/22*30/5):14/25-1

$$( 1 - \frac { 1 } { 22 } \cdot \frac { 30 } { 5 } ) : \frac { 14 } { 25 } - 1$$

Evaluate

$$\frac{23}{77}\approx 0.298701299$$

Solution Steps

Divide 30 by 5 to get 6.

$$\frac{1-\frac{1}{22}\times 6}{\frac{14}{25}}-1$$

Multiply \frac{1}{22} and 6 to get \frac{6}{22}.

$$\frac{1-\frac{6}{22}}{\frac{14}{25}}-1$$

Reduce the fraction \frac{6}{22} to lowest terms by extracting and canceling out 2.

$$\frac{1-\frac{3}{11}}{\frac{14}{25}}-1$$

Convert 1 to fraction \frac{11}{11}.

$$\frac{\frac{11}{11}-\frac{3}{11}}{\frac{14}{25}}-1$$

Since \frac{11}{11} and \frac{3}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11-3}{11}}{\frac{14}{25}}-1$$

Subtract 3 from 11 to get 8.

$$\frac{\frac{8}{11}}{\frac{14}{25}}-1$$

Divide \frac{8}{11} by \frac{14}{25} by multiplying \frac{8}{11} by the reciprocal of \frac{14}{25}.

$$\frac{8}{11}\times \frac{25}{14}-1$$

Multiply \frac{8}{11} times \frac{25}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 25}{11\times 14}-1$$

Do the multiplications in the fraction \frac{8\times 25}{11\times 14}.

$$\frac{200}{154}-1$$

Reduce the fraction \frac{200}{154} to lowest terms by extracting and canceling out 2.

$$\frac{100}{77}-1$$

Convert 1 to fraction \frac{77}{77}.

$$\frac{100}{77}-\frac{77}{77}$$

Since \frac{100}{77} and \frac{77}{77} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100-77}{77}$$

Subtract 77 from 100 to get 23.

$$\frac{23}{77}$$

Factor

$$\frac{23}{7 \cdot 11} = 0.2987012987012987$$