Solve (1-1/y-10/36)div1/45

$$( 1 - \frac { 1 } { y } - \frac { 10 } { 36 } ) \div \frac { 1 } { 45 }$$

Evaluate

$$\frac{65}{2}-\frac{45}{y}$$

Short Solution Steps

Reduce the fraction \frac{10}{36} to lowest terms by extracting and canceling out 2.

$$\frac{1-\frac{1}{y}-\frac{5}{18}}{\frac{1}{45}}$$

Convert 1 to fraction \frac{18}{18}.

$$\frac{\frac{18}{18}-\frac{1}{y}-\frac{5}{18}}{\frac{1}{45}}$$

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

$$\frac{\frac{18-5}{18}-\frac{1}{y}}{\frac{1}{45}}$$

Subtract 5 from 18 to get 13.

$$\frac{\frac{13}{18}-\frac{1}{y}}{\frac{1}{45}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 18 and y is 18y. Multiply \frac{13}{18} times \frac{y}{y}. Multiply \frac{1}{y} times \frac{18}{18}.

$$\frac{\frac{13y}{18y}-\frac{18}{18y}}{\frac{1}{45}}$$

Since \frac{13y}{18y} and \frac{18}{18y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13y-18}{18y}}{\frac{1}{45}}$$

Divide \frac{13y-18}{18y} by \frac{1}{45} by multiplying \frac{13y-18}{18y} by the reciprocal of \frac{1}{45}.

$$\frac{\left(13y-18\right)\times 45}{18y}$$

Cancel out 9 in both numerator and denominator.

$$\frac{5\left(13y-18\right)}{2y}$$

Use the distributive property to multiply 5 by 13y-18.

$$\frac{65y-90}{2y}$$

Expand

$$\frac{65}{2}-\frac{45}{y}$$

Short Solution Steps

Reduce the fraction \frac{10}{36} to lowest terms by extracting and canceling out 2.

$$\frac{1-\frac{1}{y}-\frac{5}{18}}{\frac{1}{45}}$$

Convert 1 to fraction \frac{18}{18}.

$$\frac{\frac{18}{18}-\frac{1}{y}-\frac{5}{18}}{\frac{1}{45}}$$

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

$$\frac{\frac{18-5}{18}-\frac{1}{y}}{\frac{1}{45}}$$

Subtract 5 from 18 to get 13.

$$\frac{\frac{13}{18}-\frac{1}{y}}{\frac{1}{45}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 18 and y is 18y. Multiply \frac{13}{18} times \frac{y}{y}. Multiply \frac{1}{y} times \frac{18}{18}.

$$\frac{\frac{13y}{18y}-\frac{18}{18y}}{\frac{1}{45}}$$

Since \frac{13y}{18y} and \frac{18}{18y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13y-18}{18y}}{\frac{1}{45}}$$

Divide \frac{13y-18}{18y} by \frac{1}{45} by multiplying \frac{13y-18}{18y} by the reciprocal of \frac{1}{45}.

$$\frac{\left(13y-18\right)\times 45}{18y}$$

Cancel out 9 in both numerator and denominator.

$$\frac{5\left(13y-18\right)}{2y}$$

Use the distributive property to multiply 5 by 13y-18.

$$\frac{65y-90}{2y}$$