Solve (22/5-9/10)*5/6-1=3/4

$$( 2 \frac { 2 } { 5 } - \frac { 9 } { 10 } ) \cdot \frac { 5 } { 6 } - 1 = \frac { 3 } { 4 }$$

Verify

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 5,10,6,4.

$$60\left(\frac{2\times 5+2}{5}-\frac{9}{10}\right)\times \frac{5}{6}-60=45$$

Multiply 2 and 5 to get 10.

$$60\left(\frac{10+2}{5}-\frac{9}{10}\right)\times \frac{5}{6}-60=45$$

Add 10 and 2 to get 12.

$$60\left(\frac{12}{5}-\frac{9}{10}\right)\times \frac{5}{6}-60=45$$

Least common multiple of 5 and 10 is 10. Convert \frac{12}{5} and \frac{9}{10} to fractions with denominator 10.

$$60\left(\frac{24}{10}-\frac{9}{10}\right)\times \frac{5}{6}-60=45$$

Since \frac{24}{10} and \frac{9}{10} have the same denominator, subtract them by subtracting their numerators.

$$60\times \frac{24-9}{10}\times \frac{5}{6}-60=45$$

Subtract 9 from 24 to get 15.

$$60\times \frac{15}{10}\times \frac{5}{6}-60=45$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$60\times \frac{3}{2}\times \frac{5}{6}-60=45$$

Express 60\times \frac{3}{2} as a single fraction.

$$\frac{60\times 3}{2}\times \frac{5}{6}-60=45$$

Multiply 60 and 3 to get 180.

$$\frac{180}{2}\times \frac{5}{6}-60=45$$

Divide 180 by 2 to get 90.

$$90\times \frac{5}{6}-60=45$$

Express 90\times \frac{5}{6} as a single fraction.

$$\frac{90\times 5}{6}-60=45$$

Multiply 90 and 5 to get 450.

$$\frac{450}{6}-60=45$$

Divide 450 by 6 to get 75.

$$75-60=45$$

Subtract 60 from 75 to get 15.

$$15=45$$

Compare 15 and 45.

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