Solve 24/1left(6/9-75/10015/90right)-frac{45}{10}

$$\frac{ 24 }{ 1 } \left( \frac{ 6 }{ 9 } - \frac{ 75 }{ 100 } \frac{ 15 }{ 90 } \right) - \frac{ 45 }{ 10 }$$

Evaluate

$$\frac{17}{2}=8.5$$

Solution Steps

Anything divided by one gives itself.

$$24\left(\frac{6}{9}-\frac{75}{100}\times \frac{15}{90}\right)-\frac{45}{10}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$24\left(\frac{2}{3}-\frac{75}{100}\times \frac{15}{90}\right)-\frac{45}{10}$$

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$24\left(\frac{2}{3}-\frac{3}{4}\times \frac{15}{90}\right)-\frac{45}{10}$$

Reduce the fraction \frac{15}{90} to lowest terms by extracting and canceling out 15.

$$24\left(\frac{2}{3}-\frac{3}{4}\times \frac{1}{6}\right)-\frac{45}{10}$$

Multiply \frac{3}{4} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$24\left(\frac{2}{3}-\frac{3\times 1}{4\times 6}\right)-\frac{45}{10}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 6}.

$$24\left(\frac{2}{3}-\frac{3}{24}\right)-\frac{45}{10}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$24\left(\frac{2}{3}-\frac{1}{8}\right)-\frac{45}{10}$$

Least common multiple of 3 and 8 is 24. Convert \frac{2}{3} and \frac{1}{8} to fractions with denominator 24.

$$24\left(\frac{16}{24}-\frac{3}{24}\right)-\frac{45}{10}$$

Since \frac{16}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$24\times \frac{16-3}{24}-\frac{45}{10}$$

Subtract 3 from 16 to get 13.

$$24\times \frac{13}{24}-\frac{45}{10}$$

Cancel out 24 and 24.

$$13-\frac{45}{10}$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$13-\frac{9}{2}$$

Convert 13 to fraction \frac{26}{2}.

$$\frac{26}{2}-\frac{9}{2}$$

Since \frac{26}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{26-9}{2}$$

Subtract 9 from 26 to get 17.

$$\frac{17}{2}$$

Factor

$$\frac{17}{2} = 8\frac{1}{2} = 8.5$$