Solve 24/11left(6/9-75/10015/90right)-frac{45}{10}

$$\frac{ 24 }{ 11 } \left( \frac{ 6 }{ 9 } - \frac{ 75 }{ 100 } \frac{ 15 }{ 90 } \right) - \frac{ 45 }{ 10 }$$

Evaluate

$$-\frac{73}{22}\approx -3.318181818$$

Solution Steps

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

$$\frac{24}{11}\left(\frac{2}{3}-\frac{75}{100}\times \frac{15}{90}\right)-\frac{45}{10}$$

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

$$\frac{24}{11}\left(\frac{2}{3}-\frac{3}{4}\times \frac{15}{90}\right)-\frac{45}{10}$$

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

$$\frac{24}{11}\left(\frac{2}{3}-\frac{3}{4}\times \frac{1}{6}\right)-\frac{45}{10}$$

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

$$\frac{24}{11}\left(\frac{2}{3}-\frac{3\times 1}{4\times 6}\right)-\frac{45}{10}$$

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

$$\frac{24}{11}\left(\frac{2}{3}-\frac{3}{24}\right)-\frac{45}{10}$$

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

$$\frac{24}{11}\left(\frac{2}{3}-\frac{1}{8}\right)-\frac{45}{10}$$

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

$$\frac{24}{11}\left(\frac{16}{24}-\frac{3}{24}\right)-\frac{45}{10}$$

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

$$\frac{24}{11}\times \frac{16-3}{24}-\frac{45}{10}$$

Subtract 3 from 16 to get 13.

$$\frac{24}{11}\times \frac{13}{24}-\frac{45}{10}$$

Multiply \frac{24}{11} times \frac{13}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{24\times 13}{11\times 24}-\frac{45}{10}$$

Cancel out 24 in both numerator and denominator.

$$\frac{13}{11}-\frac{45}{10}$$

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

$$\frac{13}{11}-\frac{9}{2}$$

Least common multiple of 11 and 2 is 22. Convert \frac{13}{11} and \frac{9}{2} to fractions with denominator 22.

$$\frac{26}{22}-\frac{99}{22}$$

Since \frac{26}{22} and \frac{99}{22} have the same denominator, subtract them by subtracting their numerators.

$$\frac{26-99}{22}$$

Subtract 99 from 26 to get -73.

$$-\frac{73}{22}$$

Factor

$$-\frac{73}{22} = -3\frac{7}{22} = -3.3181818181818183$$