Solve 24/10*(6/9-75/100*15/90)-frac{45}{10}

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

Evaluate

$$-\frac{16}{5}=-3.2$$

Solution Steps

Reduce the fraction \frac{24}{10} to lowest terms by extracting and canceling out 2.

$$\frac{12}{5}\left(\frac{6}{9}-\frac{75}{100}\times \frac{15}{90}\right)-\frac{45}{10}$$

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

$$\frac{12}{5}\left(\frac{2}{3}-\frac{75}{100}\times \frac{15}{90}\right)-\frac{45}{10}$$

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

$$\frac{12}{5}\left(\frac{2}{3}-\frac{3}{4}\times \frac{15}{90}\right)-\frac{45}{10}$$

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

$$\frac{12}{5}\left(\frac{2}{3}-\frac{3}{4}\times \frac{1}{6}\right)-\frac{45}{10}$$

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

$$\frac{12}{5}\left(\frac{2}{3}-\frac{3\times 1}{4\times 6}\right)-\frac{45}{10}$$

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

$$\frac{12}{5}\left(\frac{2}{3}-\frac{3}{24}\right)-\frac{45}{10}$$

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

$$\frac{12}{5}\left(\frac{2}{3}-\frac{1}{8}\right)-\frac{45}{10}$$

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

$$\frac{12}{5}\left(\frac{16}{24}-\frac{3}{24}\right)-\frac{45}{10}$$

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

$$\frac{12}{5}\times \frac{16-3}{24}-\frac{45}{10}$$

Subtract 3 from 16 to get 13.

$$\frac{12}{5}\times \frac{13}{24}-\frac{45}{10}$$

Multiply \frac{12}{5} times \frac{13}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 13}{5\times 24}-\frac{45}{10}$$

Do the multiplications in the fraction \frac{12\times 13}{5\times 24}.

$$\frac{156}{120}-\frac{45}{10}$$

Reduce the fraction \frac{156}{120} to lowest terms by extracting and canceling out 12.

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

Since \frac{13}{10} and \frac{45}{10} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 45 from 13 to get -32.

$$\frac{-32}{10}$$

Reduce the fraction \frac{-32}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{16}{5}$$

Factor

$$-\frac{16}{5} = -3\frac{1}{5} = -3.2$$