Solve (3/5-19/25)*411/16-(1div1.5)*(-33/8)

$$( \frac{ 3 }{ 5 } - \frac{ 19 }{ 25 } ) \times 4 \frac { 11 } { 16 } -(1 \div 1.5) \times (- 3 \frac { 3 } { 8 } )$$

Evaluate

$$1.5$$

Solution Steps

Least common multiple of 5 and 25 is 25. Convert \frac{3}{5} and \frac{19}{25} to fractions with denominator 25.

$$\left(\frac{15}{25}-\frac{19}{25}\right)\times \frac{4\times 16+11}{16}-\frac{1}{1.5}\left(-\frac{3\times 8+3}{8}\right)$$

Since \frac{15}{25} and \frac{19}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-19}{25}\times \frac{4\times 16+11}{16}-\frac{1}{1.5}\left(-\frac{3\times 8+3}{8}\right)$$

Subtract 19 from 15 to get -4.

$$-\frac{4}{25}\times \frac{4\times 16+11}{16}-\frac{1}{1.5}\left(-\frac{3\times 8+3}{8}\right)$$

Multiply 4 and 16 to get 64.

$$-\frac{4}{25}\times \frac{64+11}{16}-\frac{1}{1.5}\left(-\frac{3\times 8+3}{8}\right)$$

Add 64 and 11 to get 75.

$$-\frac{4}{25}\times \frac{75}{16}-\frac{1}{1.5}\left(-\frac{3\times 8+3}{8}\right)$$

Multiply -\frac{4}{25} times \frac{75}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-4\times 75}{25\times 16}-\frac{1}{1.5}\left(-\frac{3\times 8+3}{8}\right)$$

Do the multiplications in the fraction \frac{-4\times 75}{25\times 16}.

$$\frac{-300}{400}-\frac{1}{1.5}\left(-\frac{3\times 8+3}{8}\right)$$

Reduce the fraction \frac{-300}{400} to lowest terms by extracting and canceling out 100.

$$-\frac{3}{4}-\frac{1}{1.5}\left(-\frac{3\times 8+3}{8}\right)$$

Expand \frac{1}{1.5} by multiplying both numerator and the denominator by 10.

$$-\frac{3}{4}-\frac{10}{15}\left(-\frac{3\times 8+3}{8}\right)$$

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

$$-\frac{3}{4}-\frac{2}{3}\left(-\frac{3\times 8+3}{8}\right)$$

Multiply 3 and 8 to get 24.

$$-\frac{3}{4}-\frac{2}{3}\left(-\frac{24+3}{8}\right)$$

Add 24 and 3 to get 27.

$$-\frac{3}{4}-\frac{2}{3}\left(-\frac{27}{8}\right)$$

Multiply \frac{2}{3} times -\frac{27}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{4}-\frac{2\left(-27\right)}{3\times 8}$$

Do the multiplications in the fraction \frac{2\left(-27\right)}{3\times 8}.

$$-\frac{3}{4}-\frac{-54}{24}$$

Reduce the fraction \frac{-54}{24} to lowest terms by extracting and canceling out 6.

$$-\frac{3}{4}-\left(-\frac{9}{4}\right)$$

The opposite of -\frac{9}{4} is \frac{9}{4}.

$$-\frac{3}{4}+\frac{9}{4}$$

Since -\frac{3}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{-3+9}{4}$$

Add -3 and 9 to get 6.

$$\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$