Solve (2/15+19/12)*30/103-(1:9/4)*(-frac{9}{16})

$$( \frac { 2 } { 15 } + \frac { 19 } { 12 } ) \cdot \frac { 30 } { 103 } - ( 1 : \frac { 9 } { 4 } ) \cdot ( - \frac { 9 } { 16 } )$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Least common multiple of 15 and 12 is 60. Convert \frac{2}{15} and \frac{19}{12} to fractions with denominator 60.

$$\left(\frac{8}{60}+\frac{95}{60}\right)\times \frac{30}{103}-\frac{1}{\frac{9}{4}}\left(-\frac{9}{16}\right)$$

Since \frac{8}{60} and \frac{95}{60} have the same denominator, add them by adding their numerators.

$$\frac{8+95}{60}\times \frac{30}{103}-\frac{1}{\frac{9}{4}}\left(-\frac{9}{16}\right)$$

Add 8 and 95 to get 103.

$$\frac{103}{60}\times \frac{30}{103}-\frac{1}{\frac{9}{4}}\left(-\frac{9}{16}\right)$$

Multiply \frac{103}{60} times \frac{30}{103} by multiplying numerator times numerator and denominator times denominator.

$$\frac{103\times 30}{60\times 103}-\frac{1}{\frac{9}{4}}\left(-\frac{9}{16}\right)$$

Cancel out 103 in both numerator and denominator.

$$\frac{30}{60}-\frac{1}{\frac{9}{4}}\left(-\frac{9}{16}\right)$$

Reduce the fraction \frac{30}{60} to lowest terms by extracting and canceling out 30.

$$\frac{1}{2}-\frac{1}{\frac{9}{4}}\left(-\frac{9}{16}\right)$$

Divide 1 by \frac{9}{4} by multiplying 1 by the reciprocal of \frac{9}{4}.

$$\frac{1}{2}-1\times \frac{4}{9}\left(-\frac{9}{16}\right)$$

Multiply 1 and \frac{4}{9} to get \frac{4}{9}.

$$\frac{1}{2}-\frac{4}{9}\left(-\frac{9}{16}\right)$$

Multiply \frac{4}{9} times -\frac{9}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}-\frac{4\left(-9\right)}{9\times 16}$$

Do the multiplications in the fraction \frac{4\left(-9\right)}{9\times 16}.

$$\frac{1}{2}-\frac{-36}{144}$$

Reduce the fraction \frac{-36}{144} to lowest terms by extracting and canceling out 36.

$$\frac{1}{2}-\left(-\frac{1}{4}\right)$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$\frac{1}{2}+\frac{1}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{2}{4}+\frac{1}{4}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{4}$$

Add 2 and 1 to get 3.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$