Solve (2/15+19/2)*30/103-(1div9/4)-(-frac{9}{16})

$$( \frac{ 2 }{ 15 } + \frac{ 19 }{ 2 } ) \times \frac{ 30 }{ 103 } -(1 \div \frac{ 9 }{ 4 } )-(- \frac{ 9 }{ 16 } )$$

Evaluate

$$\frac{43367}{14832}\approx 2.923880798$$

Solution Steps

Least common multiple of 15 and 2 is 30. Convert \frac{2}{15} and \frac{19}{2} to fractions with denominator 30.

$$\left(\frac{4}{30}+\frac{285}{30}\right)\times \frac{30}{103}-\frac{1}{\frac{9}{4}}-\left(-\frac{9}{16}\right)$$

Since \frac{4}{30} and \frac{285}{30} have the same denominator, add them by adding their numerators.

$$\frac{4+285}{30}\times \frac{30}{103}-\frac{1}{\frac{9}{4}}-\left(-\frac{9}{16}\right)$$

Add 4 and 285 to get 289.

$$\frac{289}{30}\times \frac{30}{103}-\frac{1}{\frac{9}{4}}-\left(-\frac{9}{16}\right)$$

Multiply \frac{289}{30} times \frac{30}{103} by multiplying numerator times numerator and denominator times denominator.

$$\frac{289\times 30}{30\times 103}-\frac{1}{\frac{9}{4}}-\left(-\frac{9}{16}\right)$$

Cancel out 30 in both numerator and denominator.

$$\frac{289}{103}-\frac{1}{\frac{9}{4}}-\left(-\frac{9}{16}\right)$$

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

$$\frac{289}{103}-1\times \frac{4}{9}-\left(-\frac{9}{16}\right)$$

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

$$\frac{289}{103}-\frac{4}{9}-\left(-\frac{9}{16}\right)$$

Least common multiple of 103 and 9 is 927. Convert \frac{289}{103} and \frac{4}{9} to fractions with denominator 927.

$$\frac{2601}{927}-\frac{412}{927}-\left(-\frac{9}{16}\right)$$

Since \frac{2601}{927} and \frac{412}{927} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2601-412}{927}-\left(-\frac{9}{16}\right)$$

Subtract 412 from 2601 to get 2189.

$$\frac{2189}{927}-\left(-\frac{9}{16}\right)$$

The opposite of -\frac{9}{16} is \frac{9}{16}.

$$\frac{2189}{927}+\frac{9}{16}$$

Least common multiple of 927 and 16 is 14832. Convert \frac{2189}{927} and \frac{9}{16} to fractions with denominator 14832.

$$\frac{35024}{14832}+\frac{8343}{14832}$$

Since \frac{35024}{14832} and \frac{8343}{14832} have the same denominator, add them by adding their numerators.

$$\frac{35024+8343}{14832}$$

Add 35024 and 8343 to get 43367.

$$\frac{43367}{14832}$$

Factor

$$\frac{17 \cdot 2551}{2 ^ {4} \cdot 3 ^ {2} \cdot 103} = 2\frac{13703}{14832} = 2.923880798274002$$