Solve 7-6.35/6.5+9.9/frac{frac{1.2{36}+1.2/0.25-15/16}{frac{169}{24}}}

$$\frac{ \frac{ 7-6.35 }{ 6.5 } +9.9 }{ \frac{ \frac{ 1.2 }{ 36 } + \frac{ 1.2 }{ 0.25 } -1 \frac{ 5 }{ 16 } }{ \frac{ 169 }{ 24 } } }$$

Evaluate

$$20$$

Solution Steps

Subtract 6.35 from 7 to get 0.65.

$$\frac{\frac{0.65}{6.5}+9.9}{\frac{\frac{1.2}{36}+\frac{1.2}{0.25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Expand \frac{0.65}{6.5} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{65}{650}+9.9}{\frac{\frac{1.2}{36}+\frac{1.2}{0.25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Reduce the fraction \frac{65}{650} to lowest terms by extracting and canceling out 65.

$$\frac{\frac{1}{10}+9.9}{\frac{\frac{1.2}{36}+\frac{1.2}{0.25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Convert decimal number 9.9 to fraction \frac{99}{10}.

$$\frac{\frac{1}{10}+\frac{99}{10}}{\frac{\frac{1.2}{36}+\frac{1.2}{0.25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Since \frac{1}{10} and \frac{99}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+99}{10}}{\frac{\frac{1.2}{36}+\frac{1.2}{0.25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Add 1 and 99 to get 100.

$$\frac{\frac{100}{10}}{\frac{\frac{1.2}{36}+\frac{1.2}{0.25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Divide 100 by 10 to get 10.

$$\frac{10}{\frac{\frac{1.2}{36}+\frac{1.2}{0.25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Expand \frac{1.2}{36} by multiplying both numerator and the denominator by 10.

$$\frac{10}{\frac{\frac{12}{360}+\frac{1.2}{0.25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Reduce the fraction \frac{12}{360} to lowest terms by extracting and canceling out 12.

$$\frac{10}{\frac{\frac{1}{30}+\frac{1.2}{0.25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Expand \frac{1.2}{0.25} by multiplying both numerator and the denominator by 100.

$$\frac{10}{\frac{\frac{1}{30}+\frac{120}{25}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Reduce the fraction \frac{120}{25} to lowest terms by extracting and canceling out 5.

$$\frac{10}{\frac{\frac{1}{30}+\frac{24}{5}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Least common multiple of 30 and 5 is 30. Convert \frac{1}{30} and \frac{24}{5} to fractions with denominator 30.

$$\frac{10}{\frac{\frac{1}{30}+\frac{144}{30}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Since \frac{1}{30} and \frac{144}{30} have the same denominator, add them by adding their numerators.

$$\frac{10}{\frac{\frac{1+144}{30}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Add 1 and 144 to get 145.

$$\frac{10}{\frac{\frac{145}{30}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Reduce the fraction \frac{145}{30} to lowest terms by extracting and canceling out 5.

$$\frac{10}{\frac{\frac{29}{6}-\frac{1\times 16+5}{16}}{\frac{169}{24}}}$$

Multiply 1 and 16 to get 16.

$$\frac{10}{\frac{\frac{29}{6}-\frac{16+5}{16}}{\frac{169}{24}}}$$

Add 16 and 5 to get 21.

$$\frac{10}{\frac{\frac{29}{6}-\frac{21}{16}}{\frac{169}{24}}}$$

Least common multiple of 6 and 16 is 48. Convert \frac{29}{6} and \frac{21}{16} to fractions with denominator 48.

$$\frac{10}{\frac{\frac{232}{48}-\frac{63}{48}}{\frac{169}{24}}}$$

Since \frac{232}{48} and \frac{63}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{\frac{\frac{232-63}{48}}{\frac{169}{24}}}$$

Subtract 63 from 232 to get 169.

$$\frac{10}{\frac{\frac{169}{48}}{\frac{169}{24}}}$$

Divide \frac{169}{48} by \frac{169}{24} by multiplying \frac{169}{48} by the reciprocal of \frac{169}{24}.

$$\frac{10}{\frac{169}{48}\times \frac{24}{169}}$$

Multiply \frac{169}{48} times \frac{24}{169} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10}{\frac{169\times 24}{48\times 169}}$$

Cancel out 169 in both numerator and denominator.

$$\frac{10}{\frac{24}{48}}$$

Reduce the fraction \frac{24}{48} to lowest terms by extracting and canceling out 24.

$$\frac{10}{\frac{1}{2}}$$

Divide 10 by \frac{1}{2} by multiplying 10 by the reciprocal of \frac{1}{2}.

$$10\times 2$$

Multiply 10 and 2 to get 20.

$$20$$

Factor

$$5\times 2^{2}$$