Solve 7/18*4.5+0.16/13frac{1{3}-3.75*3.2}*(1/3+1/15+frac{1}{35}+frac{1}{63})

$$\frac { \frac { 7 } { 18 } \times 4.5 + 0.16 } { 13 \frac { 1 } { 3 } - 3.75 \times 3.2 } \times ( \frac { 1 } { 3 } + \frac { 1 } { 15 } + \frac { 1 } { 35 } + \frac { 1 } { 63 } )$$

Evaluate

$$\frac{191}{300}\approx 0.636666667$$

Solution Steps

Convert decimal number 4.5 to fraction \frac{45}{10}. Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{7}{18}\times \frac{9}{2}+0.16}{\frac{13\times 3+1}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Multiply \frac{7}{18} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 9}{18\times 2}+0.16}{\frac{13\times 3+1}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Do the multiplications in the fraction \frac{7\times 9}{18\times 2}.

$$\frac{\frac{63}{36}+0.16}{\frac{13\times 3+1}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Reduce the fraction \frac{63}{36} to lowest terms by extracting and canceling out 9.

$$\frac{\frac{7}{4}+0.16}{\frac{13\times 3+1}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Convert decimal number 0.16 to fraction \frac{16}{100}. Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7}{4}+\frac{4}{25}}{\frac{13\times 3+1}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Least common multiple of 4 and 25 is 100. Convert \frac{7}{4} and \frac{4}{25} to fractions with denominator 100.

$$\frac{\frac{175}{100}+\frac{16}{100}}{\frac{13\times 3+1}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Since \frac{175}{100} and \frac{16}{100} have the same denominator, add them by adding their numerators.

$$\frac{\frac{175+16}{100}}{\frac{13\times 3+1}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Add 175 and 16 to get 191.

$$\frac{\frac{191}{100}}{\frac{13\times 3+1}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Multiply 13 and 3 to get 39.

$$\frac{\frac{191}{100}}{\frac{39+1}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Add 39 and 1 to get 40.

$$\frac{\frac{191}{100}}{\frac{40}{3}-3.75\times 3.2}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Multiply 3.75 and 3.2 to get 12.

$$\frac{\frac{191}{100}}{\frac{40}{3}-12}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Convert 12 to fraction \frac{36}{3}.

$$\frac{\frac{191}{100}}{\frac{40}{3}-\frac{36}{3}}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Since \frac{40}{3} and \frac{36}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{191}{100}}{\frac{40-36}{3}}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Subtract 36 from 40 to get 4.

$$\frac{\frac{191}{100}}{\frac{4}{3}}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Divide \frac{191}{100} by \frac{4}{3} by multiplying \frac{191}{100} by the reciprocal of \frac{4}{3}.

$$\frac{191}{100}\times \frac{3}{4}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Multiply \frac{191}{100} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{191\times 3}{100\times 4}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Do the multiplications in the fraction \frac{191\times 3}{100\times 4}.

$$\frac{573}{400}\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Least common multiple of 3 and 15 is 15. Convert \frac{1}{3} and \frac{1}{15} to fractions with denominator 15.

$$\frac{573}{400}\left(\frac{5}{15}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Since \frac{5}{15} and \frac{1}{15} have the same denominator, add them by adding their numerators.

$$\frac{573}{400}\left(\frac{5+1}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Add 5 and 1 to get 6.

$$\frac{573}{400}\left(\frac{6}{15}+\frac{1}{35}+\frac{1}{63}\right)$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

$$\frac{573}{400}\left(\frac{2}{5}+\frac{1}{35}+\frac{1}{63}\right)$$

Least common multiple of 5 and 35 is 35. Convert \frac{2}{5} and \frac{1}{35} to fractions with denominator 35.

$$\frac{573}{400}\left(\frac{14}{35}+\frac{1}{35}+\frac{1}{63}\right)$$

Since \frac{14}{35} and \frac{1}{35} have the same denominator, add them by adding their numerators.

$$\frac{573}{400}\left(\frac{14+1}{35}+\frac{1}{63}\right)$$

Add 14 and 1 to get 15.

$$\frac{573}{400}\left(\frac{15}{35}+\frac{1}{63}\right)$$

Reduce the fraction \frac{15}{35} to lowest terms by extracting and canceling out 5.

$$\frac{573}{400}\left(\frac{3}{7}+\frac{1}{63}\right)$$

Least common multiple of 7 and 63 is 63. Convert \frac{3}{7} and \frac{1}{63} to fractions with denominator 63.

$$\frac{573}{400}\left(\frac{27}{63}+\frac{1}{63}\right)$$

Since \frac{27}{63} and \frac{1}{63} have the same denominator, add them by adding their numerators.

$$\frac{573}{400}\times \frac{27+1}{63}$$

Add 27 and 1 to get 28.

$$\frac{573}{400}\times \frac{28}{63}$$

Reduce the fraction \frac{28}{63} to lowest terms by extracting and canceling out 7.

$$\frac{573}{400}\times \frac{4}{9}$$

Multiply \frac{573}{400} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{573\times 4}{400\times 9}$$

Do the multiplications in the fraction \frac{573\times 4}{400\times 9}.

$$\frac{2292}{3600}$$

Reduce the fraction \frac{2292}{3600} to lowest terms by extracting and canceling out 12.

$$\frac{191}{300}$$

Factor

$$\frac{191}{3 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 0.6366666666666667$$