Solve 7/18*41/2+1/6/13frac{1{3}-3frac{3}{4}divfrac{5}{16}}div2frac{7}{8}=

$$\frac { \frac { 7 } { 18 } \times 4 \frac { 1 } { 2 } + \frac { 1 } { 6 } } { 13 \frac { 1 } { 3 } - 3 \frac { 3 } { 4 } \div \frac { 5 } { 16 } } \div 2 \frac { 7 } { 8 } =$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Divide \frac{\frac{7}{18}\times \frac{4\times 2+1}{2}+\frac{1}{6}}{\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}} by \frac{2\times 8+7}{8} by multiplying \frac{\frac{7}{18}\times \frac{4\times 2+1}{2}+\frac{1}{6}}{\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}} by the reciprocal of \frac{2\times 8+7}{8}.

$$\frac{\left(\frac{7}{18}\times \frac{4\times 2+1}{2}+\frac{1}{6}\right)\times 8}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Multiply 4 and 2 to get 8.

$$\frac{\left(\frac{7}{18}\times \frac{8+1}{2}+\frac{1}{6}\right)\times 8}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Add 8 and 1 to get 9.

$$\frac{\left(\frac{7}{18}\times \frac{9}{2}+\frac{1}{6}\right)\times 8}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

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

$$\frac{\left(\frac{7\times 9}{18\times 2}+\frac{1}{6}\right)\times 8}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

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

$$\frac{\left(\frac{63}{36}+\frac{1}{6}\right)\times 8}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

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

$$\frac{\left(\frac{7}{4}+\frac{1}{6}\right)\times 8}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Least common multiple of 4 and 6 is 12. Convert \frac{7}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{\left(\frac{21}{12}+\frac{2}{12}\right)\times 8}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Since \frac{21}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{21+2}{12}\times 8}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Add 21 and 2 to get 23.

$$\frac{\frac{23}{12}\times 8}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Express \frac{23}{12}\times 8 as a single fraction.

$$\frac{\frac{23\times 8}{12}}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Multiply 23 and 8 to get 184.

$$\frac{\frac{184}{12}}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Reduce the fraction \frac{184}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{46}{3}}{\left(\frac{13\times 3+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Multiply 13 and 3 to get 39.

$$\frac{\frac{46}{3}}{\left(\frac{39+1}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Add 39 and 1 to get 40.

$$\frac{\frac{46}{3}}{\left(\frac{40}{3}-\frac{\frac{3\times 4+3}{4}}{\frac{5}{16}}\right)\left(2\times 8+7\right)}$$

Divide \frac{3\times 4+3}{4} by \frac{5}{16} by multiplying \frac{3\times 4+3}{4} by the reciprocal of \frac{5}{16}.

$$\frac{\frac{46}{3}}{\left(\frac{40}{3}-\frac{\left(3\times 4+3\right)\times 16}{4\times 5}\right)\left(2\times 8+7\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{46}{3}}{\left(\frac{40}{3}-\frac{4\left(3+3\times 4\right)}{5}\right)\left(2\times 8+7\right)}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{46}{3}}{\left(\frac{40}{3}-\frac{4\left(3+12\right)}{5}\right)\left(2\times 8+7\right)}$$

Add 3 and 12 to get 15.

$$\frac{\frac{46}{3}}{\left(\frac{40}{3}-\frac{4\times 15}{5}\right)\left(2\times 8+7\right)}$$

Multiply 4 and 15 to get 60.

$$\frac{\frac{46}{3}}{\left(\frac{40}{3}-\frac{60}{5}\right)\left(2\times 8+7\right)}$$

Divide 60 by 5 to get 12.

$$\frac{\frac{46}{3}}{\left(\frac{40}{3}-12\right)\left(2\times 8+7\right)}$$

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

$$\frac{\frac{46}{3}}{\left(\frac{40}{3}-\frac{36}{3}\right)\left(2\times 8+7\right)}$$

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

$$\frac{\frac{46}{3}}{\frac{40-36}{3}\left(2\times 8+7\right)}$$

Subtract 36 from 40 to get 4.

$$\frac{\frac{46}{3}}{\frac{4}{3}\left(2\times 8+7\right)}$$

Multiply 2 and 8 to get 16.

$$\frac{\frac{46}{3}}{\frac{4}{3}\left(16+7\right)}$$

Add 16 and 7 to get 23.

$$\frac{\frac{46}{3}}{\frac{4}{3}\times 23}$$

Express \frac{4}{3}\times 23 as a single fraction.

$$\frac{\frac{46}{3}}{\frac{4\times 23}{3}}$$

Multiply 4 and 23 to get 92.

$$\frac{\frac{46}{3}}{\frac{92}{3}}$$

Divide \frac{46}{3} by \frac{92}{3} by multiplying \frac{46}{3} by the reciprocal of \frac{92}{3}.

$$\frac{46}{3}\times \frac{3}{92}$$

Multiply \frac{46}{3} times \frac{3}{92} by multiplying numerator times numerator and denominator times denominator.

$$\frac{46\times 3}{3\times 92}$$

Cancel out 3 in both numerator and denominator.

$$\frac{46}{92}$$

Reduce the fraction \frac{46}{92} to lowest terms by extracting and canceling out 46.

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

Factor

$$\frac{1}{2} = 0.5$$