Solve 2/1/3+4/1/5-5/1/6/frac{1/6{1/7}+frac{1/4}{1/8}-frac{1/8}{1/9}}=

$$\frac { \frac { 2 } { 1 / 3 } + \frac { 4 } { 1 / 5 } - \frac { 5 } { 1 / 6 } } { \frac { 1 / 6 } { 1 / 7 } + \frac { 1 / 4 } { 1 / 8 } - \frac { 1 / 8 } { 1 / 9 } } =$$

Evaluate

$$-\frac{96}{49}\approx -1.959183673$$

Solution Steps

Divide 2 by \frac{1}{3} by multiplying 2 by the reciprocal of \frac{1}{3}.

$$\frac{2\times 3+\frac{4}{\frac{1}{5}}-\frac{5}{\frac{1}{6}}}{\frac{\frac{1}{6}}{\frac{1}{7}}+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Multiply 2 and 3 to get 6.

$$\frac{6+\frac{4}{\frac{1}{5}}-\frac{5}{\frac{1}{6}}}{\frac{\frac{1}{6}}{\frac{1}{7}}+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Divide 4 by \frac{1}{5} by multiplying 4 by the reciprocal of \frac{1}{5}.

$$\frac{6+4\times 5-\frac{5}{\frac{1}{6}}}{\frac{\frac{1}{6}}{\frac{1}{7}}+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Multiply 4 and 5 to get 20.

$$\frac{6+20-\frac{5}{\frac{1}{6}}}{\frac{\frac{1}{6}}{\frac{1}{7}}+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Add 6 and 20 to get 26.

$$\frac{26-\frac{5}{\frac{1}{6}}}{\frac{\frac{1}{6}}{\frac{1}{7}}+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Divide 5 by \frac{1}{6} by multiplying 5 by the reciprocal of \frac{1}{6}.

$$\frac{26-5\times 6}{\frac{\frac{1}{6}}{\frac{1}{7}}+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Multiply 5 and 6 to get 30.

$$\frac{26-30}{\frac{\frac{1}{6}}{\frac{1}{7}}+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Subtract 30 from 26 to get -4.

$$\frac{-4}{\frac{\frac{1}{6}}{\frac{1}{7}}+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Divide \frac{1}{6} by \frac{1}{7} by multiplying \frac{1}{6} by the reciprocal of \frac{1}{7}.

$$\frac{-4}{\frac{1}{6}\times 7+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Multiply \frac{1}{6} and 7 to get \frac{7}{6}.

$$\frac{-4}{\frac{7}{6}+\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Divide \frac{1}{4} by \frac{1}{8} by multiplying \frac{1}{4} by the reciprocal of \frac{1}{8}.

$$\frac{-4}{\frac{7}{6}+\frac{1}{4}\times 8-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Multiply \frac{1}{4} and 8 to get \frac{8}{4}.

$$\frac{-4}{\frac{7}{6}+\frac{8}{4}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Divide 8 by 4 to get 2.

$$\frac{-4}{\frac{7}{6}+2-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Convert 2 to fraction \frac{12}{6}.

$$\frac{-4}{\frac{7}{6}+\frac{12}{6}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Since \frac{7}{6} and \frac{12}{6} have the same denominator, add them by adding their numerators.

$$\frac{-4}{\frac{7+12}{6}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Add 7 and 12 to get 19.

$$\frac{-4}{\frac{19}{6}-\frac{\frac{1}{8}}{\frac{1}{9}}}$$

Divide \frac{1}{8} by \frac{1}{9} by multiplying \frac{1}{8} by the reciprocal of \frac{1}{9}.

$$\frac{-4}{\frac{19}{6}-\frac{1}{8}\times 9}$$

Multiply \frac{1}{8} and 9 to get \frac{9}{8}.

$$\frac{-4}{\frac{19}{6}-\frac{9}{8}}$$

Least common multiple of 6 and 8 is 24. Convert \frac{19}{6} and \frac{9}{8} to fractions with denominator 24.

$$\frac{-4}{\frac{76}{24}-\frac{27}{24}}$$

Since \frac{76}{24} and \frac{27}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4}{\frac{76-27}{24}}$$

Subtract 27 from 76 to get 49.

$$\frac{-4}{\frac{49}{24}}$$

Divide -4 by \frac{49}{24} by multiplying -4 by the reciprocal of \frac{49}{24}.

$$-4\times \frac{24}{49}$$

Express -4\times \frac{24}{49} as a single fraction.

$$\frac{-4\times 24}{49}$$

Multiply -4 and 24 to get -96.

$$\frac{-96}{49}$$

Fraction \frac{-96}{49} can be rewritten as -\frac{96}{49} by extracting the negative sign.

$$-\frac{96}{49}$$

Factor

$$-\frac{96}{49} = -1\frac{47}{49} = -1.9591836734693877$$