Solve (7/8+0.25-1/3)div1/11

$$( \frac { 7 } { 8 } + 0.25 - \frac { 1 } { 3 } ) \div \frac { 1 } { 11 }$$

Evaluate

$$\frac{209}{24}\approx 8.708333333$$

Solution Steps

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{7}{8}+\frac{1}{4}-\frac{1}{3}}{\frac{1}{11}}$$

Least common multiple of 8 and 4 is 8. Convert \frac{7}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{\frac{7}{8}+\frac{2}{8}-\frac{1}{3}}{\frac{1}{11}}$$

Since \frac{7}{8} and \frac{2}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7+2}{8}-\frac{1}{3}}{\frac{1}{11}}$$

Add 7 and 2 to get 9.

$$\frac{\frac{9}{8}-\frac{1}{3}}{\frac{1}{11}}$$

Least common multiple of 8 and 3 is 24. Convert \frac{9}{8} and \frac{1}{3} to fractions with denominator 24.

$$\frac{\frac{27}{24}-\frac{8}{24}}{\frac{1}{11}}$$

Since \frac{27}{24} and \frac{8}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27-8}{24}}{\frac{1}{11}}$$

Subtract 8 from 27 to get 19.

$$\frac{\frac{19}{24}}{\frac{1}{11}}$$

Divide \frac{19}{24} by \frac{1}{11} by multiplying \frac{19}{24} by the reciprocal of \frac{1}{11}.

$$\frac{19}{24}\times 11$$

Express \frac{19}{24}\times 11 as a single fraction.

$$\frac{19\times 11}{24}$$

Multiply 19 and 11 to get 209.

$$\frac{209}{24}$$

Factor

$$\frac{11 \cdot 19}{3 \cdot 2 ^ {3}} = 8\frac{17}{24} = 8.708333333333334$$