Solve 7/12div(75%-5/12)-17/24

$$\frac { 7 } { 12 } \div ( 75 \% - \frac { 5 } { 12 } ) - \frac { 17 } { 24 }$$

Evaluate

$$\frac{25}{24}\approx 1.041666667$$

Solution Steps

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{7}{12}}{\frac{3}{4}-\frac{5}{12}}-\frac{17}{24}$$

Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{5}{12} to fractions with denominator 12.

$$\frac{\frac{7}{12}}{\frac{9}{12}-\frac{5}{12}}-\frac{17}{24}$$

Since \frac{9}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{12}}{\frac{9-5}{12}}-\frac{17}{24}$$

Subtract 5 from 9 to get 4.

$$\frac{\frac{7}{12}}{\frac{4}{12}}-\frac{17}{24}$$

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

$$\frac{\frac{7}{12}}{\frac{1}{3}}-\frac{17}{24}$$

Divide \frac{7}{12} by \frac{1}{3} by multiplying \frac{7}{12} by the reciprocal of \frac{1}{3}.

$$\frac{7}{12}\times 3-\frac{17}{24}$$

Express \frac{7}{12}\times 3 as a single fraction.

$$\frac{7\times 3}{12}-\frac{17}{24}$$

Multiply 7 and 3 to get 21.

$$\frac{21}{12}-\frac{17}{24}$$

Reduce the fraction \frac{21}{12} to lowest terms by extracting and canceling out 3.

$$\frac{7}{4}-\frac{17}{24}$$

Least common multiple of 4 and 24 is 24. Convert \frac{7}{4} and \frac{17}{24} to fractions with denominator 24.

$$\frac{42}{24}-\frac{17}{24}$$

Since \frac{42}{24} and \frac{17}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{42-17}{24}$$

Subtract 17 from 42 to get 25.

$$\frac{25}{24}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {3} \cdot 3} = 1\frac{1}{24} = 1.0416666666666667$$