Solve 1/12+(45/12-3.5)div11/24

$$\frac { 1 } { 12 } + ( 4 \frac { 5 } { 12 } - 3.5 ) \div \frac { 11 } { 24 }$$

Evaluate

$$\frac{25}{12}\approx 2.083333333$$

Solution Steps

Multiply 4 and 12 to get 48.

$$\frac{1}{12}+\frac{\frac{48+5}{12}-3.5}{\frac{11}{24}}$$

Add 48 and 5 to get 53.

$$\frac{1}{12}+\frac{\frac{53}{12}-3.5}{\frac{11}{24}}$$

Convert decimal number 3.5 to fraction \frac{35}{10}. Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{12}+\frac{\frac{53}{12}-\frac{7}{2}}{\frac{11}{24}}$$

Least common multiple of 12 and 2 is 12. Convert \frac{53}{12} and \frac{7}{2} to fractions with denominator 12.

$$\frac{1}{12}+\frac{\frac{53}{12}-\frac{42}{12}}{\frac{11}{24}}$$

Since \frac{53}{12} and \frac{42}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{12}+\frac{\frac{53-42}{12}}{\frac{11}{24}}$$

Subtract 42 from 53 to get 11.

$$\frac{1}{12}+\frac{\frac{11}{12}}{\frac{11}{24}}$$

Divide \frac{11}{12} by \frac{11}{24} by multiplying \frac{11}{12} by the reciprocal of \frac{11}{24}.

$$\frac{1}{12}+\frac{11}{12}\times \frac{24}{11}$$

Multiply \frac{11}{12} times \frac{24}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{12}+\frac{11\times 24}{12\times 11}$$

Cancel out 11 in both numerator and denominator.

$$\frac{1}{12}+\frac{24}{12}$$

Since \frac{1}{12} and \frac{24}{12} have the same denominator, add them by adding their numerators.

$$\frac{1+24}{12}$$

Add 1 and 24 to get 25.

$$\frac{25}{12}$$

Factor

$$\frac{5 ^ {2}}{3 \cdot 2 ^ {2}} = 2\frac{1}{12} = 2.0833333333333335$$