Solve 1/12+(45/12-35)div11/24

$$\frac { 1 } { 12 } + ( 4 \frac { 5 } { 12 } - 35 ) \div \frac { 11 } { 24 }$$

Evaluate

$$-\frac{8797}{132}\approx -66.643939394$$

Solution Steps

Multiply 4 and 12 to get 48.

$$\frac{1}{12}+\frac{\frac{48+5}{12}-35}{\frac{11}{24}}$$

Add 48 and 5 to get 53.

$$\frac{1}{12}+\frac{\frac{53}{12}-35}{\frac{11}{24}}$$

Convert 35 to fraction \frac{420}{12}.

$$\frac{1}{12}+\frac{\frac{53}{12}-\frac{420}{12}}{\frac{11}{24}}$$

Since \frac{53}{12} and \frac{420}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{12}+\frac{\frac{53-420}{12}}{\frac{11}{24}}$$

Subtract 420 from 53 to get -367.

$$\frac{1}{12}+\frac{-\frac{367}{12}}{\frac{11}{24}}$$

Divide -\frac{367}{12} by \frac{11}{24} by multiplying -\frac{367}{12} by the reciprocal of \frac{11}{24}.

$$\frac{1}{12}-\frac{367}{12}\times \frac{24}{11}$$

Multiply -\frac{367}{12} times \frac{24}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{12}+\frac{-367\times 24}{12\times 11}$$

Do the multiplications in the fraction \frac{-367\times 24}{12\times 11}.

$$\frac{1}{12}+\frac{-8808}{132}$$

Reduce the fraction \frac{-8808}{132} to lowest terms by extracting and canceling out 12.

$$\frac{1}{12}-\frac{734}{11}$$

Least common multiple of 12 and 11 is 132. Convert \frac{1}{12} and \frac{734}{11} to fractions with denominator 132.

$$\frac{11}{132}-\frac{8808}{132}$$

Since \frac{11}{132} and \frac{8808}{132} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-8808}{132}$$

Subtract 8808 from 11 to get -8797.

$$-\frac{8797}{132}$$

Factor

$$-\frac{8797}{132} = -66\frac{85}{132} = -66.64393939393939$$