Solve f(11/12-7/15)*10/9+1/2

$$f ( \frac { 11 } { 12 } - \frac { 7 } { 15 } ) \cdot \frac { 10 } { 9 } + \frac { 1 } { 2 }$$

Evaluate

$$\frac{f+1}{2}$$

Solution Steps

Least common multiple of 12 and 15 is 60. Convert \frac{11}{12} and \frac{7}{15} to fractions with denominator 60.

$$f\left(\frac{55}{60}-\frac{28}{60}\right)\times \frac{10}{9}+\frac{1}{2}$$

Since \frac{55}{60} and \frac{28}{60} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{55-28}{60}\times \frac{10}{9}+\frac{1}{2}$$

Subtract 28 from 55 to get 27.

$$f\times \frac{27}{60}\times \frac{10}{9}+\frac{1}{2}$$

Reduce the fraction \frac{27}{60} to lowest terms by extracting and canceling out 3.

$$f\times \frac{9}{20}\times \frac{10}{9}+\frac{1}{2}$$

Multiply \frac{9}{20} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$f\times \frac{9\times 10}{20\times 9}+\frac{1}{2}$$

Cancel out 9 in both numerator and denominator.

$$f\times \frac{10}{20}+\frac{1}{2}$$

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

$$f\times \frac{1}{2}+\frac{1}{2}$$

Expand

$$\frac{f+1}{2}$$

Solution Steps

Least common multiple of 12 and 15 is 60. Convert \frac{11}{12} and \frac{7}{15} to fractions with denominator 60.

$$f\left(\frac{55}{60}-\frac{28}{60}\right)\times \frac{10}{9}+\frac{1}{2}$$

Since \frac{55}{60} and \frac{28}{60} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{55-28}{60}\times \frac{10}{9}+\frac{1}{2}$$

Subtract 28 from 55 to get 27.

$$f\times \frac{27}{60}\times \frac{10}{9}+\frac{1}{2}$$

Reduce the fraction \frac{27}{60} to lowest terms by extracting and canceling out 3.

$$f\times \frac{9}{20}\times \frac{10}{9}+\frac{1}{2}$$

Multiply \frac{9}{20} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$f\times \frac{9\times 10}{20\times 9}+\frac{1}{2}$$

Cancel out 9 in both numerator and denominator.

$$f\times \frac{10}{20}+\frac{1}{2}$$

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

$$f\times \frac{1}{2}+\frac{1}{2}$$