Solve f(16/7+(-3/14)]+[16/7-(-3/14)]

$$f ( \frac { 16 } { 7 } + ( \frac { - 3 } { 14 } ) ] + [ \frac { 16 } { 7 } - ( \frac { - 3 } { 14 } ) ]$$

Evaluate

$$\frac{29f}{14}+\frac{5}{2}$$

Solution Steps

Fraction \frac{-3}{14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$f\left(\frac{16}{7}-\frac{3}{14}\right)+\frac{16}{7}-\frac{-3}{14}$$

Least common multiple of 7 and 14 is 14. Convert \frac{16}{7} and \frac{3}{14} to fractions with denominator 14.

$$f\left(\frac{32}{14}-\frac{3}{14}\right)+\frac{16}{7}-\frac{-3}{14}$$

Since \frac{32}{14} and \frac{3}{14} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{32-3}{14}+\frac{16}{7}-\frac{-3}{14}$$

Subtract 3 from 32 to get 29.

$$f\times \frac{29}{14}+\frac{16}{7}-\frac{-3}{14}$$

Fraction \frac{-3}{14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$f\times \frac{29}{14}+\frac{16}{7}-\left(-\frac{3}{14}\right)$$

The opposite of -\frac{3}{14} is \frac{3}{14}.

$$f\times \frac{29}{14}+\frac{16}{7}+\frac{3}{14}$$

Least common multiple of 7 and 14 is 14. Convert \frac{16}{7} and \frac{3}{14} to fractions with denominator 14.

$$f\times \frac{29}{14}+\frac{32}{14}+\frac{3}{14}$$

Since \frac{32}{14} and \frac{3}{14} have the same denominator, add them by adding their numerators.

$$f\times \frac{29}{14}+\frac{32+3}{14}$$

Add 32 and 3 to get 35.

$$f\times \frac{29}{14}+\frac{35}{14}$$

Reduce the fraction \frac{35}{14} to lowest terms by extracting and canceling out 7.

$$f\times \frac{29}{14}+\frac{5}{2}$$

Expand

$$\frac{29f}{14}+\frac{5}{2}$$

Solution Steps

Fraction \frac{-3}{14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$f\left(\frac{16}{7}-\frac{3}{14}\right)+\frac{16}{7}-\frac{-3}{14}$$

Least common multiple of 7 and 14 is 14. Convert \frac{16}{7} and \frac{3}{14} to fractions with denominator 14.

$$f\left(\frac{32}{14}-\frac{3}{14}\right)+\frac{16}{7}-\frac{-3}{14}$$

Since \frac{32}{14} and \frac{3}{14} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{32-3}{14}+\frac{16}{7}-\frac{-3}{14}$$

Subtract 3 from 32 to get 29.

$$f\times \frac{29}{14}+\frac{16}{7}-\frac{-3}{14}$$

Fraction \frac{-3}{14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$f\times \frac{29}{14}+\frac{16}{7}-\left(-\frac{3}{14}\right)$$

The opposite of -\frac{3}{14} is \frac{3}{14}.

$$f\times \frac{29}{14}+\frac{16}{7}+\frac{3}{14}$$

Least common multiple of 7 and 14 is 14. Convert \frac{16}{7} and \frac{3}{14} to fractions with denominator 14.

$$f\times \frac{29}{14}+\frac{32}{14}+\frac{3}{14}$$

Since \frac{32}{14} and \frac{3}{14} have the same denominator, add them by adding their numerators.

$$f\times \frac{29}{14}+\frac{32+3}{14}$$

Add 32 and 3 to get 35.

$$f\times \frac{29}{14}+\frac{35}{14}$$

Reduce the fraction \frac{35}{14} to lowest terms by extracting and canceling out 7.

$$f\times \frac{29}{14}+\frac{5}{2}$$