Solve 23/7--11/21+-7/14--7/28=

$$\frac { 23 } { 7 } - \frac { - 11 } { 21 } + \frac { - 7 } { 14 } - \frac { - 7 } { 28 } =$$

Evaluate

$$\frac{299}{84}\approx 3.55952381$$

Solution Steps

Fraction \frac{-11}{21} can be rewritten as -\frac{11}{21} by extracting the negative sign.

$$\frac{23}{7}-\left(-\frac{11}{21}\right)+\frac{-7}{14}-\frac{-7}{28}$$

The opposite of -\frac{11}{21} is \frac{11}{21}.

$$\frac{23}{7}+\frac{11}{21}+\frac{-7}{14}-\frac{-7}{28}$$

Least common multiple of 7 and 21 is 21. Convert \frac{23}{7} and \frac{11}{21} to fractions with denominator 21.

$$\frac{69}{21}+\frac{11}{21}+\frac{-7}{14}-\frac{-7}{28}$$

Since \frac{69}{21} and \frac{11}{21} have the same denominator, add them by adding their numerators.

$$\frac{69+11}{21}+\frac{-7}{14}-\frac{-7}{28}$$

Add 69 and 11 to get 80.

$$\frac{80}{21}+\frac{-7}{14}-\frac{-7}{28}$$

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

$$\frac{80}{21}-\frac{1}{2}-\frac{-7}{28}$$

Least common multiple of 21 and 2 is 42. Convert \frac{80}{21} and \frac{1}{2} to fractions with denominator 42.

$$\frac{160}{42}-\frac{21}{42}-\frac{-7}{28}$$

Since \frac{160}{42} and \frac{21}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{160-21}{42}-\frac{-7}{28}$$

Subtract 21 from 160 to get 139.

$$\frac{139}{42}-\frac{-7}{28}$$

Reduce the fraction \frac{-7}{28} to lowest terms by extracting and canceling out 7.

$$\frac{139}{42}-\left(-\frac{1}{4}\right)$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$\frac{139}{42}+\frac{1}{4}$$

Least common multiple of 42 and 4 is 84. Convert \frac{139}{42} and \frac{1}{4} to fractions with denominator 84.

$$\frac{278}{84}+\frac{21}{84}$$

Since \frac{278}{84} and \frac{21}{84} have the same denominator, add them by adding their numerators.

$$\frac{278+21}{84}$$

Add 278 and 21 to get 299.

$$\frac{299}{84}$$

Factor

$$\frac{13 \cdot 23}{2 ^ {2} \cdot 3 \cdot 7} = 3\frac{47}{84} = 3.5595238095238093$$