Solve (-65/21--85/13)+(13/7-7/15)

$$( \frac{ -65 }{ 21 } - \frac{ -85 }{ 13 } )+( \frac{ 13 }{ 7 } - \frac{ 7 }{ 15 } )$$

Evaluate

$$\frac{6598}{1365}\approx 4.833699634$$

Solution Steps

Fraction \frac{-65}{21} can be rewritten as -\frac{65}{21} by extracting the negative sign.

$$-\frac{65}{21}-\frac{-85}{13}+\frac{13}{7}-\frac{7}{15}$$

Fraction \frac{-85}{13} can be rewritten as -\frac{85}{13} by extracting the negative sign.

$$-\frac{65}{21}-\left(-\frac{85}{13}\right)+\frac{13}{7}-\frac{7}{15}$$

The opposite of -\frac{85}{13} is \frac{85}{13}.

$$-\frac{65}{21}+\frac{85}{13}+\frac{13}{7}-\frac{7}{15}$$

Least common multiple of 21 and 13 is 273. Convert -\frac{65}{21} and \frac{85}{13} to fractions with denominator 273.

$$-\frac{845}{273}+\frac{1785}{273}+\frac{13}{7}-\frac{7}{15}$$

Since -\frac{845}{273} and \frac{1785}{273} have the same denominator, add them by adding their numerators.

$$\frac{-845+1785}{273}+\frac{13}{7}-\frac{7}{15}$$

Add -845 and 1785 to get 940.

$$\frac{940}{273}+\frac{13}{7}-\frac{7}{15}$$

Least common multiple of 273 and 7 is 273. Convert \frac{940}{273} and \frac{13}{7} to fractions with denominator 273.

$$\frac{940}{273}+\frac{507}{273}-\frac{7}{15}$$

Since \frac{940}{273} and \frac{507}{273} have the same denominator, add them by adding their numerators.

$$\frac{940+507}{273}-\frac{7}{15}$$

Add 940 and 507 to get 1447.

$$\frac{1447}{273}-\frac{7}{15}$$

Least common multiple of 273 and 15 is 1365. Convert \frac{1447}{273} and \frac{7}{15} to fractions with denominator 1365.

$$\frac{7235}{1365}-\frac{637}{1365}$$

Since \frac{7235}{1365} and \frac{637}{1365} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7235-637}{1365}$$

Subtract 637 from 7235 to get 6598.

$$\frac{6598}{1365}$$

Factor

$$\frac{2 \cdot 3299}{3 \cdot 5 \cdot 7 \cdot 13} = 4\frac{1138}{1365} = 4.833699633699633$$