Solve (-5/15-(6/24+12/18-15/25)]+[-2-6/9+415]

$$( - 5 / 15 - ( 6 / 24 + 12 / 18 - 15 / 25 ) ] + [ - 2 - 6 / 9 + 415 ]$$

Evaluate

$$\frac{24701}{60}\approx 411.683333333$$

Solution Steps

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{3}-\left(\frac{6}{24}+\frac{12}{18}-\frac{15}{25}\right)-2-\frac{6}{9}+415$$

Reduce the fraction \frac{6}{24} to lowest terms by extracting and canceling out 6.

$$-\frac{1}{3}-\left(\frac{1}{4}+\frac{12}{18}-\frac{15}{25}\right)-2-\frac{6}{9}+415$$

Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.

$$-\frac{1}{3}-\left(\frac{1}{4}+\frac{2}{3}-\frac{15}{25}\right)-2-\frac{6}{9}+415$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{2}{3} to fractions with denominator 12.

$$-\frac{1}{3}-\left(\frac{3}{12}+\frac{8}{12}-\frac{15}{25}\right)-2-\frac{6}{9}+415$$

Since \frac{3}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$-\frac{1}{3}-\left(\frac{3+8}{12}-\frac{15}{25}\right)-2-\frac{6}{9}+415$$

Add 3 and 8 to get 11.

$$-\frac{1}{3}-\left(\frac{11}{12}-\frac{15}{25}\right)-2-\frac{6}{9}+415$$

Reduce the fraction \frac{15}{25} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{3}-\left(\frac{11}{12}-\frac{3}{5}\right)-2-\frac{6}{9}+415$$

Least common multiple of 12 and 5 is 60. Convert \frac{11}{12} and \frac{3}{5} to fractions with denominator 60.

$$-\frac{1}{3}-\left(\frac{55}{60}-\frac{36}{60}\right)-2-\frac{6}{9}+415$$

Since \frac{55}{60} and \frac{36}{60} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}-\frac{55-36}{60}-2-\frac{6}{9}+415$$

Subtract 36 from 55 to get 19.

$$-\frac{1}{3}-\frac{19}{60}-2-\frac{6}{9}+415$$

Least common multiple of 3 and 60 is 60. Convert -\frac{1}{3} and \frac{19}{60} to fractions with denominator 60.

$$-\frac{20}{60}-\frac{19}{60}-2-\frac{6}{9}+415$$

Since -\frac{20}{60} and \frac{19}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-20-19}{60}-2-\frac{6}{9}+415$$

Subtract 19 from -20 to get -39.

$$\frac{-39}{60}-2-\frac{6}{9}+415$$

Reduce the fraction \frac{-39}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{13}{20}-2-\frac{6}{9}+415$$

Convert 2 to fraction \frac{40}{20}.

$$-\frac{13}{20}-\frac{40}{20}-\frac{6}{9}+415$$

Since -\frac{13}{20} and \frac{40}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-13-40}{20}-\frac{6}{9}+415$$

Subtract 40 from -13 to get -53.

$$-\frac{53}{20}-\frac{6}{9}+415$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$-\frac{53}{20}-\frac{2}{3}+415$$

Least common multiple of 20 and 3 is 60. Convert -\frac{53}{20} and \frac{2}{3} to fractions with denominator 60.

$$-\frac{159}{60}-\frac{40}{60}+415$$

Since -\frac{159}{60} and \frac{40}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-159-40}{60}+415$$

Subtract 40 from -159 to get -199.

$$-\frac{199}{60}+415$$

Convert 415 to fraction \frac{24900}{60}.

$$-\frac{199}{60}+\frac{24900}{60}$$

Since -\frac{199}{60} and \frac{24900}{60} have the same denominator, add them by adding their numerators.

$$\frac{-199+24900}{60}$$

Add -199 and 24900 to get 24701.

$$\frac{24701}{60}$$

Factor

$$\frac{17 \cdot 1453}{2 ^ {2} \cdot 3 \cdot 5} = 411\frac{41}{60} = 411.68333333333334$$