Solve 5/24+7/60+9/40+11/210+frac{15}{504}+frac{17}{720}+frac{19}{990}

$$\frac { 5 } { 24 } + \frac { 7 } { 60 } + \frac { 9 } { 40 } + \frac { 11 } { 210 } + \frac { 15 } { 504 } + \frac { 17 } { 720 } + \frac { 19 } { 990 }$$

Evaluate

$$\frac{12473}{18480}\approx 0.674945887$$

Solution Steps

Least common multiple of 24 and 60 is 120. Convert \frac{5}{24} and \frac{7}{60} to fractions with denominator 120.

$$\frac{25}{120}+\frac{14}{120}+\frac{9}{40}+\frac{11}{210}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Since \frac{25}{120} and \frac{14}{120} have the same denominator, add them by adding their numerators.

$$\frac{25+14}{120}+\frac{9}{40}+\frac{11}{210}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Add 25 and 14 to get 39.

$$\frac{39}{120}+\frac{9}{40}+\frac{11}{210}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Reduce the fraction \frac{39}{120} to lowest terms by extracting and canceling out 3.

$$\frac{13}{40}+\frac{9}{40}+\frac{11}{210}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Since \frac{13}{40} and \frac{9}{40} have the same denominator, add them by adding their numerators.

$$\frac{13+9}{40}+\frac{11}{210}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Add 13 and 9 to get 22.

$$\frac{22}{40}+\frac{11}{210}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Reduce the fraction \frac{22}{40} to lowest terms by extracting and canceling out 2.

$$\frac{11}{20}+\frac{11}{210}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Least common multiple of 20 and 210 is 420. Convert \frac{11}{20} and \frac{11}{210} to fractions with denominator 420.

$$\frac{231}{420}+\frac{22}{420}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Since \frac{231}{420} and \frac{22}{420} have the same denominator, add them by adding their numerators.

$$\frac{231+22}{420}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Add 231 and 22 to get 253.

$$\frac{253}{420}+\frac{15}{504}+\frac{17}{720}+\frac{19}{990}$$

Reduce the fraction \frac{15}{504} to lowest terms by extracting and canceling out 3.

$$\frac{253}{420}+\frac{5}{168}+\frac{17}{720}+\frac{19}{990}$$

Least common multiple of 420 and 168 is 840. Convert \frac{253}{420} and \frac{5}{168} to fractions with denominator 840.

$$\frac{506}{840}+\frac{25}{840}+\frac{17}{720}+\frac{19}{990}$$

Since \frac{506}{840} and \frac{25}{840} have the same denominator, add them by adding their numerators.

$$\frac{506+25}{840}+\frac{17}{720}+\frac{19}{990}$$

Add 506 and 25 to get 531.

$$\frac{531}{840}+\frac{17}{720}+\frac{19}{990}$$

Reduce the fraction \frac{531}{840} to lowest terms by extracting and canceling out 3.

$$\frac{177}{280}+\frac{17}{720}+\frac{19}{990}$$

Least common multiple of 280 and 720 is 5040. Convert \frac{177}{280} and \frac{17}{720} to fractions with denominator 5040.

$$\frac{3186}{5040}+\frac{119}{5040}+\frac{19}{990}$$

Since \frac{3186}{5040} and \frac{119}{5040} have the same denominator, add them by adding their numerators.

$$\frac{3186+119}{5040}+\frac{19}{990}$$

Add 3186 and 119 to get 3305.

$$\frac{3305}{5040}+\frac{19}{990}$$

Reduce the fraction \frac{3305}{5040} to lowest terms by extracting and canceling out 5.

$$\frac{661}{1008}+\frac{19}{990}$$

Least common multiple of 1008 and 990 is 55440. Convert \frac{661}{1008} and \frac{19}{990} to fractions with denominator 55440.

$$\frac{36355}{55440}+\frac{1064}{55440}$$

Since \frac{36355}{55440} and \frac{1064}{55440} have the same denominator, add them by adding their numerators.

$$\frac{36355+1064}{55440}$$

Add 36355 and 1064 to get 37419.

$$\frac{37419}{55440}$$

Reduce the fraction \frac{37419}{55440} to lowest terms by extracting and canceling out 3.

$$\frac{12473}{18480}$$

Factor

$$\frac{12473}{2 ^ {4} \cdot 3 \cdot 5 \cdot 7 \cdot 11} = 0.6749458874458875$$