Solve 3/2+7/6+13/12+19/18+frac{21}{24}

$$\frac { 3 } { 2 } + \frac { 7 } { 6 } + \frac { 13 } { 12 } + \frac { 19 } { 18 } + \frac { 21 } { 24 }$$

Evaluate

$$\frac{409}{72}\approx 5.680555556$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert \frac{3}{2} and \frac{7}{6} to fractions with denominator 6.

$$\frac{9}{6}+\frac{7}{6}+\frac{13}{12}+\frac{19}{18}+\frac{21}{24}$$

Since \frac{9}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+7}{6}+\frac{13}{12}+\frac{19}{18}+\frac{21}{24}$$

Add 9 and 7 to get 16.

$$\frac{16}{6}+\frac{13}{12}+\frac{19}{18}+\frac{21}{24}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}+\frac{13}{12}+\frac{19}{18}+\frac{21}{24}$$

Least common multiple of 3 and 12 is 12. Convert \frac{8}{3} and \frac{13}{12} to fractions with denominator 12.

$$\frac{32}{12}+\frac{13}{12}+\frac{19}{18}+\frac{21}{24}$$

Since \frac{32}{12} and \frac{13}{12} have the same denominator, add them by adding their numerators.

$$\frac{32+13}{12}+\frac{19}{18}+\frac{21}{24}$$

Add 32 and 13 to get 45.

$$\frac{45}{12}+\frac{19}{18}+\frac{21}{24}$$

Reduce the fraction \frac{45}{12} to lowest terms by extracting and canceling out 3.

$$\frac{15}{4}+\frac{19}{18}+\frac{21}{24}$$

Least common multiple of 4 and 18 is 36. Convert \frac{15}{4} and \frac{19}{18} to fractions with denominator 36.

$$\frac{135}{36}+\frac{38}{36}+\frac{21}{24}$$

Since \frac{135}{36} and \frac{38}{36} have the same denominator, add them by adding their numerators.

$$\frac{135+38}{36}+\frac{21}{24}$$

Add 135 and 38 to get 173.

$$\frac{173}{36}+\frac{21}{24}$$

Reduce the fraction \frac{21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{173}{36}+\frac{7}{8}$$

Least common multiple of 36 and 8 is 72. Convert \frac{173}{36} and \frac{7}{8} to fractions with denominator 72.

$$\frac{346}{72}+\frac{63}{72}$$

Since \frac{346}{72} and \frac{63}{72} have the same denominator, add them by adding their numerators.

$$\frac{346+63}{72}$$

Add 346 and 63 to get 409.

$$\frac{409}{72}$$

Factor

$$\frac{409}{2 ^ {3} \cdot 3 ^ {2}} = 5\frac{49}{72} = 5.680555555555555$$