Solve 1/2+1/6+2/15+2/35+frac{3}{70}+frac{2}{120}+frac{3}{180}+frac{5}{300}

$$\frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 2 } { 15 } + \frac { 2 } { 35 } + \frac { 3 } { 70 } + \frac { 2 } { 120 } + \frac { 3 } { 180 } + \frac { 5 } { 300 }$$

Evaluate

$$\frac{19}{20}=0.95$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{3}{6}+\frac{1}{6}+\frac{2}{15}+\frac{2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{6}+\frac{2}{15}+\frac{2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Add 3 and 1 to get 4.

$$\frac{4}{6}+\frac{2}{15}+\frac{2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Least common multiple of 3 and 15 is 15. Convert \frac{2}{3} and \frac{2}{15} to fractions with denominator 15.

$$\frac{10}{15}+\frac{2}{15}+\frac{2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Since \frac{10}{15} and \frac{2}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+2}{15}+\frac{2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Add 10 and 2 to get 12.

$$\frac{12}{15}+\frac{2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}+\frac{2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Least common multiple of 5 and 35 is 35. Convert \frac{4}{5} and \frac{2}{35} to fractions with denominator 35.

$$\frac{28}{35}+\frac{2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Since \frac{28}{35} and \frac{2}{35} have the same denominator, add them by adding their numerators.

$$\frac{28+2}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Add 28 and 2 to get 30.

$$\frac{30}{35}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Reduce the fraction \frac{30}{35} to lowest terms by extracting and canceling out 5.

$$\frac{6}{7}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Least common multiple of 7 and 70 is 70. Convert \frac{6}{7} and \frac{3}{70} to fractions with denominator 70.

$$\frac{60}{70}+\frac{3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Since \frac{60}{70} and \frac{3}{70} have the same denominator, add them by adding their numerators.

$$\frac{60+3}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Add 60 and 3 to get 63.

$$\frac{63}{70}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Reduce the fraction \frac{63}{70} to lowest terms by extracting and canceling out 7.

$$\frac{9}{10}+\frac{2}{120}+\frac{3}{180}+\frac{5}{300}$$

Reduce the fraction \frac{2}{120} to lowest terms by extracting and canceling out 2.

$$\frac{9}{10}+\frac{1}{60}+\frac{3}{180}+\frac{5}{300}$$

Least common multiple of 10 and 60 is 60. Convert \frac{9}{10} and \frac{1}{60} to fractions with denominator 60.

$$\frac{54}{60}+\frac{1}{60}+\frac{3}{180}+\frac{5}{300}$$

Since \frac{54}{60} and \frac{1}{60} have the same denominator, add them by adding their numerators.

$$\frac{54+1}{60}+\frac{3}{180}+\frac{5}{300}$$

Add 54 and 1 to get 55.

$$\frac{55}{60}+\frac{3}{180}+\frac{5}{300}$$

Reduce the fraction \frac{55}{60} to lowest terms by extracting and canceling out 5.

$$\frac{11}{12}+\frac{3}{180}+\frac{5}{300}$$

Reduce the fraction \frac{3}{180} to lowest terms by extracting and canceling out 3.

$$\frac{11}{12}+\frac{1}{60}+\frac{5}{300}$$

Least common multiple of 12 and 60 is 60. Convert \frac{11}{12} and \frac{1}{60} to fractions with denominator 60.

$$\frac{55}{60}+\frac{1}{60}+\frac{5}{300}$$

Since \frac{55}{60} and \frac{1}{60} have the same denominator, add them by adding their numerators.

$$\frac{55+1}{60}+\frac{5}{300}$$

Add 55 and 1 to get 56.

$$\frac{56}{60}+\frac{5}{300}$$

Reduce the fraction \frac{56}{60} to lowest terms by extracting and canceling out 4.

$$\frac{14}{15}+\frac{5}{300}$$

Reduce the fraction \frac{5}{300} to lowest terms by extracting and canceling out 5.

$$\frac{14}{15}+\frac{1}{60}$$

Least common multiple of 15 and 60 is 60. Convert \frac{14}{15} and \frac{1}{60} to fractions with denominator 60.

$$\frac{56}{60}+\frac{1}{60}$$

Since \frac{56}{60} and \frac{1}{60} have the same denominator, add them by adding their numerators.

$$\frac{56+1}{60}$$

Add 56 and 1 to get 57.

$$\frac{57}{60}$$

Reduce the fraction \frac{57}{60} to lowest terms by extracting and canceling out 3.

$$\frac{19}{20}$$

Factor

$$\frac{19}{2 ^ {2} \cdot 5} = 0.95$$