Solve 1/1+2/4+3/9+4/16+frac{5}{25}

$$\frac{ 1 }{ 1 } + \frac{ 2 }{ 4 } + \frac{ 3 }{ 9 } + \frac{ 4 }{ 16 } + \frac{ 5 }{ 25 }$$

Evaluate

$$\frac{137}{60}\approx 2.283333333$$

Solution Steps

Divide 1 by 1 to get 1.

$$1+\frac{2}{4}+\frac{3}{9}+\frac{4}{16}+\frac{5}{25}$$

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

$$1+\frac{1}{2}+\frac{3}{9}+\frac{4}{16}+\frac{5}{25}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{2}{2}+\frac{1}{2}+\frac{3}{9}+\frac{4}{16}+\frac{5}{25}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{2}+\frac{3}{9}+\frac{4}{16}+\frac{5}{25}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}+\frac{3}{9}+\frac{4}{16}+\frac{5}{25}$$

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

$$\frac{3}{2}+\frac{1}{3}+\frac{4}{16}+\frac{5}{25}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{9}{6}+\frac{2}{6}+\frac{4}{16}+\frac{5}{25}$$

Since \frac{9}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{6}+\frac{4}{16}+\frac{5}{25}$$

Add 9 and 2 to get 11.

$$\frac{11}{6}+\frac{4}{16}+\frac{5}{25}$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{11}{6}+\frac{1}{4}+\frac{5}{25}$$

Least common multiple of 6 and 4 is 12. Convert \frac{11}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{22}{12}+\frac{3}{12}+\frac{5}{25}$$

Since \frac{22}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{22+3}{12}+\frac{5}{25}$$

Add 22 and 3 to get 25.

$$\frac{25}{12}+\frac{5}{25}$$

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

$$\frac{25}{12}+\frac{1}{5}$$

Least common multiple of 12 and 5 is 60. Convert \frac{25}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{125}{60}+\frac{12}{60}$$

Since \frac{125}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$\frac{125+12}{60}$$

Add 125 and 12 to get 137.

$$\frac{137}{60}$$

Factor

$$\frac{137}{2 ^ {2} \cdot 3 \cdot 5} = 2\frac{17}{60} = 2.283333333333333$$