Solve 1+4/3+9/5+16/7+25/9

$$1 + \frac { 4 } { 3 } + \frac { 9 } { 5 } + \frac { 16 } { 7 } + \frac { 25 } { 9 }$$

Evaluate

$$\frac{2897}{315}\approx 9.196825397$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}+\frac{4}{3}+\frac{9}{5}+\frac{16}{7}+\frac{25}{9}$$

Since \frac{3}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{3}+\frac{9}{5}+\frac{16}{7}+\frac{25}{9}$$

Add 3 and 4 to get 7.

$$\frac{7}{3}+\frac{9}{5}+\frac{16}{7}+\frac{25}{9}$$

Least common multiple of 3 and 5 is 15. Convert \frac{7}{3} and \frac{9}{5} to fractions with denominator 15.

$$\frac{35}{15}+\frac{27}{15}+\frac{16}{7}+\frac{25}{9}$$

Since \frac{35}{15} and \frac{27}{15} have the same denominator, add them by adding their numerators.

$$\frac{35+27}{15}+\frac{16}{7}+\frac{25}{9}$$

Add 35 and 27 to get 62.

$$\frac{62}{15}+\frac{16}{7}+\frac{25}{9}$$

Least common multiple of 15 and 7 is 105. Convert \frac{62}{15} and \frac{16}{7} to fractions with denominator 105.

$$\frac{434}{105}+\frac{240}{105}+\frac{25}{9}$$

Since \frac{434}{105} and \frac{240}{105} have the same denominator, add them by adding their numerators.

$$\frac{434+240}{105}+\frac{25}{9}$$

Add 434 and 240 to get 674.

$$\frac{674}{105}+\frac{25}{9}$$

Least common multiple of 105 and 9 is 315. Convert \frac{674}{105} and \frac{25}{9} to fractions with denominator 315.

$$\frac{2022}{315}+\frac{875}{315}$$

Since \frac{2022}{315} and \frac{875}{315} have the same denominator, add them by adding their numerators.

$$\frac{2022+875}{315}$$

Add 2022 and 875 to get 2897.

$$\frac{2897}{315}$$

Factor

$$\frac{2897}{3 ^ {2} \cdot 5 \cdot 7} = 9\frac{62}{315} = 9.196825396825396$$