Solve frac{2^{2}}{1*3}+4^2/3*5+6^2/5*7+8^2/7*9+10^2/9*11

$$\frac { 2 ^ { 2 } } { 1 \times 3 } + \frac { 4 ^ { 2 } } { 3 \times 5 } + \frac { 6 ^ { 2 } } { 5 \times 7 } + \frac { 8 ^ { 2 } } { 7 \times 9 } + \frac { 10 ^ { 2 } } { 9 \times 11 }$$

Evaluate

$$\frac{60}{11}\approx 5.454545455$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{4}{1\times 3}+\frac{4^{2}}{3\times 5}+\frac{6^{2}}{5\times 7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Multiply 1 and 3 to get 3.

$$\frac{4}{3}+\frac{4^{2}}{3\times 5}+\frac{6^{2}}{5\times 7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{4}{3}+\frac{16}{3\times 5}+\frac{6^{2}}{5\times 7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Multiply 3 and 5 to get 15.

$$\frac{4}{3}+\frac{16}{15}+\frac{6^{2}}{5\times 7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Least common multiple of 3 and 15 is 15. Convert \frac{4}{3} and \frac{16}{15} to fractions with denominator 15.

$$\frac{20}{15}+\frac{16}{15}+\frac{6^{2}}{5\times 7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Since \frac{20}{15} and \frac{16}{15} have the same denominator, add them by adding their numerators.

$$\frac{20+16}{15}+\frac{6^{2}}{5\times 7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Add 20 and 16 to get 36.

$$\frac{36}{15}+\frac{6^{2}}{5\times 7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Reduce the fraction \frac{36}{15} to lowest terms by extracting and canceling out 3.

$$\frac{12}{5}+\frac{6^{2}}{5\times 7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{12}{5}+\frac{36}{5\times 7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Multiply 5 and 7 to get 35.

$$\frac{12}{5}+\frac{36}{35}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Least common multiple of 5 and 35 is 35. Convert \frac{12}{5} and \frac{36}{35} to fractions with denominator 35.

$$\frac{84}{35}+\frac{36}{35}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Since \frac{84}{35} and \frac{36}{35} have the same denominator, add them by adding their numerators.

$$\frac{84+36}{35}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Add 84 and 36 to get 120.

$$\frac{120}{35}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Reduce the fraction \frac{120}{35} to lowest terms by extracting and canceling out 5.

$$\frac{24}{7}+\frac{8^{2}}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{24}{7}+\frac{64}{7\times 9}+\frac{10^{2}}{9\times 11}$$

Multiply 7 and 9 to get 63.

$$\frac{24}{7}+\frac{64}{63}+\frac{10^{2}}{9\times 11}$$

Least common multiple of 7 and 63 is 63. Convert \frac{24}{7} and \frac{64}{63} to fractions with denominator 63.

$$\frac{216}{63}+\frac{64}{63}+\frac{10^{2}}{9\times 11}$$

Since \frac{216}{63} and \frac{64}{63} have the same denominator, add them by adding their numerators.

$$\frac{216+64}{63}+\frac{10^{2}}{9\times 11}$$

Add 216 and 64 to get 280.

$$\frac{280}{63}+\frac{10^{2}}{9\times 11}$$

Reduce the fraction \frac{280}{63} to lowest terms by extracting and canceling out 7.

$$\frac{40}{9}+\frac{10^{2}}{9\times 11}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{40}{9}+\frac{100}{9\times 11}$$

Multiply 9 and 11 to get 99.

$$\frac{40}{9}+\frac{100}{99}$$

Least common multiple of 9 and 99 is 99. Convert \frac{40}{9} and \frac{100}{99} to fractions with denominator 99.

$$\frac{440}{99}+\frac{100}{99}$$

Since \frac{440}{99} and \frac{100}{99} have the same denominator, add them by adding their numerators.

$$\frac{440+100}{99}$$

Add 440 and 100 to get 540.

$$\frac{540}{99}$$

Reduce the fraction \frac{540}{99} to lowest terms by extracting and canceling out 9.

$$\frac{60}{11}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 5}{11} = 5\frac{5}{11} = 5.454545454545454$$