Solve (5/3*5/3^2)+(6/4*5/4^2)+(frac{2}{5}*frac{5}{5})+(frac{8}{6}*frac{5}{6^2})+(frac{9}{7}*frac{5}{7})

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

Evaluate

$$\frac{204499}{70560}\approx 2.898228458$$

Solution Steps

Divide 5 by 5 to get 1.

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

Calculate 3 to the power of 2 and get 9.

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

Multiply \frac{5}{3} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 5}{3\times 9}.

$$\frac{25}{27}+\frac{6}{4}\times \frac{5}{4^{2}}+\frac{2}{5}\times 1+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

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

$$\frac{25}{27}+\frac{3}{2}\times \frac{5}{4^{2}}+\frac{2}{5}\times 1+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{25}{27}+\frac{3}{2}\times \frac{5}{16}+\frac{2}{5}\times 1+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Multiply \frac{3}{2} times \frac{5}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25}{27}+\frac{3\times 5}{2\times 16}+\frac{2}{5}\times 1+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Do the multiplications in the fraction \frac{3\times 5}{2\times 16}.

$$\frac{25}{27}+\frac{15}{32}+\frac{2}{5}\times 1+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Least common multiple of 27 and 32 is 864. Convert \frac{25}{27} and \frac{15}{32} to fractions with denominator 864.

$$\frac{800}{864}+\frac{405}{864}+\frac{2}{5}\times 1+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Since \frac{800}{864} and \frac{405}{864} have the same denominator, add them by adding their numerators.

$$\frac{800+405}{864}+\frac{2}{5}\times 1+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Add 800 and 405 to get 1205.

$$\frac{1205}{864}+\frac{2}{5}\times 1+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Multiply \frac{2}{5} and 1 to get \frac{2}{5}.

$$\frac{1205}{864}+\frac{2}{5}+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Least common multiple of 864 and 5 is 4320. Convert \frac{1205}{864} and \frac{2}{5} to fractions with denominator 4320.

$$\frac{6025}{4320}+\frac{1728}{4320}+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Since \frac{6025}{4320} and \frac{1728}{4320} have the same denominator, add them by adding their numerators.

$$\frac{6025+1728}{4320}+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Add 6025 and 1728 to get 7753.

$$\frac{7753}{4320}+\frac{8}{6}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{7753}{4320}+\frac{4}{3}\times \frac{5}{6^{2}}+\frac{9}{7}\times \frac{5}{7}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{7753}{4320}+\frac{4}{3}\times \frac{5}{36}+\frac{9}{7}\times \frac{5}{7}$$

Multiply \frac{4}{3} times \frac{5}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7753}{4320}+\frac{4\times 5}{3\times 36}+\frac{9}{7}\times \frac{5}{7}$$

Do the multiplications in the fraction \frac{4\times 5}{3\times 36}.

$$\frac{7753}{4320}+\frac{20}{108}+\frac{9}{7}\times \frac{5}{7}$$

Reduce the fraction \frac{20}{108} to lowest terms by extracting and canceling out 4.

$$\frac{7753}{4320}+\frac{5}{27}+\frac{9}{7}\times \frac{5}{7}$$

Least common multiple of 4320 and 27 is 4320. Convert \frac{7753}{4320} and \frac{5}{27} to fractions with denominator 4320.

$$\frac{7753}{4320}+\frac{800}{4320}+\frac{9}{7}\times \frac{5}{7}$$

Since \frac{7753}{4320} and \frac{800}{4320} have the same denominator, add them by adding their numerators.

$$\frac{7753+800}{4320}+\frac{9}{7}\times \frac{5}{7}$$

Add 7753 and 800 to get 8553.

$$\frac{8553}{4320}+\frac{9}{7}\times \frac{5}{7}$$

Reduce the fraction \frac{8553}{4320} to lowest terms by extracting and canceling out 3.

$$\frac{2851}{1440}+\frac{9}{7}\times \frac{5}{7}$$

Multiply \frac{9}{7} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2851}{1440}+\frac{9\times 5}{7\times 7}$$

Do the multiplications in the fraction \frac{9\times 5}{7\times 7}.

$$\frac{2851}{1440}+\frac{45}{49}$$

Least common multiple of 1440 and 49 is 70560. Convert \frac{2851}{1440} and \frac{45}{49} to fractions with denominator 70560.

$$\frac{139699}{70560}+\frac{64800}{70560}$$

Since \frac{139699}{70560} and \frac{64800}{70560} have the same denominator, add them by adding their numerators.

$$\frac{139699+64800}{70560}$$

Add 139699 and 64800 to get 204499.

$$\frac{204499}{70560}$$

Factor

$$\frac{37 \cdot 5527}{2 ^ {5} \cdot 3 ^ {2} \cdot 5 \cdot 7 ^ {2}} = 2\frac{63379}{70560} = 2.8982284580498865$$