Solve sum1/400+1/50+3/10+1/25+frac{9}{16}+frac{3}{40}

$$\sum \frac { 1 } { 400 } + \frac { 1 } { 50 } + \frac { 3 } { 10 } + \frac { 1 } { 25 } + \frac { 9 } { 16 } + \frac { 3 } { 40 }$$

Evaluate

$$\frac{Σ+399}{400}$$

Solution Steps

Least common multiple of 50 and 10 is 50. Convert \frac{1}{50} and \frac{3}{10} to fractions with denominator 50.

$$Σ\times \frac{1}{400}+\frac{1}{50}+\frac{15}{50}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Since \frac{1}{50} and \frac{15}{50} have the same denominator, add them by adding their numerators.

$$Σ\times \frac{1}{400}+\frac{1+15}{50}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Add 1 and 15 to get 16.

$$Σ\times \frac{1}{400}+\frac{16}{50}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Reduce the fraction \frac{16}{50} to lowest terms by extracting and canceling out 2.

$$Σ\times \frac{1}{400}+\frac{8}{25}+\frac{1}{25}+\frac{9}{16}+\frac{3}{40}$$

Since \frac{8}{25} and \frac{1}{25} have the same denominator, add them by adding their numerators.

$$Σ\times \frac{1}{400}+\frac{8+1}{25}+\frac{9}{16}+\frac{3}{40}$$

Add 8 and 1 to get 9.

$$Σ\times \frac{1}{400}+\frac{9}{25}+\frac{9}{16}+\frac{3}{40}$$

Least common multiple of 25 and 16 is 400. Convert \frac{9}{25} and \frac{9}{16} to fractions with denominator 400.

$$Σ\times \frac{1}{400}+\frac{144}{400}+\frac{225}{400}+\frac{3}{40}$$

Since \frac{144}{400} and \frac{225}{400} have the same denominator, add them by adding their numerators.

$$Σ\times \frac{1}{400}+\frac{144+225}{400}+\frac{3}{40}$$

Add 144 and 225 to get 369.

$$Σ\times \frac{1}{400}+\frac{369}{400}+\frac{3}{40}$$

Least common multiple of 400 and 40 is 400. Convert \frac{369}{400} and \frac{3}{40} to fractions with denominator 400.

$$Σ\times \frac{1}{400}+\frac{369}{400}+\frac{30}{400}$$

Since \frac{369}{400} and \frac{30}{400} have the same denominator, add them by adding their numerators.

$$Σ\times \frac{1}{400}+\frac{369+30}{400}$$

Add 369 and 30 to get 399.

$$Σ\times \frac{1}{400}+\frac{399}{400}$$

Factor

$$\frac{Σ+399}{400}$$

Solution Steps

Factor out \frac{1}{400}.

$$\frac{Σ+399}{400}$$

Consider Σ+8+120+16+225+30. Multiply and combine like terms.

$$Σ+399$$

Rewrite the complete factored expression.

$$\frac{Σ+399}{400}$$