Solve {l}{1/20+1/10+2/10}{+1/4+frac{3}{10}}

$$\left. \begin{array} { l } { \frac { 1 } { 20 } + \frac { 1 } { 10 } + \frac { 2 } { 10 } } \\ { + \frac { 1 } { 4 } + \frac { 3 } { 10 } } \end{array} \right.$$

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

Least common multiple of 20 and 10 is 20. Convert \frac{1}{20} and \frac{1}{10} to fractions with denominator 20.

$$\frac{1}{20}+\frac{2}{20}+\frac{2}{10}+\frac{1}{4}+\frac{3}{10}$$

Since \frac{1}{20} and \frac{2}{20} have the same denominator, add them by adding their numerators.

$$\frac{1+2}{20}+\frac{2}{10}+\frac{1}{4}+\frac{3}{10}$$

Add 1 and 2 to get 3.

$$\frac{3}{20}+\frac{2}{10}+\frac{1}{4}+\frac{3}{10}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{20}+\frac{1}{5}+\frac{1}{4}+\frac{3}{10}$$

Least common multiple of 20 and 5 is 20. Convert \frac{3}{20} and \frac{1}{5} to fractions with denominator 20.

$$\frac{3}{20}+\frac{4}{20}+\frac{1}{4}+\frac{3}{10}$$

Since \frac{3}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{20}+\frac{1}{4}+\frac{3}{10}$$

Add 3 and 4 to get 7.

$$\frac{7}{20}+\frac{1}{4}+\frac{3}{10}$$

Least common multiple of 20 and 4 is 20. Convert \frac{7}{20} and \frac{1}{4} to fractions with denominator 20.

$$\frac{7}{20}+\frac{5}{20}+\frac{3}{10}$$

Since \frac{7}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{7+5}{20}+\frac{3}{10}$$

Add 7 and 5 to get 12.

$$\frac{12}{20}+\frac{3}{10}$$

Reduce the fraction \frac{12}{20} to lowest terms by extracting and canceling out 4.

$$\frac{3}{5}+\frac{3}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{3}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{6}{10}+\frac{3}{10}$$

Since \frac{6}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{6+3}{10}$$

Add 6 and 3 to get 9.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$