Solve 5/20*1+3/20*2+3/20*3+2/20*4+frac{4}{20}*5+frac{1}{20}*6

$$\frac { 5 } { 20 } \cdot 1 + \frac { 3 } { 20 } \cdot 2 + \frac { 3 } { 20 } \cdot 3 + \frac { 2 } { 20 } \cdot 4 + \frac { 4 } { 20 } \cdot 5 + \frac { 1 } { 20 } \cdot 6$$

Evaluate

$$\frac{27}{10}=2.7$$

Solution Steps

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$\frac{1}{4}\times 1+\frac{3}{20}\times 2+\frac{3}{20}\times 3+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Multiply \frac{1}{4} and 1 to get \frac{1}{4}.

$$\frac{1}{4}+\frac{3}{20}\times 2+\frac{3}{20}\times 3+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Express \frac{3}{20}\times 2 as a single fraction.

$$\frac{1}{4}+\frac{3\times 2}{20}+\frac{3}{20}\times 3+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Multiply 3 and 2 to get 6.

$$\frac{1}{4}+\frac{6}{20}+\frac{3}{20}\times 3+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}+\frac{3}{10}+\frac{3}{20}\times 3+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Least common multiple of 4 and 10 is 20. Convert \frac{1}{4} and \frac{3}{10} to fractions with denominator 20.

$$\frac{5}{20}+\frac{6}{20}+\frac{3}{20}\times 3+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Since \frac{5}{20} and \frac{6}{20} have the same denominator, add them by adding their numerators.

$$\frac{5+6}{20}+\frac{3}{20}\times 3+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Add 5 and 6 to get 11.

$$\frac{11}{20}+\frac{3}{20}\times 3+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Express \frac{3}{20}\times 3 as a single fraction.

$$\frac{11}{20}+\frac{3\times 3}{20}+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Multiply 3 and 3 to get 9.

$$\frac{11}{20}+\frac{9}{20}+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Since \frac{11}{20} and \frac{9}{20} have the same denominator, add them by adding their numerators.

$$\frac{11+9}{20}+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Add 11 and 9 to get 20.

$$\frac{20}{20}+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Divide 20 by 20 to get 1.

$$1+\frac{2}{20}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Reduce the fraction \frac{2}{20} to lowest terms by extracting and canceling out 2.

$$1+\frac{1}{10}\times 4+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Multiply \frac{1}{10} and 4 to get \frac{4}{10}.

$$1+\frac{4}{10}+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$1+\frac{2}{5}+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{5}{5}+\frac{2}{5}+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{5+2}{5}+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

Add 5 and 2 to get 7.

$$\frac{7}{5}+\frac{4}{20}\times 5+\frac{1}{20}\times 6$$

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

$$\frac{7}{5}+\frac{1}{5}\times 5+\frac{1}{20}\times 6$$

Cancel out 5 and 5.

$$\frac{7}{5}+1+\frac{1}{20}\times 6$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{7}{5}+\frac{5}{5}+\frac{1}{20}\times 6$$

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

$$\frac{7+5}{5}+\frac{1}{20}\times 6$$

Add 7 and 5 to get 12.

$$\frac{12}{5}+\frac{1}{20}\times 6$$

Multiply \frac{1}{20} and 6 to get \frac{6}{20}.

$$\frac{12}{5}+\frac{6}{20}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{12}{5}+\frac{3}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{12}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{24}{10}+\frac{3}{10}$$

Since \frac{24}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{24+3}{10}$$

Add 24 and 3 to get 27.

$$\frac{27}{10}$$

Factor

$$\frac{3 ^ {3}}{2 \cdot 5} = 2\frac{7}{10} = 2.7$$