Solve 8/27*3+1/4*4+1/6*5+1/27*6

$$\frac { 8 } { 27 } \times 3 + \frac { 1 } { 4 } \times 4 + \frac { 1 } { 6 } \times 5 + \frac { 1 } { 27 } \times 6$$

Evaluate

$$\frac{53}{18}\approx 2.944444444$$

Solution Steps

Express \frac{8}{27}\times 3 as a single fraction.

$$\frac{8\times 3}{27}+\frac{1}{4}\times 4+\frac{1}{6}\times 5+\frac{1}{27}\times 6$$

Multiply 8 and 3 to get 24.

$$\frac{24}{27}+\frac{1}{4}\times 4+\frac{1}{6}\times 5+\frac{1}{27}\times 6$$

Reduce the fraction \frac{24}{27} to lowest terms by extracting and canceling out 3.

$$\frac{8}{9}+\frac{1}{4}\times 4+\frac{1}{6}\times 5+\frac{1}{27}\times 6$$

Cancel out 4 and 4.

$$\frac{8}{9}+1+\frac{1}{6}\times 5+\frac{1}{27}\times 6$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{8}{9}+\frac{9}{9}+\frac{1}{6}\times 5+\frac{1}{27}\times 6$$

Since \frac{8}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{8+9}{9}+\frac{1}{6}\times 5+\frac{1}{27}\times 6$$

Add 8 and 9 to get 17.

$$\frac{17}{9}+\frac{1}{6}\times 5+\frac{1}{27}\times 6$$

Multiply \frac{1}{6} and 5 to get \frac{5}{6}.

$$\frac{17}{9}+\frac{5}{6}+\frac{1}{27}\times 6$$

Least common multiple of 9 and 6 is 18. Convert \frac{17}{9} and \frac{5}{6} to fractions with denominator 18.

$$\frac{34}{18}+\frac{15}{18}+\frac{1}{27}\times 6$$

Since \frac{34}{18} and \frac{15}{18} have the same denominator, add them by adding their numerators.

$$\frac{34+15}{18}+\frac{1}{27}\times 6$$

Add 34 and 15 to get 49.

$$\frac{49}{18}+\frac{1}{27}\times 6$$

Multiply \frac{1}{27} and 6 to get \frac{6}{27}.

$$\frac{49}{18}+\frac{6}{27}$$

Reduce the fraction \frac{6}{27} to lowest terms by extracting and canceling out 3.

$$\frac{49}{18}+\frac{2}{9}$$

Least common multiple of 18 and 9 is 18. Convert \frac{49}{18} and \frac{2}{9} to fractions with denominator 18.

$$\frac{49}{18}+\frac{4}{18}$$

Since \frac{49}{18} and \frac{4}{18} have the same denominator, add them by adding their numerators.

$$\frac{49+4}{18}$$

Add 49 and 4 to get 53.

$$\frac{53}{18}$$

Factor

$$\frac{53}{2 \cdot 3 ^ {2}} = 2\frac{17}{18} = 2.9444444444444446$$