Solve 11/2frac{3{6}}+25/6

$$1 \frac { 1 } { 2 \frac { 3 } { 6 } } + 2 \frac { 5 } { 6 }$$

Evaluate

$$\frac{97}{30}\approx 3.233333333$$

Solution Steps

Divide 1 by \frac{2\times 6+3}{6} by multiplying 1 by the reciprocal of \frac{2\times 6+3}{6}.

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

Multiply 2 and 6 to get 12.

$$1\times \frac{6}{12+3}+\frac{2\times 6+5}{6}$$

Add 12 and 3 to get 15.

$$1\times \frac{6}{15}+\frac{2\times 6+5}{6}$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

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

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

$$\frac{2}{5}+\frac{2\times 6+5}{6}$$

Multiply 2 and 6 to get 12.

$$\frac{2}{5}+\frac{12+5}{6}$$

Add 12 and 5 to get 17.

$$\frac{2}{5}+\frac{17}{6}$$

Least common multiple of 5 and 6 is 30. Convert \frac{2}{5} and \frac{17}{6} to fractions with denominator 30.

$$\frac{12}{30}+\frac{85}{30}$$

Since \frac{12}{30} and \frac{85}{30} have the same denominator, add them by adding their numerators.

$$\frac{12+85}{30}$$

Add 12 and 85 to get 97.

$$\frac{97}{30}$$

Factor

$$\frac{97}{2 \cdot 3 \cdot 5} = 3\frac{7}{30} = 3.2333333333333334$$