Solve 8.2+111/2-11/4

$$8.2+ 11 \frac { 1 } { 2 } - 1 \frac { 1 } { 4 }$$

Evaluate

$$18.45$$

Solution Steps

Multiply 11 and 2 to get 22.

$$8.2+\frac{22+1}{2}-\frac{1\times 4+1}{4}$$

Add 22 and 1 to get 23.

$$8.2+\frac{23}{2}-\frac{1\times 4+1}{4}$$

Convert decimal number 8.2 to fraction \frac{82}{10}. Reduce the fraction \frac{82}{10} to lowest terms by extracting and canceling out 2.

$$\frac{41}{5}+\frac{23}{2}-\frac{1\times 4+1}{4}$$

Least common multiple of 5 and 2 is 10. Convert \frac{41}{5} and \frac{23}{2} to fractions with denominator 10.

$$\frac{82}{10}+\frac{115}{10}-\frac{1\times 4+1}{4}$$

Since \frac{82}{10} and \frac{115}{10} have the same denominator, add them by adding their numerators.

$$\frac{82+115}{10}-\frac{1\times 4+1}{4}$$

Add 82 and 115 to get 197.

$$\frac{197}{10}-\frac{1\times 4+1}{4}$$

Multiply 1 and 4 to get 4.

$$\frac{197}{10}-\frac{4+1}{4}$$

Add 4 and 1 to get 5.

$$\frac{197}{10}-\frac{5}{4}$$

Least common multiple of 10 and 4 is 20. Convert \frac{197}{10} and \frac{5}{4} to fractions with denominator 20.

$$\frac{394}{20}-\frac{25}{20}$$

Since \frac{394}{20} and \frac{25}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{394-25}{20}$$

Subtract 25 from 394 to get 369.

$$\frac{369}{20}$$

Factor

$$\frac{41 \cdot 3 ^ {2}}{5 \cdot 2 ^ {2}} = 18\frac{9}{20} = 18.45$$