Solve 434/9-49/18+27+434/9

$$\frac{ 434 }{ 9 } - \frac{ 49 }{ 18 } +27+ \frac{ 434 }{ 9 }$$

Evaluate

$$\frac{2173}{18}\approx 120.722222222$$

Solution Steps

Least common multiple of 9 and 18 is 18. Convert \frac{434}{9} and \frac{49}{18} to fractions with denominator 18.

$$\frac{868}{18}-\frac{49}{18}+27+\frac{434}{9}$$

Since \frac{868}{18} and \frac{49}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{868-49}{18}+27+\frac{434}{9}$$

Subtract 49 from 868 to get 819.

$$\frac{819}{18}+27+\frac{434}{9}$$

Reduce the fraction \frac{819}{18} to lowest terms by extracting and canceling out 9.

$$\frac{91}{2}+27+\frac{434}{9}$$

Convert 27 to fraction \frac{54}{2}.

$$\frac{91}{2}+\frac{54}{2}+\frac{434}{9}$$

Since \frac{91}{2} and \frac{54}{2} have the same denominator, add them by adding their numerators.

$$\frac{91+54}{2}+\frac{434}{9}$$

Add 91 and 54 to get 145.

$$\frac{145}{2}+\frac{434}{9}$$

Least common multiple of 2 and 9 is 18. Convert \frac{145}{2} and \frac{434}{9} to fractions with denominator 18.

$$\frac{1305}{18}+\frac{868}{18}$$

Since \frac{1305}{18} and \frac{868}{18} have the same denominator, add them by adding their numerators.

$$\frac{1305+868}{18}$$

Add 1305 and 868 to get 2173.

$$\frac{2173}{18}$$

Factor

$$\frac{41 \cdot 53}{2 \cdot 3 ^ {2}} = 120\frac{13}{18} = 120.72222222222223$$