Solve 43/10+82/15-51/22-49/10

$$\frac { 43 } { 10 } + \frac { 82 } { 15 } - \frac { 51 } { 22 } - \frac { 49 } { 10 }$$

Evaluate

$$\frac{841}{330}\approx 2.548484848$$

Solution Steps

Least common multiple of 10 and 15 is 30. Convert \frac{43}{10} and \frac{82}{15} to fractions with denominator 30.

$$\frac{129}{30}+\frac{164}{30}-\frac{51}{22}-\frac{49}{10}$$

Since \frac{129}{30} and \frac{164}{30} have the same denominator, add them by adding their numerators.

$$\frac{129+164}{30}-\frac{51}{22}-\frac{49}{10}$$

Add 129 and 164 to get 293.

$$\frac{293}{30}-\frac{51}{22}-\frac{49}{10}$$

Least common multiple of 30 and 22 is 330. Convert \frac{293}{30} and \frac{51}{22} to fractions with denominator 330.

$$\frac{3223}{330}-\frac{765}{330}-\frac{49}{10}$$

Since \frac{3223}{330} and \frac{765}{330} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3223-765}{330}-\frac{49}{10}$$

Subtract 765 from 3223 to get 2458.

$$\frac{2458}{330}-\frac{49}{10}$$

Reduce the fraction \frac{2458}{330} to lowest terms by extracting and canceling out 2.

$$\frac{1229}{165}-\frac{49}{10}$$

Least common multiple of 165 and 10 is 330. Convert \frac{1229}{165} and \frac{49}{10} to fractions with denominator 330.

$$\frac{2458}{330}-\frac{1617}{330}$$

Since \frac{2458}{330} and \frac{1617}{330} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2458-1617}{330}$$

Subtract 1617 from 2458 to get 841.

$$\frac{841}{330}$$

Factor

$$\frac{29 ^ {2}}{2 \cdot 3 \cdot 5 \cdot 11} = 2\frac{181}{330} = 2.5484848484848484$$