Solve 43/11-51/22+82/15-49/10

$$\frac { 43 } { 11 } - \frac { 51 } { 22 } + \frac { 82 } { 15 } - \frac { 49 } { 10 }$$

Evaluate

$$\frac{356}{165}\approx 2.157575758$$

Solution Steps

Least common multiple of 11 and 22 is 22. Convert \frac{43}{11} and \frac{51}{22} to fractions with denominator 22.

$$\frac{86}{22}-\frac{51}{22}+\frac{82}{15}-\frac{49}{10}$$

Since \frac{86}{22} and \frac{51}{22} have the same denominator, subtract them by subtracting their numerators.

$$\frac{86-51}{22}+\frac{82}{15}-\frac{49}{10}$$

Subtract 51 from 86 to get 35.

$$\frac{35}{22}+\frac{82}{15}-\frac{49}{10}$$

Least common multiple of 22 and 15 is 330. Convert \frac{35}{22} and \frac{82}{15} to fractions with denominator 330.

$$\frac{525}{330}+\frac{1804}{330}-\frac{49}{10}$$

Since \frac{525}{330} and \frac{1804}{330} have the same denominator, add them by adding their numerators.

$$\frac{525+1804}{330}-\frac{49}{10}$$

Add 525 and 1804 to get 2329.

$$\frac{2329}{330}-\frac{49}{10}$$

Least common multiple of 330 and 10 is 330. Convert \frac{2329}{330} and \frac{49}{10} to fractions with denominator 330.

$$\frac{2329}{330}-\frac{1617}{330}$$

Since \frac{2329}{330} and \frac{1617}{330} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2329-1617}{330}$$

Subtract 1617 from 2329 to get 712.

$$\frac{712}{330}$$

Reduce the fraction \frac{712}{330} to lowest terms by extracting and canceling out 2.

$$\frac{356}{165}$$

Factor

$$\frac{2 ^ {2} \cdot 89}{3 \cdot 5 \cdot 11} = 2\frac{26}{165} = 2.1575757575757577$$