Solve (20111/5-20101/6)*129/31

$$( 2011 \frac { 1 } { 5 } - 2010 \frac { 1 } { 6 } ) \cdot 1 \frac { 29 } { 31 }$$

Evaluate

$$2$$

Solution Steps

Multiply 2011 and 5 to get 10055.

$$\left(\frac{10055+1}{5}-\frac{2010\times 6+1}{6}\right)\times \frac{1\times 31+29}{31}$$

Add 10055 and 1 to get 10056.

$$\left(\frac{10056}{5}-\frac{2010\times 6+1}{6}\right)\times \frac{1\times 31+29}{31}$$

Multiply 2010 and 6 to get 12060.

$$\left(\frac{10056}{5}-\frac{12060+1}{6}\right)\times \frac{1\times 31+29}{31}$$

Add 12060 and 1 to get 12061.

$$\left(\frac{10056}{5}-\frac{12061}{6}\right)\times \frac{1\times 31+29}{31}$$

Least common multiple of 5 and 6 is 30. Convert \frac{10056}{5} and \frac{12061}{6} to fractions with denominator 30.

$$\left(\frac{60336}{30}-\frac{60305}{30}\right)\times \frac{1\times 31+29}{31}$$

Since \frac{60336}{30} and \frac{60305}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{60336-60305}{30}\times \frac{1\times 31+29}{31}$$

Subtract 60305 from 60336 to get 31.

$$\frac{31}{30}\times \frac{1\times 31+29}{31}$$

Multiply 1 and 31 to get 31.

$$\frac{31}{30}\times \frac{31+29}{31}$$

Add 31 and 29 to get 60.

$$\frac{31}{30}\times \frac{60}{31}$$

Multiply \frac{31}{30} times \frac{60}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31\times 60}{30\times 31}$$

Cancel out 31 in both numerator and denominator.

$$\frac{60}{30}$$

Divide 60 by 30 to get 2.

$$2$$

Factor

$$2$$