# How do you evaluate 5 1/10 - 1 1/5 ?

Aug 2, 2017

Find a common denominator so that the fractions can be subtracted

#### Explanation:

The common denominator between 10 and 5 is 10. To make 5 into 10 multiply by 2.

$1 \frac{1}{5} \times \frac{2}{2} = 1 \frac{2}{10}$

$5 \frac{1}{10} - 1 \frac{2}{10} = 4 \frac{11}{10} - 1 \frac{2}{10}$ Changing 1 whole into 10/10th

$4 \frac{11}{10} - 1 \frac{2}{10} = 3 \frac{9}{10}$

Aug 3, 2017

$\frac{39}{10}$ or $3 \frac{9}{10}$

#### Explanation:

$5 \frac{1}{10} - 1 \frac{1}{5}$

The easiest way to do this is to start by changing the mixed fractions into improper fractions.

This is done by multiplying the whole number by the denominator, adding the product to the numerator, and placing the result on the denominator.

$\implies 5 \frac{1}{10} = \frac{51}{10}$ AND $\implies 1 \frac{1}{5} = \frac{6}{5}$

So now we can write:

$\frac{51}{10} - \frac{6}{5}$

To subtract fractions, the denominators need to be the same. Hence we calculate the LCM (Lowest Common Multiple) of the two denominators and adjust the fractions accordingly by multiplying the numerator and the denominator by the same number so as to retain the value and get the denominator to become the LCM.

$\implies 10 \times 1 = 10$ AND $\implies 5 \times 2 = 10$

The LCM is $10$ and the numerator and denominator of the second fraction have to be multiplied by $2$.

$\frac{51}{10} - \left(\frac{6}{5} \times \frac{2}{2}\right)$

$\frac{51}{10} - \frac{12}{10}$

Keeping the same denominator, we subtract the numerators.

$\frac{51 - 12}{10}$

$\frac{39}{10}$

This can be converted to a mixed fraction by dividing the numerator by the denominator to get the whole number and then placing the remnant on the denominator.

$\frac{39}{10} = 3 \frac{9}{10}$