# How do you evaluate 5\frac{1}{10}-1\frac{1}{5}?

Aug 3, 2017

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

#### Explanation:

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

We first convert the mixed fractions to improper fractions.

To do this, we multiply the whole number by the denominator, add the product to the numerator, and place the result over the same denominator.

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

$\implies 1 \frac{1}{5} = \frac{6}{5}$

So now we have:

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

In order to complete the problem, we need to have the same denominator.

To do that we first find the LCM of the two denominators and then multiply the numerator and denominator of either fraction by the same number to get the denominators to match.

$\implies 10 \cdot 1 = 10$

$\implies 5 \cdot 2 = 10$

Hence we multiply the second fraction by $\frac{2}{2}$ so as to retain the same value as well as get the denominators to be the same.

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

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

Keeping the same denominator, we subtract the numerators.

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

$\frac{39}{10}$

We can change this into a mixed fraction by dividing the numerator by the denominator to get the whole number, and keeping the remnant on the denominator.

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

Aug 3, 2017

$5 \frac{1}{10} - 1 \frac{1}{5} = \frac{39}{10} = 3 \frac{2}{9}$

#### Explanation:

Evaluate:

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

Convert each mixed fraction to an improper fraction by multiplying the denominator by the whole number, adding the numerator, and placing the result over the original denominator.

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

Simplify.

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

In order to add or subtract fractions, they must have the same denominator. The least common denominator for $10$ and $5$ is $10$. Multiply $\frac{6}{5}$ by an equivalent fraction to give it the denominator of $10$. An equivalent fraction is equal to 1 (e.g. 4/4=1), so it does not change the value of the fraction.

$\frac{51}{10} - \frac{6}{5} \times \frac{2}{2}$

Simplify.

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

Simplify.

$\frac{39}{10}$

To convert to a mixed fraction, divide $39$ by $10$. The whole number quotient becomes the whole number of the mixed fraction, and the remainder becomes the numerator over the same denominator.

$39 \div 10 = \text{3 remainder 9}$

Simplify.

$3 \frac{9}{10}$