# Question 3b032

Feb 3, 2017

see explanation.

#### Explanation:

If you check again it appears that the question is.

$\frac{5 x}{6} - \frac{3}{10} \text{ and not } \frac{5}{x} - \frac{3}{10}$

This accounts for the LCD of 30

Before we can add/subtract fractions they must have a $\textcolor{b l u e}{\text{common denominator}}$ That is they have to be the same number on the denominator of both fractions.

We have to find a number then that is common to both 6 and 10, usually called the $\textcolor{b l u e}{\text{lowest common multiple}}$

One way to find it, is to divide the larger of the 2 numbers by the smaller and if it divides into it exactly , with a remainder of 0 then the larger number is the lowest common multiple. Repeat this process with multiples of the larger number until this happens.

10÷6=1" remainder 4 so not 10 , now try 20"

20÷6=3" remainder 2 so not 20, now try 30"

30÷6=5" remainder 0"# thus 30 is the value.

The 2 fractions can now be expressed with a LCD of 30

$\Rightarrow \frac{5 x}{6} \times \frac{5}{5} = \frac{25 x}{30} \text{ and } \frac{3}{10} \times \frac{3}{3} = \frac{9}{30}$

Now that the fractions have the same denominator we can add/subtract the numerators but NOT the denominators.

$\Rightarrow \frac{5 x}{6} - \frac{3}{10} = \frac{25 x}{30} - \frac{9}{30} = \frac{25 x - 9}{30}$