Question 3

We need to add two fractions with different denominators.

Step 1 — Find common denominator

Let's find the Least Common Multiple (LCM). The denominators are 4 and 12. The LCM of 4 and 12 is 12.

We convert the first fraction to have denominator 12. $-\frac{1}{4} = -\frac{1 \times 3}{4 \times 3}$

$\boxed{-\frac{3}{12}}$

Step 2 — Add the fractions

Now we add the fractions with the same denominator. $-\frac{3}{12} + \frac{5}{12}$ $= \frac{-3 + 5}{12}$ $= \frac{2}{12}$ $= \frac{1}{6}$

Answer

(i) The simplified expression is $\frac{1}{6}$.