Question 2

We need to find three rational numbers that are strictly between the given numbers.

Step 1 — Find a common denominator

Let's write down the given rational numbers. They are $-\frac{1}{2}$ and $\frac{1}{4}$. We need to find a common denominator for 2 and 4. The least common multiple of 2 and 4 is 4. Now, we convert $-\frac{1}{2}$ to a fraction with denominator 4.

$-\frac{1}{2} = -\frac{1 \times 2}{2 \times 2}$

$\boxed{-\frac{2}{4}}$

The other number, $\frac{1}{4}$, already has a denominator of 4.

Step 2 — Identify numbers between them

We need numbers strictly between $-\frac{2}{4}$ and $\frac{1}{4}$. We can look at the numerators -2 and 1. The integers between -2 and 1 are -1 and 0. So, two rational numbers are $-\frac{1}{4}$ and $\frac{0}{4}$. $\frac{0}{4}$ simplifies to 0. We still need to find one more distinct rational number. To find more numbers, we can use a larger common denominator. Let's multiply both fractions by $\frac{2}{2}$. This will change the denominator to 8.

$-\frac{2}{4} = -\frac{2 \times 2}{4 \times 2}$

$= -\frac{4}{8}$

$\frac{1}{4} = \frac{1 \times 2}{4 \times 2}$

$= \frac{2}{8}$

Now we need numbers strictly between $-\frac{4}{8}$ and $\frac{2}{8}$. We can choose from numbers like $-\frac{3}{8}$, $-\frac{2}{8}$, $-\frac{1}{8}$, $\frac{0}{8}$, $\frac{1}{8}$. Let's pick three distinct numbers from this list. We can choose $-\frac{1}{4}$, 0, and $\frac{1}{8}$. Remember that $-\frac{1}{4}$ is the same as $-\frac{2}{8}$. Also, 0 is the same as $\frac{0}{8}$. These three numbers are all strictly between $-\frac{1}{2}$ and $\frac{1}{4}$.

Answer

(i) $-\frac{1}{4}$ (ii) $0$ (iii) $\frac{1}{8}$