Question 1

Let's find the position of each number on the number line.

Step 1 — Understand the values

We have three rational numbers. Let's convert them to decimals. This helps us find their positions.

For $\frac{2}{3}$: $\frac{2}{3}$ $= 0.666...$

$\boxed{\approx 0.67}$

For $-\frac{5}{4}$: $-\frac{5}{4}$ $= -1.25$

$\boxed{-1.25}$

For $1\frac{1}{2}$: $1\frac{1}{2}$ $= \frac{3}{2}$ $= 1.5$

$\boxed{1.5}$

Now we know their approximate values. We can see their order clearly. The smallest is -1.25. The next is 0.67. The largest is 1.5.

Step 2 — Draw the number line

We will draw a number line. We mark the integers first. Then we place our numbers. $-\frac{5}{4}$ is between $-2$ and $-1$. It is one-quarter past $-1$ towards $-2$. $\frac{2}{3}$ is between $0$ and $1$. It is two-thirds of the way from $0$ to $1$. $1\frac{1}{2}$ is between $1$ and $2$. It is exactly halfway between $1$ and $2$.

Answer

(i) $-\frac{5}{4}$ is located between $-2$ and $-1$. It is one-quarter of the way from $-1$ to $-2$. (ii) $\frac{2}{3}$ is located between $0$ and $1$. It is two-thirds of the way from $0$ to $1$. (iii) $1\frac{1}{2}$ is located between $1$ and $2$. It is exactly halfway between $1$ and $2$.