Question

Locate and label the following on a number line:$-2,\frac{2}{3},\frac{7}{5},-\frac{7}{4},\frac{7}{2},3,-\frac{7}{3}$

Short answer

The required number line is

Step-by-step solution

Step 1. Given information 

Given numbers are$-2,\frac{2}{3},\frac{7}{5},-\frac{7}{4},\frac{7}{2},3,-\frac{7}{3}$

Sep 2. Procedure to locate numbers in a number line 

A number line is a line on which the numbers are located to perform some calculations. We draw the number line as a horizontal straight line expanded from left to right and from $-\infty$to $+\infty$, and mark the numbers corresponding to them.

Sep 3. Converting he numbers to decimals 

To plot the given numbers in the number line, we convert all the numbers to the accurate or nearest decimals and mark them in the number line.

Now,

$$\begin{gathered} \frac{2}{3}=0.66667; \\ \frac{7}{5}=1.4; \\ -\frac{7}{4}=-1.75; \\ \frac{7}{2}=3.5; \\ -\frac{7}{3}=-2.33333...=-2.\stackrel{-}{3} \end{gathered}$$

The Line

We plot all the numbers in the number line in ascending order and get the required line as,