# Pre-Algebra : Number Lines

## Example Questions

### Example Question #1 : Number Lines

Which of the following numbers is depicted by the point on the number line?

Explanation:

The point lies halfway between  and , or at .

### Example Question #1 : How To Plot Fractions On A Number Line

Plot the fraction  on the number line.

Explanation:

The fraction  is less than  and greater than , so it must fall between those points on the number line. Negative numbers are to the left of  while positive numbers are to the right.

Because  is less than , the point must be closer to  than .

### Example Question #1 : Number Lines

Find the distance between  and  on a number line.

Explanation:

To find the distance on a number line:

### Example Question #1 : Number Lines

Express this inequality statement using symbols.

Explanation:

= less than

= greater than

= less than or equal to

= greater than or equal to

### Example Question #2 : Number Lines

Find the inequality that corresponds to the following number line.

Explanation:

When looking at the number line, we can see that x is any integer between 2 and 7.

Anything to the right of an integer is considered "greater than" and anything left of an integer is considered "less than".

So, we know that x is greater than 2, but less than 7.

Now, since the circle above the 2 is shaded in, 2 is included in the solution.  The circle above the 7 is not shaded in, so 7 is not included in the solution.

We now know that is greater than or equal to 2, and it is still less than 7.

Using the statement above, we will create 2 inequalities.

Now,    can also be written as    .  It has the same value, it just looks a little different.

So we have the two inequalities

and

We can combine them, and it'll look like this

### Example Question #2 : Number Lines

Put in order from least to greatest.

Explanation:

Thus, in increasing order:

### Example Question #3 : Number Lines

Find the inequality that corresponds with this number line.

Explanation:

When looking at the number line,

we see at -5 there is a filled in circle.  We also see there is an arrow going to the right of -5.  Every integer to the right of -5 is greater than -5 itself.  Because the circle above -5 is filled in, we know -5 is included in the inequality.  We get

### Example Question #5 : Number Lines

Put the following numbers in order from least to greatest.

Explanation:

There is only one negative number in the numbers.

The next biggest is ,

Next is ,

Next is ,

Lastly is