# The Number Line - Examples, Exercises and Solutions

The real line looks like this: a horizontal line in which small equidistant vertical lines are inserted.

### Real number line

Characteristics of the number line:

• Below each vertical line a whole number is inserted in ascending order from left to right.
• The distance between two consecutive numbers is called a "segment".

The operations of addition and subtraction can be seen as a horizontal movement on the number line.

• When adding, we move to the right.
• When subtracting, we move to the left.

## examples with solutions for the number line

### Exercise #1

What is the distance between F and B?

### Step-by-Step Solution

It is true that because the displacement on the axis is towards the negative domain, one might think that the result is also negative.

But it is important to keep in mind that here we are asking about the distance.

Distance can never be negative.

Even if the displacement is towards the negative domain, the distance is an existing value.

4

### Exercise #2

What is the distance between A and K?

### Step-by-Step Solution

It is true that because there are numbers on the axis that go into the negative domain, one might think that the result is also negative.

But it is important to keep in mind that here we are asking about distance.

Distance can never be negative.

Even if we move towards or from the domain of negativity, distance is an existing value (absolute value).

We can think of it as if we were counting the number of steps, and it doesn't matter if we start from five or minus five, both are 5 steps away from zero.

10

5 < -5

### Step-by-Step Solution

Since there cannot be a situation where a negative number is greater than a positive number, the answer is incorrect.

Not true

-2 < 0

### Step-by-Step Solution

Since every negative number is necessarily less than zero, the answer is indeed correct

True

### Exercise #5

4\frac{1}{2} < -5

### Step-by-Step Solution

The answer is incorrect because a negative number cannot be greater than a positive number:

4\frac{1}{2} > -5

Not true

-4>-3

### Step-by-Step Solution

The answer is incorrect because neative 3 is greater than negative 4:

-4 < -3

Not true

### Exercise #7

Every positive number is greater than zero

### Step-by-Step Solution

The answer is indeed correct, any positive number to the right of zero is necessarily greater than zero.

True

### Exercise #8

Fill in the corresponding sign

$+3?0$

### Step-by-Step Solution

Since the number 3 comes after the number 0, it is necessarily greater:

3 > 0

>

### Exercise #9

Fill in the corresponding sign

$17?+17$

### Step-by-Step Solution

Since both numbers are positive and identical, they are equal to each other:

$17=+17$

$=$

K < A

### Step-by-Step Solution

Let's locate the numerical representation of the point on the number line:

$K=5$

$A=-5$

Now let's place:

5 < -5

It appears that the answer is not correct.

Not true

-4>A

### Step-by-Step Solution

Let's locate the numerical representation of the letter on the number line:

$A=-5$

Now let's place:

-4 > -5

It appears that the answer is indeed correct.

True

B>A

### Step-by-Step Solution

Let's locate the numerical representation of the letter on the number line:

$B=-4$

$A=-5$

Now let's place:

-4 > -5

It appears that the answer is indeed correct.

True

### Exercise #13

What are the missing numbers?

### Step-by-Step Solution

Let's look at the numbers from left to right:

$-6,-4,-2$

We notice that the common operation is:

$+2$

$-6+2=-4$

$-4+2=-2$

Therefore, the next sequence will be:

$-2+2=0$

$0+2=2$

0,2

### Exercise #14

Fill in the corresponding sign

$0?-3.9$

### Step-by-Step Solution

Since the number -3.9 is further from zero, it must be smaller, therefore:

0 > -3.9

> 

### Exercise #15

Fill in the missing number

### Step-by-Step Solution

Let's look at the numbers from left to right:

$0,\frac{1}{2},1,1\frac{1}{2}$

We notice that the common operation is:

$+\frac{1}{2}$

$0+\frac{1}{2}=\frac{1}{2}$

$\frac{1}{2}+\frac{1}{2}=1$

$1+\frac{1}{2}=1\frac{1}{2}$

Therefore, the next sequence will be:

$1\frac{1}{2}+\frac{1}{2}=2$

$2+\frac{1}{2}=2\frac{1}{2}$

$2\frac{1}{2}+\frac{1}{2}=3$

$2,2\frac{1}{2},3$