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

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

**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.

Fill in the corresponding sign

D ? J

To be more precise, we must point out that the number line is infinite. Therefore, when we refer to an image of the real line, we are referring to the image of a part of the whole line.

**Decimal numbers can also be represented on the real line, for example:**

**For example, let's look at the following two exercises that have already been solved:**

- $-9+5=-4$
- $32-7=25$

Let us now focus on each of them and look at them as if they were a horizontal movement on the real line.

**Exercise No. 1:**We start from -9, move 5 segments to the right and reach -4.**Exercise #2:**Starting from 32, we move 7 segments to the left and get to 25.

Test your knowledge

Question 1

Solve the exercise

F ? 0

Question 2

Solve the exercise

B ? J

Question 3

Solve the exercise

C ? 3

- Draw a number line starting with -28 and ending in -18.
- Draw a number line beginning with -3 and ending in 6.
- Draw a number line beginning with $-2\frac{1}{4}$ and ending in $2\frac{1}{4}$.

- Using the following number line

Point out the following numbers on it:- $\Large 0.8$
- $\Large 0.8$
- $\Large -{3 \over5}$
- $\Large -1.2$
- $\Large 2{4 \over5}$
- $\Large -2{9 \over 15}$

Do you know what the answer is?

Question 1

What is the distance between 0 and F?

Question 2

What is the distance between C and H?

Question 3

What is the distance between F and B?

**Draw a number line starting with -8 and ending with 3. Then, reflect the following exercises on the number line using dots and arrows:**

- $\Large (-8)+(+7)=$
- $\Large (-2)+(-5)=$
- $\Large (-5)+(+2)=$
- $\Large (-6)+(+6)=$
- $\Large (+1)+(-2)=$
- $\Large 0+(-5)=$
- $\Large 0+(+2)=$

Observe the following real line and point out whether it is correct or not

- $\Large 5<-5$
- $\Large -2<0$
- $\Large -3=-3$
- $\Large 4{1 \over 2}=-5$
- $\Large -4>-3$
- $\Large B>A$
- $\Large E<C$
- $\Large K<F$
- $\Large -4>A$
- $\Large C>E$

**If you are interested in this article you may also be interested in the following articles:**

Positive numbers, negative numbers and zero

Elimination of parentheses in real numbers

Addition and subtraction of real numbers

Multiplication and division of real numbers

**On the** **Tutorela**** blog** **you will find a variety of articles on mathematics**.

Check your understanding

Question 1

What is the distance between D and K?

Question 2

What is the distance between J and D?

Question 3

What is the distance between A and K?

**Consignee**

What is the distance between $0$ and $F$?

**Solution**

$f=0$

Therefore the distance is $0$ skipped

$0=0$

**Answer**

$0$

What number appears at the red dot marked on the axis?

**Solution:**

By means of the axis we notice that the jumps between numbers are in multiplying the previous term by $2$

$-2\times2=-4$

$-4\times2=-8$

$-8\times2=-16$

$-16\times2=-32$

Therefore

$-16$ is the point

**Answer**

$-16$

Do you think you will be able to solve it?

Question 1

What is the distance between I and E?

Question 2

What is the distance between D and I?

Question 3

\( 5 < -5 \)

**Query**

Fill in the missing numbers

**Solution**

We note that the jumps between the numbers are at $6$

Therefore

$15+6=21$

$21+6=27$

**Answer**

$21,27$

**Request**According to the axis:

$L-E=$

**Solution:**

$L=5$

$E=-2$

We solve the exercise

$5-\left(-2\right)=$

Pay attention that minus multiplied by minus becomes plus.

$5+2=7$

**Answer**

$7$

Test your knowledge

Question 1

\( -2 < 0 \)

Question 2

\( -3=-3 \)