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.

All negative numbers appear on the number line to the left of the number 0.

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

Every positive number is greater than zero

Question 2

\( -2 < 0 \)

Question 3

\( -3=-3 \)

- 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

\( 3.98 \) and \( +3.98 \) are two ways of writing the same number.

Question 2

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

Question 3

\( -4>-3 \)

**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

\( 5 < -5 \)

Question 2

The minus sign can be omitted

Question 3

The sign is always written to the left of the number.

**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

Does the number \( -6 \) appear on the number line to the right of number \( 2\text{?} \)

Question 2

What is the distance between A and K?

Question 3

What is the distance between D and I?

**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

What is the distance between J and D?

Question 2

What is the distance between 0 and F?

Question 3

All negative numbers appear on the number line to the left of the number 0.

**Request**

Solve according to the axis

$G-B+K=$

**Solution:**

$G=1$

$B=-4$

$K=5$

Solve the exercise

$1-\left(-4\right)+5=$

Pay attention that minus multiplied by minus becomes plus.

$1+4+5=10$

**Answer**

$10$

The number line or real line is a horizontal line divided into equidistant segments, i.e. at the same distance from each other, which serves to represent numbers in each segment, in which real numbers are indicated.

Do you know what the answer is?

Question 1

Every positive number is greater than zero

Question 2

\( -2 < 0 \)

Question 3

\( -3=-3 \)

The real line is a horizontal line where it is divided by intervals of the same distance, in these segments we can find the following elements:

- The zero, the positive and negative. The zero is a point where the line is divided into two equal parts, where to the right we can find the positive numbers and to the left of the zero are the negative numbers.
- Whole numbers
- Rational numbers
- Irrational numbers

It is called the number line or real line, since it contains all the real numbers, that is, the set of natural numbers, integers, rational numbers and irrational numbers, all these numbers are a subset of the real numbers, in other words, they are all the numbers.

Check your understanding

Question 1

\( 3.98 \) and \( +3.98 \) are two ways of writing the same number.

Question 2

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

Question 3

\( -4>-3 \)

On the number line we will place the positive numbers on the right side of zero and the negative numbers on the left side, so when we add we will move to the right side of the line, and when we subtract we will move to the left.

**Task.** Perform the following addition on the number line:

$\left(-4\right)+\left(7\right)=$

**Solution:** We locate the first term of the sum on the number line, and as we can observe it is a sum then, we are located at $-4$ and we move $7$ segments to the right.

On the number line we can see that by going $7$ segments to the right we have fallen on the number $3$, Therefore:

$\left(-4\right)+\left(7\right)=3$

**Result:**

$3$

**Task.** Represent the following subtraction on a number line:

$\left(+3\right)-\left(+8\right)=$

**Solution:**

We locate the minuend of the subtraction on the number line, then, we start at $3$ and then subtract the subtrahend, that is, the second term of the subtraction $8$:

We observe that we have fallen in the $-5$, Using laws of signs less by more, will give us less, therefore this subtraction we can represent it as:

$\left(+3\right)-\left(+8\right)=3-8=$

Therefore:

$3-8=-5$

**Result:**

$-5$

Do you think you will be able to solve it?

Question 1

\( 5 < -5 \)

Question 2

The minus sign can be omitted

Question 3

The sign is always written to the left of the number.

What is the distance between F and B?

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

What is the distance between A and K?

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

All negative numbers appear on the number line to the left of the number 0.

True.

-2 < 0

True

$-3=-3$

True

Related Subjects

- The Order of Basic Operations: Addition, Subtraction, and Multiplication
- Positive and negative numbers and zero
- Opposite numbers
- Elimination of Parentheses in Real Numbers
- Addition and Subtraction of Real Numbers
- Multiplication and Division of Real Numbers
- Integer powering
- The commutative property
- The Commutative Property of Addition
- The Commutative Property of Multiplication
- The Associative Property
- The Associative Property of Addition
- The Associative Property of Multiplication
- The Distributive Property
- The Distributive Property for Seventh Graders
- The Distributive Property of Division
- The Distributive Property in the Case of Multiplication
- The commutative properties of addition and multiplication, and the distributive property
- Exponents and roots
- What is a square root?
- Square Root of a Negative Number
- Powers
- Exponents for Seventh Graders
- Basis of a power
- The exponent of a power