Real line or Numerical line

🏆Practice the number line

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.

Test yourself on the number line!

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:

Addition and subtraction on the number line

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.

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Real line practice exercises

Practice No. 1

• 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 $2\frac{1}{4}$.

Practice No. 2

• 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?

Practice No. 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:

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

Practice No. 4

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
• $\Large K
• $\Large -4>A$
• $\Large C>E$

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

Positive numbers, negative numbers and zero

Opposite numbers

Absolute value

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.

Exercises on the real line o The number line

Exercise 1

Consignee

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

Solution

$f=0$

Therefore the distance is $0$ skipped

$0=0$

$0$

Exercise 2

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

$-16$

Do you think you will be able to solve it?

Exercise 3

Query

Fill in the missing numbers

Solution

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

Therefore

$15+6=21$

$21+6=27$

$21,27$

Exercise 4

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.

$5+2=7$

$7$