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

A1 - 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.
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Test yourself on the number line!

einstein

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

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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:

A2 - The_real_right_also_in_decimal_numbers


Addition and subtraction on the number line

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

  • 9+5=4-9+5=-4
  • 327=2532-7=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.
image 3 practice - the real line


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Test your knowledge

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 214 -2\frac{1}{4} and ending in 214 2\frac{1}{4} .

Practice No. 2

Practice image - the real line-Exercise04

  • Using the following number line
    Point out the following numbers on it:
    • 0.8\Large 0.8
    • 0.8\Large 0.8
    • 35\Large -{3 \over5}
    • 1.2\Large -1.2
    • 245\Large 2{4 \over5}
    • 2915\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:

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

Practice No. 4

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

practice - the real line 1

  • 5<5\Large 5<-5
  • 2<0\Large -2<0
  • 3=3\Large -3=-3
  • 412=5\Large 4{1 \over 2}=-5
  • 4>3\Large -4>-3
  • B>A\Large B>A
  • E<C\Large E<C
  • K<F\Large K<F
  • 4>A\Large -4>A
  • C>E\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.


Check your understanding

Exercises on the real line o The number line

Exercise 1

What is the distance between 0 and F

Consignee

What is the distance between 0 0 and F F ?

Solution

f=0 f=0

Therefore the distance is 00 skipped

0=0 0=0

Answer

0 0


Exercise 2

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

Which 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

2×2=4 -2\times2=-4

4×2=8 -4\times2=-8

8×2=16 -8\times2=-16

16×2=32 -16\times2=-32

Therefore

16 -16 is the point

Answer

16 -16


Do you think you will be able to solve it?

Exercise 3

1- Fill in the missing numbers

Query

Fill in the missing numbers

Solution

We note that the jumps between the numbers are at 66

Therefore

15+6=21 15+6=21

21+6=27 21+6=27

Answer

21,27 21,27


Exercise 4

Request
According to the axis:

LE= L-E=

Exercise 5 Target According to axis

Solution:

L=5 L=5

E=2 E=-2

We solve the exercise

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

Pay attention that minus multiplied by minus becomes plus.

5+2=7 5+2=7

Answer

7 7


Test your knowledge

Exercise 5

Request

Solve according to the axis

GB+K= G-B+K=

Exercise 6 Assignment Solve according to axis

Solution:

G=1 G=1

B=4 B=-4

K=5 K=5

Solve the exercise

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

Pay attention that minus multiplied by minus becomes plus.

1+4+5=10 1+4+5=10

Answer

10 10


Review questions

What is the number line and what is it used for?

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?

What are the elements of a real line?

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

Why is it called a real line?

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

What is the numerical rule for addition and subtraction on the real line?

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.

A10 -Real number line

Examples of addition and subtraction on the number line

Example 1

Task. Perform the following addition on the number line:

(4)+(7)= \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 -4 and we move 7 7 segments to the right.

A11 -Real number line

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

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

Result:

3 3


Example 2

Task. Represent the following subtraction on a number line:

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

Solution:

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

A12 -Real number line

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

(+3)(+8)=38= \left(+3\right)-\left(+8\right)=3-8=

Therefore:

38=5 3-8=-5

Result:

5 -5


Do you think you will be able to solve it?

examples with solutions for the number line

Exercise #1

What is the distance between F and B?

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Video Solution

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.

Answer

4

Exercise #2

What is the distance between A and K?

AAA-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444

Video Solution

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.

Answer

10

Exercise #3

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

Video Solution

Answer

True.

Exercise #4

-2 < 0

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Video Solution

Answer

True

Exercise #5

3=3 -3=-3

AAAKKK-5-5-5BBB-4-4-4CCC-3-3-3DDD-2-2-2EEE-1-1-1FFF000GGG111HHH222III333JJJ444555

Video Solution

Answer

True

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