Real line or Numerical line

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.

• 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:
  • $\Large 0.8$
  • $\Large 0.8$
  • $\Large -{3 \over5}$
  • $\Large -1.2$
  • $\Large 2{4 \over5}$
  • $\Large -2{9 \over 15}$

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

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.

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

$-16$

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

$7$

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.

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.

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:

$-5$