The real line looks like this: a horizontal line in which small equidistant vertical lines are inserted.
Real number line
![A1 - Real number line](/_ipx/f_png,s_500x190/https://cdn.tutorela.com/images/A1_-_Real_number_line.width-500.png)
The real line looks like this: a horizontal line in which small equidistant vertical lines are inserted.
Characteristics of the number line:
The operations of addition and subtraction can be seen as a horizontal movement on the number line.
What is the distance between 0 and F?
What is the distance between C and H?
What is the distance between F and B?
What is the distance between D and K?
What is the distance between J and D?
What is the distance between 0 and F?
We mark F and 0 on the number line
Let's note that:
Therefore, the distance is 0 steps
0
What is the distance between C and H?
We'll mark C on the number line and move towards H:
Note that the distance is 5 steps.
5
What is the distance between F and B?
One might think that as a consequence of the displacement on the axis being towards the negative domain, the result is also negative.
However it is important to keep in mind that here we are referring to 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 D and K?
We'll mark D on the number line and move towards K:
Note that the distance is 7 steps
7
What is the distance between J and D?
We'll mark J on the number line and move towards D:
Note that the distance is 6 steps
6
What is the distance between A and K?
What is the distance between I and E?
What is the distance between D and I?
\( 5 < -5 \)
\( -2 < 0 \)
What is the distance between A and K?
One might think that because there are numbers on the axis that go into the negative domain, that the result must also negative.
However 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
What is the distance between I and E?
We'll mark I on the number line and move towards E:
Note that the distance is 4 steps
4
What is the distance between D and I?
We'll mark D on the number line and move towards I:
Note that the distance is 5 steps
5
5 < -5
As per the fact that there cannot be a situation where a negative number is greater than a positive number, the answer is incorrect.
Not true
-2 < 0
Since every negative number is necessarily less than zero, the answer is indeed correct
True
\( 4\frac{1}{2} < -5 \)
\( -4>-3 \)
Every positive number is greater than zero
The minus sign can be omitted
Does the number \( -6 \) appear on the number line to the right of number \( 2\text{?} \)
4\frac{1}{2} < -5
The answer is incorrect because a negative number cannot be greater than a positive number:
4\frac{1}{2} > -5
Not true
-4>-3
The answer is incorrect because neative 3 is greater than negative 4:
-4 < -3
Not true
Every positive number is greater than zero
The answer is indeed correct, any positive number to the right of zero is inevitably greater than zero.
True
The minus sign can be omitted
The sign cannot be omitted as it determines whether the number will be negative or positive.
Not true
Does the number appear on the number line to the right of number
If we draw a number line, we can see that the number minus 6 is located to the left of the number 2:
Therefore, the answer is not correct.
No