Representing numbers on the number line

Look at the following number line and identify which integer corresponds to each of the letters marked with a dot:

Draw a number line in your notebook and represent the following integers on it: $+4$, $-3$, $0$, $+1$ and $-5$. Use a distance of $1$ cm between each number.

Look at the number line and write the missing integers in the empty boxes, knowing that the distance between each mark is $1$ unit.

State which integer is the opposite of the one represented by the orange dot on the line. Also represent that opposite on the same line.

Write the integers whose absolute value is equal to $3$. Then, represent them on a number line like the one in the figure and explain what you notice about their position relative to zero.

A thermal inspection drone makes the following movements along the vertical axis of an industrial chimney. If we consider the top of the chimney to be at $0$ metres:

• It starts at a height of $+12$ m.

• It descends $15$ metres to inspect a crack.

• It climbs $6$ metres again to take a reading.

Represent the path on a vertical line and mark the final position of the drone with a highlighted dot. What height is it at relative to the top of the chimney?

Remember that on the number line, the further to the right a number is, the greater it is. Based on this, use the symbols $>$ (greater than) or $<$ (less than) to compare these pairs of numbers:

1. a) $-4$ _____ $+2$
2. b) $-1$ _____ $-5$
3. c) $+3$ _____ $0$
4. d) $-2$ _____ $+1$

Look at the following number line on which three points, $A$, $B$, and $C$, have been marked. Taking into account the positions of the numbers $0$ and $+2$, identify which integer each letter represents.

In an exam, Aoife had to calculate the distance on the number line between the number $-6$ and the number $+3$. On her answer sheet, she wrote:

"Since distance is the difference between the numbers, I do $+3 - 6 = -3$. Therefore, the distance between both is $-3$ units".

1. a) Identify the two mistakes Aoife made (one conceptual about the result of a distance and another about how to set up the subtraction with negative numbers).
2. b) Explain in your own words why a distance can never be negative on the number line.
3. c) Write the correct operation and calculate the actual distance between $-6$ and $+3$.

On the number line, the midpoint between two integers is the position that is exactly the same distance from both.

• Represent the numbers $-6$ and $+2$.

• Visually find the midpoint between them and state what number it represents.

• What is the distance (in units) from that midpoint to either of the two endpoints?

Draw a number line and plot the number $-3$ on it. Next, represent:

• Point $A$, which is the opposite of $-3$.

• Point $B$, which is $5$ units to the left of $-3$.

• Point $C$, which is $2$ units to the right of $A$.

Which number does point $C$ represent? Which is the smallest of the four numbers marked on the line?

You can do it on paper and send a photo with your answer.

Two integers, $A$ and $B$, are marked on a number line. We know that the exact midpoint between both is the number $-2$. In addition, you are given that point $A$ is the number $+4$.

1. a) Calculate the distance from point $A$ to the midpoint $-2$.
2. b) Knowing that the midpoint is equidistant from both endpoints, deduce with reasoning at which integer point $B$ must be located.
3. c) Apply the midpoint formula, $\dfrac{A+B}{2}$, substituting the values of $A$ and $B$ to check that your result gives exactly $-2$.

Draw a number line and represent on it all the integers $x$ that simultaneously satisfy these two conditions:

1. Their absolute value is less than $5$, that is: $|x| < 5$.

2. They are numbers strictly less than $-1$.

You can do it on paper and send a photo with your answer.

Represent the following integers on a number line. Choose a suitable scale (where each mark on the line can represent more than 1 unit) so that they all fit in your drawing:

$S = \{ -15, +5, -20, +25, 0, -5 \}$

An explorer is looking for a treasure buried on a straight path that we represent as a number line. The map gives him the following clues:

1. The treasure is at a position represented by an integer $x$.

2. The distance between $x$ and the number $-2$ is exactly $5$ units.

3. The absolute value of $x$ is greater than $4$.

Represent on the number line the possible locations of the treasure and determine at which exact number or numbers it could be. You can copy this number line to work on it:

You can do it on paper and send a photo with your answer.