On a number line, a number and its additive inverse are at the same distance from zero but on opposite sides. Remember that the distance of a number from zero is given by its absolute value.
For instance, the only two numbers that are at a distance of from zero are and So, is the additive inverse of (and vice versa).
How can we represent the additive inverse of on the number line?
The additive inverse of a number is the number that lies at the same distance from zero on the number line, but on the opposite side.
As we can see on the number line below, the distance of from zero is units. The only other number that is at a distance of units from zero is
Therefore, the additive inverse of is , and it can be represented on the number line as follows:
On which number line does the red dot represent the additive inverse of $6?$
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a
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b
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c
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d
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e
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On which number line does the red dot represent the additive inverse of $-3?$
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a
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b
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c
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d
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e
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On which number line does the red dot represent the additive inverse of $-\dfrac73?$
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a
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b
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c
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d
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e
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Suppose that a bank account had an initial balance of During the day, there was a withdrawal of Then there was a deposit of later.
What is the resulting amount in the account?
In our situation:
During the day, the account had a withdrawal of which is a change of
Later, the account had a deposit of which is a change of
These two changes are opposite quantities. When opposite quantities combine, they make
Therefore, the balance returns to its original value of
A drone’s elevation dropped by while descending into a valley. Then it rose by while flying back up. Which of the following statements are true?
- The drone’s elevation is now higher than the initial elevation.
- The drone’s elevation is now lower than the initial elevation.
- The drone returned to the initial elevation.
In our situation:
While descending, the drone’s elevation dropped by , which is a change of
While climbing back up, the drone’s elevation rose by which is a change of
These two changes are opposite quantities. When opposite quantities combine, they make
This means the total elevation change is so the drone returns to the original elevation.
So, statements I and II are false, while statement III is true.
Therefore, the correct answer is "III only".
The temperature rose by $7^\circ\,\text{C}$ during the day. Then it dropped by $7^\circ\,\text{C}$ during the night. Which of the following statements are true?
- The temperature is now larger than the initial value.
- The temperature returned to the initial value.
- The temperature is now lower than the initial value.
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a
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I only |
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b
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II only |
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c
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II and III only |
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d
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III only |
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e
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None |
A hiker’s elevation rose by $120\text{ m}$ while climbing a hill. Then it dropped by $120\text{ m}$ while descending the other side. Which of the following statements are true?
- The hiker returned to the initial elevation.
- The hiker’s elevation is now lower than the initial elevation.
- The hiker’s elevation is now higher than the initial elevation.
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a
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III only |
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b
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None |
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c
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I and II only |
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d
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I only |
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e
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II only |
A bank account had an initial balance of $\$0.$ During the day, there was a deposit of $\$50.$ Then there was a withdrawal of $\$50$ later. What is the resulting amount in the account?
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a
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$\$100$ |
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b
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$-\$100$ |
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c
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$\$50$ |
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d
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$-\$50$ |
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e
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$\$0$ |
Now, let and What point on the number line corresponds to
The value of is the number located a distance from on the number line,
moving to the right if is positive, and
moving to the left if is negative.
In our situation:
We start at on the number line.
Here, , so the distance we move is
Because is negative, we move units to the left from
This point corresponds to the number
Let and What point on the number line corresponds to
The value of is the number located a distance from on the number line,
moving to the right if is positive, and
moving to the left if is negative.
In our situation:
We start at on the number line.
Here, , so the distance we move is
Because is positive, we move units to the right from
This point corresponds to the number
Let $p=-4$ and $q=6.$ What point on the number line corresponds to $p+q?$
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a
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It's the number $2$ located $6$ units to the left of $-4.$ |
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b
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It's the number $-2$ located $6$ units to the left of $-4.$ |
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c
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It's the number $-2$ located $6$ units to the right of $-4.$ |
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d
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It's the number $2$ located $4$ units to the right of $6.$ |
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e
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It's the number $2$ located $6$ units to the right of $-4.$ |
Let $p=5$ and $q=-7.$ What point on the number line corresponds to $p+q?$
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a
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It's the number $-2$ located $7$ units to the right of $5.$ |
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b
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It's the number $2$ located $7$ units to the left of $5.$ |
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c
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It's the number $-2$ located $5$ units to the right of $7.$ |
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d
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It's the number $-2$ located $7$ units to the left of $5.$ |
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e
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It's the number $2$ located $7$ units to the right of $5.$ |
