Question

hich of the following describes the sum p + (−q) where p and q are positive numbers??(1 point) Responses The sum p+(−q) is the number located a distance |p| from q in the positive direction. The sum negative p plus left parenthesis negative q right parenthesis is the number located a distance absolute value of p from q in the positive direction. The sum p+(−q) is the number located a distance |p| from q in the negative direction. The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value p End Absolute Value from q in the negative direction. The sum p+(−q) is the number located a distance |q| from p in the negative direction. The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value q End Absolute Value from p in the negative direction. The sum p+(−q) is the number located a distance |q| from p in the positive direction. The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value q End Absolute Value from p in the positive direction.

Answer 1

To analyze the sum $p+(-q)$, we can rewrite it as $p-q$. Since both $p$ and $q$ are positive numbers, the result will depend on their relative sizes.

1. If $p>q$, then $p-q$ is positive and represents the distance from $q$ moving in the positive direction.
2. If $p<q$, then $p-q$ is negative and represents the distance from $p$ moving in the negative direction.
3. If $p=q$, then $p-q=0$.

Now, out of the given options, the correct interpretation of the sum $p+(-q)$ or $p-q$ can be summarized as follows:

• If $p>q$: It is $p-q$, and you can visualize this as starting at $q$ and moving a distance of $p$ to the right (positive direction).

• If $p<q$: The absolute value $|p|$ indicates how far you are from $q$ in the negative direction.

The best choice to express this generally, without assuming more about the relationship between $p$ and $q$, is:

The sum $p+(-q)$ is the number located a distance $|q|$ from $p$ in the negative direction.

When $p<q$, you're moving left and vice versa, confirming that $p+(-q)$ could represent different positions based on the values of $p$ and $q$.

Answer 2

Question Use properties of operations to add (−3) and (−17) .(1 point) Responses −14 negative 14 20 20 −20 negative 20 14

Answer 3

To add $(-3)$ and $(-17)$, you can use the following steps:

$$(-3)+(-17)=-3-17$$

When adding two negative numbers, you add their absolute values and keep the negative sign:

$$3+17=20$$

Thus,

$$(-3)+(-17)=-20$$

So, the correct answer is:

−20

Answer 4

Add (4) and (−15).(1 point) Responses −19 negative 19 19 19 −11 negative 11 11

Answer 5

To add $4$ and $-15$, you can set it up as follows:

$$4+(-15)=4-15$$

When you subtract a positive number from a smaller positive number, you get a negative result:

$$4-15=-11$$

So, the correct answer is:

−11

Answer 6

Add (−18) and (5) .(1 point) Responses −13 negative 13 23 23 −23 negative 23 13

Answer 7

To add $(-18)$ and $5$, you can set it up as follows:

$$-18+5$$

This can be interpreted as starting at $-18$ and moving $5$ units to the right (towards the positive direction).

Calculating that:

$$-18+5=-13$$

So, the correct answer is:

−13

Answer 8

Which number line shows the correct way to find the sum p+q if p is positive and q is negative?(1 point) Responses Image with alt text: A number line ranging from 0 in unit increments shows an arrow, labeled absolute value of q, starting at point p and ending 4 units to the right. Image with alt text: A number line is shown with arrows at both ends, and hash marks at unit intervals. Point p is marked on the seventh interval from the left. Zero is marked 2 intervals to the right of p. A leftward curved arrow, labeled absolute value of q, points from p to the second interval from the left. Image with alt text: A number line is shown with arrows at both ends, and hash marks at unit intervals. The second point from the left is labeled p. Zero is marked at 6 intervals to the right of point p. A rightward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the right of p.

Answer 9

To find the sum $p+q$ where $p$ is a positive number and $q$ is a negative number, you need to start at the position of $p$ on the number line and then move left by the absolute value of $q$.

Since $q$ is negative, the arrow should point to the left from $p$, indicating a decrease in value.

Given that understanding, the correct number line would be the one that shows:

• Point $p$ on the number line, representing the positive value.
• An arrow pointing leftward from $p$, indicating that you are subtracting the absolute value of $q$.

From your descriptions, the correct option would be:

The number line where point p is marked on the seventh interval from the left and shows a leftward curved arrow labeled absolute value of q pointing from p to the second interval from the left.

This correctly illustrates moving from the positive position $p$ left by the magnitude of $q$ to find the sum $p+q$.