Which number line shows the correct way to find the sum p+q if p is positive and q is negative?
To find the sum p+q where p is positive and q is negative, we need to follow these steps:
1. Start from the point on the number line that represents the value of p. Since p is positive, this point will be to the right of zero.
2. From the point representing p, move q units to the left on the number line. Since q is negative, moving to the left corresponds to adding the absolute value of q.
Here is an example of a number line showing the correct way to find the sum p+q:
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
| | | | | | | | | | | | |
P Q
In this example, the point P represents the value of p, and the point Q represents the value of q. To find the sum p+q, we start from P and move 4 units to the left to reach Q.
To find the sum p+q when p is positive and q is negative, follow these steps:
1. Place your finger or a pencil at the starting point of zero on the number line.
2. Move your finger or pencil to the right by the value of p.
3. Place a dot or mark to indicate the positive value p.
4. Now, move your finger or pencil to the left by the magnitude of q (ignore the negative sign).
5. Place a dot or mark to indicate the negative value q.
6. Draw a line connecting the two dots or marks.
7. The point where the line intersects the number line represents the sum p+q.
Note: The sum p+q will be a negative value since q is negative.
Here is an example of how the number line might look:
-3 -2 -1 0 1 2 3
| |x x|
In this example, p = 2 and q = -3. The positive value 2 is marked with "x" to the right of zero, and the negative value -3 is marked with "x" to the left of zero. The line connecting the two "x" marks intersects at -1, which represents the sum p+q.
To find the sum p + q when p is positive and q is negative, we need to combine the magnitudes of the two numbers and determine the sign of the sum based on their respective signs.
To illustrate this on a number line, we can follow these steps:
1. Place a point on the number line representing the value of p. Since p is positive, the point should be to the right of zero.
2. Place another point on the number line representing the value of -q. Since q is negative, the point should be to the left of zero.
3. Draw an arrow connecting these two points. The arrow starts at the point representing p and ends at the point representing -q.
4. The sum p + q is given by the point where the arrow ends. Determine the sign of this sum based on the greater magnitude of p and q:
- If the magnitude of p is greater than the magnitude of q, the sum will be positive.
- If the magnitude of q is greater than the magnitude of p, the sum will be negative.
So, on the number line, the correct way to find the sum p + q for a positive p and negative q is to observe where the arrow ends.