Question

Describe how to find the sum p+q using a number line if p=−19 and q=12.1 .(1 point) First find on a number line, then count spaces to the right.

Answer 1

To find the sum \( p + q \) using a number line, follow these steps:

1. **Locate p on the number line**: Start by placing the point for \( p = -19 \). Since -19 is a negative number, locate it to the left of 0. You might count back 19 units from 0 to find this point.

2. **Locate q on the number line**: Next, find the point for \( q = 12.1 \). Since 12.1 is a positive number, locate it to the right of 0. You can approximate this by finding 12 first and then moving slightly right to place the point for 12.1.

3. **Add p and q**: To find \( p + q \), you will start at the point for \( p \) (-19) and move to the right by the amount of \( q \) (12.1 units).

4. **Count the spaces to the right**:
- From -19, if you move 19 spaces to the right, you will land on 0.
- Now, you have to move an additional 12.1 spaces from 0. Since you will move beyond 12, you can leave it as follows:
- Moving from 0 to 12 will take 12 spaces.
- Moving an additional 0.1 from 12 will take you slightly beyond 12.

5. **Determine the final position**: After counting the total moves, you will land at \( 0 + 12.1 = 12.1 \).

Therefore, the sum \( p + q = -19 + 12.1 = -6.9 \).

You can also visualize this by noting that moving from -19 all the way to zero cancels out -19, and then you are left with a distance of 12.1 into the positive range, culminating in -6.9 when added together.