Question
A car backs up 5 feet, followed by 6 more feet. The car's position can be represented by the sum -5 +(- 6). Find the sum. Use pencil and paper. Represent the situation with a drawing. Superimpose a number line in the drawing to represent the situation in a third way.
- 5+(-6)=
- 5+(-6)=
Answers
GPT-4o mini
To solve \( -5 + (-6) \) and represent the situation visually, let's break it down step by step.
### Step 1: Understanding the Problem
The car is backing up:
1. The first movement is back 5 feet, which we represent as \( -5 \).
2. The second movement is back another 6 feet, represented as \( -6 \).
### Step 2: Representing the Sum
Now, we add these two movements:
\[
-5 + (-6) = -5 - 6
\]
When we add these two negative numbers, we simply combine their absolute values:
1. The absolute value of 5 is 5.
2. The absolute value of 6 is 6.
So, \( 5 + 6 = 11 \) and since both are negative, the result is \( -11 \).
Thus, \( -5 + (-6) = -11 \).
### Step 3: Drawing the Situation
You can create a simple drawing as follows:
1. Draw a horizontal line to represent the ground or the path.
2. Mark a point labeled "0" to denote the starting position of the car.
3. Mark a point at -5 (5 feet back from 0) and label it "Position after 1st movement".
4. From the point -5, move 6 feet back to -11 and label it "Final Position".
Here is how it might look in a drawing format (text representation):
```
|--------|--------|--------|--------|--------|--------|
-11 -10 -9 -8 -7 -6 -5
↑
Position after 1st movement (-5)
```
### Step 4: Superimposing a Number Line
You can also represent the same situation using a number line:
1. Draw a straight horizontal line.
2. Mark evenly spaced intervals with numbers going from left to right (in the negative direction, -1, -2, -3, etc.).
3. Highlight the movements from 0 to -5, and then from -5 to -11, showing the total movement back.
```
|---|----|----|----|----|----|----|-----|
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
```
### Conclusion
The final answer to the addition is:
\[
-5 + (-6) = -11
\]
And visually, you can see the car's total movement back to the position of -11 feet on the number line.
### Step 1: Understanding the Problem
The car is backing up:
1. The first movement is back 5 feet, which we represent as \( -5 \).
2. The second movement is back another 6 feet, represented as \( -6 \).
### Step 2: Representing the Sum
Now, we add these two movements:
\[
-5 + (-6) = -5 - 6
\]
When we add these two negative numbers, we simply combine their absolute values:
1. The absolute value of 5 is 5.
2. The absolute value of 6 is 6.
So, \( 5 + 6 = 11 \) and since both are negative, the result is \( -11 \).
Thus, \( -5 + (-6) = -11 \).
### Step 3: Drawing the Situation
You can create a simple drawing as follows:
1. Draw a horizontal line to represent the ground or the path.
2. Mark a point labeled "0" to denote the starting position of the car.
3. Mark a point at -5 (5 feet back from 0) and label it "Position after 1st movement".
4. From the point -5, move 6 feet back to -11 and label it "Final Position".
Here is how it might look in a drawing format (text representation):
```
|--------|--------|--------|--------|--------|--------|
-11 -10 -9 -8 -7 -6 -5
↑
Position after 1st movement (-5)
```
### Step 4: Superimposing a Number Line
You can also represent the same situation using a number line:
1. Draw a straight horizontal line.
2. Mark evenly spaced intervals with numbers going from left to right (in the negative direction, -1, -2, -3, etc.).
3. Highlight the movements from 0 to -5, and then from -5 to -11, showing the total movement back.
```
|---|----|----|----|----|----|----|-----|
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
```
### Conclusion
The final answer to the addition is:
\[
-5 + (-6) = -11
\]
And visually, you can see the car's total movement back to the position of -11 feet on the number line.