Question 1 :
Add 3 and 2 using a number line.
Question 2 :
Add 3 and -2 using a number line.
Question 3 :
The temperature was 2°F below zero. The temperature drops by 5°F. What is the temperature now ?
Question 4 :
Suppose the temperature is -1°F and drops by 3°F. Explain how to use the number line to find the new temperature.
Question 5 :
How would using a number line to find the sum (2 + 5) be different from using a number line to find the sum -2 + (-5) ?
Question 6 :
What are two other negative integers that have the same sum as - 2 and - 5 ?
Question 1 :
Add 3 and 2 using a number line.
Answer :
Here, the integers 3 and 2 are having the same sign. That is positive.
To find the sum of integers 3 and 2, we have to start at 3
Because the second number '2' is positive, we have to move 2 units in the positive direction as given in the picture below.
After having move 2 units in the positive direction, we are in the position of '5'.
So,
3 + 2 = 5
Question 2 :
Add 3 and -2 using a number line.
Answer :
Here, the integers 3 and -2 are having different signs.
To find the sum of integers 3 and -2, we have to start at 3
Because the second number -2 is negative, we have to move 2 units in the negative direction as given in the picture below.
After having move 2 units in the negative direction, we are in the position of '1'.
So,
3 + (-2) = 1
Question 3 :
The temperature was 2°F below zero. The temperature drops by 5°F. What is the temperature now ?
Answer :
Step 1 :
According to the question, the initial temperature was 2°F below zero. 2 below zero is -2.
So, the initial temperature is -2°F
Step 2 :
Let us mark the initial temperature on the number line.
Step 3 :
A drop in temperature of 5° is like adding -5° to the temperature.
Because the temperature is dropping, we have to go below the initial temperature. The temperature drops by 5°. So, we have to count 5 units on the number line below -2 to find the final temperature.
That is -7.
Mark the temperature now on the number line.
Step 4 :
From the above figure, the final temperature is -7°.
Justify and Evaluate :
In the above example, we have just added -2 and -5.
From the above example problem, it is clear that when we add two negative numbers, we have to add them as usual and take negative sign to the result.
Question 4 :
Suppose the temperature is -1°F and drops by 3°F. Explain how to use the number line to find the new temperature.
Answer :
Start at -1. Move 3 units in a negative direction to -4; the new temperature is -4 °F.
Question 5 :
How would using a number line to find the sum (2 + 5) be different from using a number line to find the sum -2 + (-5) ?
Answer :
Instead of starting at 2 and moving 5 units in a positive direction to get 7, you would start at -2, move 5 units in a negative direction, and get -7.
Question 6 :
What are two other negative integers that have the same sum as - 2 and - 5 ?
Answer :
Sample answer: - 3 and - 4.
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