ADDING INTEGERS ON A NUMBER LINE WORKSHEET

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 ?

Detailed Answer Key

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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