INTEGERS AND OPPOSITES

Positive and negative numbers can be used to represent real-world quantities.

For example, 3 can represent a temperature that is 3 °F above 0. -3 can represent a temperature that is 3 °F below 0. Both 3 and -3 are 3 units from 0.

Practice problems

Problem 1 :

Daniel kept track of the weekly low temperature in his town for several weeks. The table shows the low temperature in °F for each week.

From the above information, answer the following questions. 

(i) Graph the temperature from Week 3 and its opposite on a number line. What do the numbers represent ?

(ii)  The value for Week 5 is the opposite of the opposite of the value from Week 1. What was the temperature in Week 5 ?

Solution (i) :

Step 1 :

The value from Week 3 is -4. 

Graph a point 4 units below 0.

Step 2 :

Graph the opposite of -4.

Graph a point 4 units above 0.

The opposite of -4 is 4.

Solution (ii) :

Step 1 :

Graph the value from Week 1 on the number line. 

The value from Week 1 is -1.

Step 2 :

Graph the opposite of -1.

The opposite of -1 is 1.

Step 3 :

Graph the opposite of 1.

The opposite of 1 is -1.

The opposite of the opposite of -1 is -1. The low temperature in Week 5 was -1 °F.

Problem 2 :

Compare the integers -4 and 4

Solution : 

Let us locate the two integers -4 and 4 on a number line and mark them. 

Here, the positive integer 4 comes to the right of -4.

Therefore "4" is greater than "-4"

And -4 comes to the left of 4.  

Therefore "-4" is smaller than "4"

Problem 3 :

Compare the integers -1 and 1

Solution : 

Let us locate the two integers -1 and 1 on a number line and mark them. 

Here, the positive integer 1 comes to the right of -1.

Therefore "1" is greater than "-1"

And -1 comes to the left of 1.  

Therefore "-1" is smaller than "1".

Problem 4 :

Order the integers 1, -5, 5, 4, 0, -2, -1, 3 from least to greatest. 

Solution : 

Let us locate the integers 1, -5, 5, 4, 0, -2, -1, 3 on a number line and mark them. 

From the above number line, write the integers from left to right to list them in order from least to greatest.  

Thus, we get

-5, -2, -1, 0, 1, 3, 4, 5

Problem 5 :

John recorded the following golf scores during his first week at a golf academy. Negative numbers represent scores below par, a standard score. In golf, a lower score beats a higher score.

Graph John’s scores on the number line, and then list the numbers in order from least to greatest.

Solution :

Step 1 :

Graph the scores on the number line.

Step 2 :

Read from left to right to list the scores in order from least to greatest.

The scores listed from least to greatest are

–5, –3, –2, –1, 0, 3, 4

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