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.
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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