Every one can easily understand comparing two positive numbers.
For example, when we compare 7 and 9, we can say that 9 is greater than 7.
Because, in comparing two positive numbers, greater number is always is greater and smaller number is always smaller.
But, if we take a number with negative sign, it becomes smaller and smaller, when it gets increased with negative sign.
For example,
-9 is less than -7
-100 is less than -1
-0.25 is less than 0
-8 is less than 5
We use number line to compare positive and negative integers.
That is, if we want to compare positive and negative integers, first we have to locate the integers on the number line and mark them.
The integer which comes to the right of the other integer is greater. The integer which comes to the left of the other integer is smaller.
Example 1 :
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".
Example 2 :
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".
Example 3 :
Compare the integers given below and order them from least to greatest.
1, -5, 5, 4, 0, -2, -1, 3
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
Example 4 :
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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