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Ordering of Integers

All positive integers which are greater than 0 are located to the right of zero, while all negative
integers which are less than 0 are located to the left of zero.

Decreasing Order Increasing Order
–ve +ve
–5 –4 –3 –2 –1 0 1 2 3 4 5
Between two given integers, the integer occurring on the right side of the number line is greater
than that occurring on the left side. For example,
5 > 2, since 5 is to the right of 2.

3 > 0, since 3 is to the right of 0.
1 > −2, since 1 is to the right of −2.

−3 > −5, since −3 is to the right of −5.
Hence, we arrive at the following points:

1. Every positive integer is greater than ‘0’, since 0 is at the left side of every positive integer.

2. Zero is greater than every negative integer.
3. Every positive integer is greater than every negative integer.
4. A negative integer with a bigger numerical value is always smaller than a negative integer
with a smaller numerical value.

Note: 1 is the smallest positive integer and –1 is the greatest negative integer.

Example 3: Arrange the integers –2, 1, 0, –3, +4, –5 in the ascending order.
Solution: When we move from left to right along with the number line, then the integers increase.
So, the ascending order of the given integers is –5 < –3 < –2 < 0 < 1 < +4.

Think and Answer

Gayatri and her friends participated in an online quiz where 4 marks were awarded for each
correct answer and 1 mark is deducted for each incorrect answer. Following are the marks obtained by Gayatri
and her friends:
Aarti Shailza Neetu Smita Vaishali Gayatri
15 –12 9 –15 17 12
1. Who scored the maximum marks and who scored the minimum marks?
2. Who scored less marks than Shailza?
Mirror
Negative of a Negative Integer

Look at the mirror image of a number. If we put a mirror
at 0 facing positive integers, we observe that each –5 –4 –3 –2 –1 0 1 2 3 4 5
positive integer on the right side will have its image on

Teacher’s Explain to students that a mirror image of a number is a reflected duplication of the number that seems to be
Tip appear identical at the same distance behind the mirror.

283 The Other Side of Zero