Page 117 - ICSE Math 5

Comparison of Integers Using a Number Line

A number line is often used to compare integers.
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Similar to the whole numbers, for any two integers that are
represented on a number line, the one that is on the right is Numbers always
increase from left to
considered as the greater number than the one that is on the
right on a number
left. We can also say that the number on the left is smaller line.
than the number on the right.
Value of numbers increase from left to right.

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

Value of numbers decrease from right to left.
From this, we may conclude the following.

(a) Every positive number is greater than the negative Mental Maths
number.
1. Find all integers that lie
(b) Zero is smaller than every positive number. between –3 and 5. How
many of them are smaller
(c) Zero is greater than every negative number.
than 0?
(d) Farther a number is to the right of zero, greater is 2. Write three negative
its value. integers greater than –7.

(e) Farther a number is to the left of zero, smaller is its
value.

Ordering of Integers

It is convenient for us to arrange positive numbers in any order like ascending or descending.
When it comes to negative numbers, it can be a little tricky to arrange them in an order. Thus,
we can use a number line to arrange the given integers in an appropriate order, i.e., from the
smallest to the greatest and from the greatest to the smallest.
To arrange the given integers in any order, we follow the given steps.

• Draw a number line and mark the given integers on it.
• Write the integers as they appear on the number line from left to right for ascending order
and from right to left for descending order.

Descending Ascending order
order of integers of integers

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Example 5: Write all the integers between –9 and 5.

Solution: Integers between –9 and 5 are –8, –7, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3 and 4.
Example 6: Which number in each of the following pairs is to the right of the other on the
number line?

(a) 10, 4 (b) –1, 0

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