Page 16 - ICSE Math 7

Points to remember

• Every integer has a successor and a predecessor.
• There is no smallest or greatest integer.

Comparison of Integers
Given any two integers, one of them is always greater than the other. To compare integers, follow the
steps given as:
(a) Every positive integer is greater than every negative integer. Try These

(b) Every positive integer is greater than zero and zero is greater than 1. Put the correct sign >, < or
every negative integer. = in the blank.

(c) If both the integers are positive, then the integer with greater (a) –7 __ 6 (b) –11 __ –18
absolute value is greater. (c) 0 __ 8 (d) –10 __ –(–10)

(d) If both the integers are negative, then the integer with smaller 2. What is the predecessor
absolute value is greater. of –4?

Example 1: Write the following as an integer.

(a) |–15| + |9| (b) |–21| + |5| – |–10| – |29|
Solution: (a) |–15| + |9| = 15 + 9 = 24 (b) |–21| + |5| – |–10| – |29| = 21 + 5 – 10 – 29 = –13
Example 2: Arrange –38, 0, 133, –135, 25 and –49 in ascending order.

Solution: Every positive integer is greater than zero and zero is greater than every negative integer.
So, –135 < –49 < –38 < 0 < 25 < 133.

EXERCISE 1.1

1. Represent the following on a number line.
(a) Integers greater than 4 and less than 6

(b) Integers greater than or equal to –1 and less than or equal to 2
2. Write the following as an integer.
(a) |3| + |2| – |11| (b) |–273| + |370| – |–571| (c) |142 – 2| – |–14| + |21| – |–215|
3. Arrange the following integers in ascending order.
(a) 123, –56, 96, –132, 132, –76 (b) 99, –55, 60, 125, –185, –215
4. Arrange the following integers in descending order.
(a) –365, 473, –222, 99, 175 (b) 156, –88, –74, 216, –193, 0

Fundamental Operations on Integers

Addition

For addition of integers, we have two cases:
(a) When the integers to be added are of the same sign, i.e., either all of them are positive or all of
them are negative, then add their absolute values and assign the same sign to the sum.
(b) When the integers to be added are not of the same sign, then add all the integers with the plus
sign together and all the integers with the minus sign together. Then find the absolute values of
both the sums. Finally, find the difference between these absolute values and assign the sign of
the greater sum to this difference.

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