Page 15 - ICSE Math 7

1 Integers

Key Concepts

• Integers • Fundamental Operations on Integers
• Representation of Integers on a Number Line • Simplification of an Expression
• Comparison of Integers • Word Problems

In the previous class, we have learnt about addition and subtraction of integers, comparison and
ordering of integers. In this chapter, we will learn various properties of integers. These include
closure, commutative, associative and distributive property. Existence of identity element and
inverse of an element will also be discussed. We will also deal with multiplication and division
of integers.

Integers Maths Info

The negative numbers …, –3, –2, –1, along with whole numbers
are called integers. The set of integers is given by • 0 is neither a positive nor a negative
integer.
Z = {…, –3, –2, –1, 0, 1, 2, 3, …}. • All negative integers along with 0 are
The numbers 1, 2, 3, 4, … are called positive integers and the called non-positive integers.
numbers …, –4, –3, –2, –1 are called negative integers. • All positive integers along with 0 are
called non-negative integers.
Absolute value

The numerical value of an integer, regardless of its positive
or negative sign, is known as the modulus or absolute value Maths Info
of the integer. It is denoted by writing the integer in between two The absolute value of an integer is
vertical line segments or bars. For example, the absolute value of always non-negative.
–85 = |–85| = 85. The absolute value of an integer indicates its
distance from 0 on the number line.

Points to remember

• The absolute value of 0 is 0.
• The absolute value of a negative integer is always greater than itself.

Representation of Integers on a Number Line

All the positive integers 1, 2, 3, … are marked on the right hand Maths Info
side of 0 at equal distances and the negative integers …, –3, –2, –1
are marked on the left hand side of 0 at the same equal distances. On the number line, 0 is called the
origin.
A number line representing integers is given below.

–6 –5 –4 –3 –2 –1 0 1 2 3 4

The arrows on both sides of the number line indicate that both positive and negative integers continue
upto infinity.

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