Numbers
Numbers are an integral
part of our everyday lives, right from the number of hours we sleep at night to
the number of rounds we run around the racing track and much more. In math,
numbers can be even and odd numbers, prime and composite numbers, decimals,
fractions, rational and irrational numbers, natural numbers, integers, real
numbers, rational numbers, irrational numbers, and whole numbers. In this
chapter, we will get an introduction to the different types of numbers and to
all the concepts related to them.
What
are Numbers?
A number is a basic
component of mathematics. Numbers are used for counting, measuring, keeping
things in order, indexing, etc. We have different types of numbers based on
their properties such as natural numbers, whole numbers, rational and
irrational numbers, integers, real numbers, complex numbers, even and odd
numbers, etc. We can apply the basic fundamental arithmetic operations of
numbers and determine the resulting number. Initially, tally marks were used
before the use of numbers. Let us now introduce the concept of numbers and
understand their different types and their properties.
Definition
of Numbers
An arithmetic value
that is expressed using a word, a symbol or a figure that represents a quantity
is called a number. Numbers are used in counting and calculations.
Introduction
to Numbers
Numbers form the basis
of mathematics. We should befriend numbers in order to understand math. Numbers
are of various kinds. We have a long list that includes ordinal numbers,
consecutive numbers, odd numbers, even numbers, natural numbers, whole numbers,
integers, real numbers, rational numbers, irrational numbers, and complex
numbers.
Along with numbers, we
come across the interesting world of factors and multiples. This world includes
prime numbers, composite numbers, co-prime numbers, perfect numbers (yes,
numbers could be perfect!) HCF, LCM, and prime factorization.
Let us get started on
our journey of numbers. You can go ahead and explore all important topics in
Numbers by selecting the topics from the list given below:
Pre-number
Math
Building pre-number
math skills is a prerequisite to understanding numbers. Pre-number skills like
matching, sorting, classifying, ordering, and comparing sets the stage to build
a strong number sense. Pre-number Math skills are built-in preschool years.
Kids learn how to stand before they start taking small steps. In the same way,
the pre-number concept is very important for them to start understanding
Mathematics. In this section, we will cover the different pre-number concepts
like Matching and Sorting, Comparing and Ordering, Classification, and Shapes
and patterns.
Example:
Observe the figure given below which shows 2 columns. The left column displays
the numbers 1 to 4. The right column displays rows of items. The numbers are
matched to the quantities they represent. This is an essential skill for
children aged 3 to 4 years.
Number
Names
Number names are used
to represent numbers in an alphabetical format. A specific word is used to
refer to each number. To write a number in words in English, we should know the
place value of each digit in the number.
Example: Observe the
figure given below which shows that 37 is written as 'thirty-seven' in the
number names form.
PEMDAS
The rules of PEMDAS
outline the order of the operations and give structure to nested operations. In
mathematics, PEMDAS is an acronym that stands for P- Parentheses, E- Exponents,
M- Multiplication, D- Division, A- Addition, and S- Subtraction.
EXAMPLE:
1. 2 + 5 ´ (4 - 1) : 3
= 2 + 5 ´ 3 : 3
(Parentheses are done first)
= 2 + 15 : 3 (Multiplication
are done first)
= 2 + 5 (Division
are done first)
= 7
2. 6 - 4 : 2 +
23 ´ (5 + 1)
= 6 - 4 : 2 + 8 ´ (5 + 1) (Exponents are
done first)
= 6 - 4 : 2
+ 8 ´ 6 (Parentheses
are done first)
= 6 - 4 : 2
+ 48 (Multiplication are done first)
= 6 - 2 + 48 (Division are done
first)
= 4 + 48 (Subtraction are
done first)
= 52
