Basics of mathematics

1. BASICS OF MATHEMATICS
Prepared by
Ms. R. Umadevi
Assistant Professor
Department of Mathematics
Bon Secours College For Women
Thanjavur

2. NUMBER SYSTEM

3. Natural numbers (ℕ) : The natural numbers is the set
of counting numbers.
ℕ = 1, 2, 3, 4, 5, … . . .
The natural numbers is the set of positive whole
numbers. This set does not include the number 0.
Integers (ℤ) : The set of integers is the set of all whole
numbers, positive negative and zero.
ℤ = … . . −3, −2, −1, 0, 1, 2, 3, … . . .

4. Even Numbers
A number divisible by 2 is called an even number
Example:
2,4,6,8,…..
Odd Numbers
A number not divisible by 2 is called an odd number
Example:
1,3,5,7,…..

5. Prime Numbers
A number which has exactly two factors , namely 1
and the number itself.
Example : 2,3,5,7,11,13,17,….
Composite Numbers
Numbers which are not prime are known as
composite numbers
Example : 4,6,8,9,10……

6. A Rational number(ℚ) is a number that can be written
as a ratio of two integers
𝑝
𝑞
, where p, q ∈ ℤ & q≠ 0.
A Rational number will have a decimal expansion that
is terminating or recurring.
Examples:
0.25 is rational , because it can be written as the ratio
1
4
.

7. An Irrational number (R / Q) is any number that
cannot be expressed as a ratio of two integers
𝑝
𝑞
, where
p and q ∈ ℤ and q≠0.
Irrational numbers are numbers that can be written as
decimals that go on forever without recurring.

8. The set of Rational and Irrational numbers together
make up the Real number system (ℝ).

9. The diagram represents the sets: Natural Numbers
ℕ, Integers ℤ, Rational Numbers ℚ 𝑎𝑛𝑑 Real Numbers
ℝ.
ℤ Type equation
here.
ℝ ℚ
ℕ

10. Keywords and Symbols

11. Mathematical Symbols

12. Order of Operations

13. Order of operations are rules that you must follow
when solving expressions
1st – parenthesis
2nd – Exponents
3rd – Multiply and divide from left to right
4th – Add and subtract from left to right

14. Example : 1
23 + (5 + 3) x 3 /2
23+ 8 x 3 / 2
8 + 24 / 2
8 + 12
20

15. Example : 2
(8 – (3 x 2)+ 3 ) – 22 / 2
(8 – 6 + 3 ) – 4 / 2
5 – 4 / 2
5 – 2
3

16. Ratio and Rates

17. Ratio – a comparison of two quantities using
division
Equivalent ratios – ratios that name the same
comparison
Rate – compares two quantities that have different
units of measures
Unit rate – when the comparison is to one unit
(price per 1 litre)

18. Probability

19. Probability is a mathematical term for the likelihood
that something will occur. It is the ability to understand
and estimate the likelihood of any different combination
of outcomes.

20. Flipping a coin is one of the most important events before the
start of the match. There is no surety, either head will come or
not. Both head and tail have 1 out of 2, i.e., 50% chances to
occur. Hence, the probability of getting the desired outcome is
0.5. Similarly, while playing with dice, there are 1 out of 6
chances, that the required number will come.

21. Weather Forecasting
Before planning for an outing or a picnic, we always
check the weather forecast. Suppose it says that there is
a 60% chance that rain may occur. Do you ever wonder
where this 60% comes from? Meteorologists use a
specific tool and technique to predict the weather rained.

22. forecast. They look at all the
other historical databases of the
day, which have similar
characteristics of temperature,
humidity, and pressure, etc. And
determine that on 60 out of 100
similar days in the past, it had