**TS 6**^{th}Maths Concept**TS 7**^{th}Maths Concept**TS 8**^{th}Maths Concept**TS 9**^{th}Maths Concept**TS 10**^{th}Maths Concept

## TS IX CLASS MATHS CONCEPT

Studying maths in IX class successfully means that children take responsibility for their own learning and learn to apply the concepts to solve problems.

# This note is designed by the ‘Basics in Maths’ team. These notes to do help students fall in love with mathematics and overcome fear.

## 1.REAL NUMBERS

### Rational numbers:-

- The numbers which are written in the form of, where p, q are integers and q≠ 0 are called rational numbers. Rational numbers are denoted by Q.

ex:- 3/2, 3/5, 2, 1 and so on

- Natural numbers, Whole numbers, and Integers are rational numbers.

- The rational numbers do not have a unique representation.

** Representation of rational number:**

**To find a rational number between given numbers:**

** Mean method:- **A rational number between two numbers a and b is

** **Ex:- insert two rational number between 1 and 2

**To find a rational number in a single step:-**

Ex:- insert two rational number between 1 and 2

To find two rational numbers, we 1 and 2 as rational numbers with same denominator 3 (∵ 1 + 2 = 3)

**The decimal form of rational numbers:**

- Note:- Every rational number can be expressed as a terminating decimal or non-terminating repeating decimal.
**Converting decimal form into a****fraction:**

**Terminating decimals:-**(i) 1.2 = 12/10 = 6/5

(ii) 1.35 =135/100 = 135/100 = 27/20

**Non-Terminating repeating decimals:-**

**Irrational numbers:**

- The numbers which are not written in the form of, where p, q are integers and q ≠ 0 are called rational numbers. Rational numbers are denoted by Q
^{I }or S.

- Every irrational number can be expressed as a non-terminating decimal or non-repeating decimal.

** Calculation of square roots:**

- There is a reference of irrationals in the calculation of square roots in Sulbha Sutra.
- Procedure to find value:

**Representing irrational numbers on a number line:**

- At ‘O’ draw a unit square OABC on a number line with each side 1 unit in length.

- By Pythagoras theorem OB
^{2}= OA^{2}+ AB^{2}

= 1^{2} + 1^{2}

OB^{2} = 2

- Using a compass with centre O and radius OB, draw an arc on the right side to O intersecting the number line at the point
- The location of is now at k.

**Note:- If a and b are two positive rational numbers such that ab is not a perfect square, this****an irrational number lies between a and b.**

**Real numbers**

- The collection of all rational and irrational numbers is called real numbers.
- Real numbers cover all the points on the number line.
- Every real number is represented by a unique point on the number line.
- Ex:- are some examples of real numbers.

**Representing real numbers on the number line through successive magnifications:-**

locating 2. 775 on a number line

**Operation on real numbers**

- The sum, difference, product and quotient of irrational numbers need not be an irrational number.
- Irrational numbers are not closed under addition, subtraction, multiplication, and division.
- For any two real numbers a and b

**Rationalizing the denominator:**

**Rationalizing factor(R.F):-**If the product of two irrational numbers is rational, then each of the two is the rationalizing factor to others.

- The rationalizing factor of a given irrational number is not unique. It is convenient to use the simplest of all R.F.s of given irrational number.
- Note:-