Class 10 Mathematics – Algebra (Part 1)
Chapter 1: Real Numbers (English Notes)
Class 10 Algebra typically begins with Real Numbers, followed by Polynomials, Pair of
Linear Equations in Two Variables, Quadratic Equations, and Arithmetic Progressions.
1. Real Numbers
Learning Objectives
After completing this chapter, you will be able to:
Understand real numbers.
Apply the Euclid Division Algorithm.
Find the HCF (Highest Common Factor) of two numbers.
Understand the Fundamental Theorem of Arithmetic.
Find the LCM using prime factorization.
Identify rational and irrational numbers.
What are Real Numbers?
Real numbers are all the numbers that can be represented on a number line.
Examples:
Integers: -5, -2, 0, 3, 8
Fractions: 1/2, -7/4
Decimals: 2.75, -0.125
Irrational Numbers: √2, √3, π
Types of Real Numbers
1. Natural Numbers (N)
Counting numbers.
Example:
1, 2, 3, 4, ...
,2. Whole Numbers (W)
0, 1, 2, 3, 4, ...
3. Integers (Z)
..., -3, -2, -1, 0, 1, 2, 3, ...
4. Rational Numbers (Q)
Numbers that can be written as
p/q
where q ≠ 0.
Examples:
3/5
-8/7
0.25
5. Irrational Numbers
Numbers that cannot be written as p/q.
Examples:
√2
√5
π
Their decimal expansion is non-terminating and non-repeating.
Euclid's Division Lemma
For any two positive integers a and b,
a = bq + r
, where
0≤r<b
Example:
Find HCF of 48 and 18.
48 = 18 × 2 + 12
18 = 12 × 1 + 6
12 = 6 × 2 + 0
Therefore,
HCF = 6
Prime Numbers
A prime number has exactly two factors:
1 and itself.
Examples:
2, 3, 5, 7, 11, 13
Composite Numbers
Composite numbers have more than two factors.
Examples:
4, 6, 8, 9, 12
Fundamental Theorem of Arithmetic
Every composite number can be expressed as a product of prime numbers.
Example:
60
Chapter 1: Real Numbers (English Notes)
Class 10 Algebra typically begins with Real Numbers, followed by Polynomials, Pair of
Linear Equations in Two Variables, Quadratic Equations, and Arithmetic Progressions.
1. Real Numbers
Learning Objectives
After completing this chapter, you will be able to:
Understand real numbers.
Apply the Euclid Division Algorithm.
Find the HCF (Highest Common Factor) of two numbers.
Understand the Fundamental Theorem of Arithmetic.
Find the LCM using prime factorization.
Identify rational and irrational numbers.
What are Real Numbers?
Real numbers are all the numbers that can be represented on a number line.
Examples:
Integers: -5, -2, 0, 3, 8
Fractions: 1/2, -7/4
Decimals: 2.75, -0.125
Irrational Numbers: √2, √3, π
Types of Real Numbers
1. Natural Numbers (N)
Counting numbers.
Example:
1, 2, 3, 4, ...
,2. Whole Numbers (W)
0, 1, 2, 3, 4, ...
3. Integers (Z)
..., -3, -2, -1, 0, 1, 2, 3, ...
4. Rational Numbers (Q)
Numbers that can be written as
p/q
where q ≠ 0.
Examples:
3/5
-8/7
0.25
5. Irrational Numbers
Numbers that cannot be written as p/q.
Examples:
√2
√5
π
Their decimal expansion is non-terminating and non-repeating.
Euclid's Division Lemma
For any two positive integers a and b,
a = bq + r
, where
0≤r<b
Example:
Find HCF of 48 and 18.
48 = 18 × 2 + 12
18 = 12 × 1 + 6
12 = 6 × 2 + 0
Therefore,
HCF = 6
Prime Numbers
A prime number has exactly two factors:
1 and itself.
Examples:
2, 3, 5, 7, 11, 13
Composite Numbers
Composite numbers have more than two factors.
Examples:
4, 6, 8, 9, 12
Fundamental Theorem of Arithmetic
Every composite number can be expressed as a product of prime numbers.
Example:
60
