Natural Numbers
Definition: Numbers used for counting starting from 1, 2, 3...
Examples:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
Even Numbers
Definition: Numbers divisible by 2.
Examples:
- 2
- 4
- 6
- 8
- 10
- 12
- 14
- 16
Odd Numbers
Definition: Numbers not divisible by 2.
Examples:
- 1
- 3
- 5
- 7
- 9
- 11
- 13
- 15
Prime Numbers
Definition: Numbers greater than 1 that have only 1 and itself as factors.
Examples:
- 2
- 3
- 5
- 7
- 11
- 13
- 17
- 19
Decimal Numbers
Definition: Numbers with a fractional part separated by a decimal point.
Examples:
- 0.1
- 0.25
- 0.5
- 1.1
- 2.75
- 3.14
- 4.5
- 5.9
Whole Numbers
Definition: Natural numbers including zero.
Examples:
- 0
- 1
- 2
- 3
- 4
- 5
- 6
- 7
Rounding Off
Definition: Replacing a number with a nearby value having fewer digits.
Examples:
- 3.67 → 3.7
- 5.24 → 5.2
- 12.58 → 13
- 9.99 → 10
- 7.49 → 7
- 0.456 → 0.46
- 123.89 → 124
- 0.999 → 1
Simple Linear Equations
Definition: An equation of the form ax + b = 0, where x is unknown.
Examples:
- x + 3 = 7 → x = 4
- 2x + 5 = 9 → x = 2
- 3x - 4 = 8 → x = 4
- 5x + 10 = 35 → x = 5
- 4x - 7 = 9 → x = 4
- 6x + 2 = 20 → x = 3
- x - 5 = 10 → x = 15
- 2x - 3 = 7 → x = 5
Statistics
Definition: Collection, organization, analysis, and presentation of data.
Examples with Numbers:
- Test scores of students: 78, 85, 92, 67, 74, 88, 91, 79
- Daily temperature readings (°C): 22, 24, 25, 23, 26, 27, 24, 22
- Population of a village over years: 1020, 1055, 1088, 1120, 1150, 1180, 1205, 1230
- Number of books read per month: 3, 5, 2, 4, 6, 3, 5, 4
- Sports scores in a league: 2-1, 3-0, 1-1, 0-2, 4-3, 3-2, 2-2, 1-0
- Monthly rainfall data (mm): 120, 85, 90, 110, 95, 100, 130, 105
- Height of students in class (cm): 150, 155, 160, 162, 158, 165, 170, 168
- Number of cars passing a junction daily: 220, 250, 240, 230, 260, 270, 255, 245
LCM and HCF
Definition:
- HCF (Highest Common Factor): The largest number that divides two or more numbers exactly.
- LCM (Lowest Common Multiple): The smallest number that is exactly divisible by two or more numbers.
Examples with Numbers:
- HCF of 12 and 18: 6
- LCM of 12 and 18: 36
- HCF of 24, 36, 60: 12
- LCM of 24, 36, 60: 360
Examples with Variables:
- HCF of a and b (where a = 8x, b = 12x): HCF = 4x
- LCM of a and b (where a = 8x, b = 12x): LCM = 24x
- HCF of p and q (where p = 15y, q = 25y): HCF = 5y
- LCM of p and q (where p = 15y, q = 25y): LCM = 75y