🌈 THE WONDERFUL WORLD OF NUMBERS
Explore • Understand • Visualise • Practise
Interactive Mathematics Learning Centre
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📚 Interactive Learning Index
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1. Understanding Numbers
Numbers are mathematical symbols used for counting, measuring, comparing and calculating quantities.
Counting
Measuring
Comparing
2. Natural Numbers (N)
Natural numbers are counting numbers beginning with 1.
Examples
N = {1, 2, 3, 4, 5, 6, 7, ...}
They are used to count students, books, trees and other objects.
Important: Zero is not included in natural numbers under this convention.
3. Whole Numbers (W)
Whole numbers consist of zero and all natural numbers.
W = {0, 1, 2, 3, 4, 5, ...}
Example: Number of apples in an empty basket is zero.
4. Integers (Z)
Integers include negative numbers, zero and positive numbers.
Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}
Examples: Temperature -5°C, bank balance -100, floor 3.
5. Rational Numbers (Q)
A rational number can be expressed in the form p/q, where p and q are integers and q is not zero.
Examples: 1/2, 3/4, -5/2, 7, 0.25
Terminating and repeating decimals are rational numbers.
6. Irrational Numbers
Numbers that cannot be expressed as a ratio of two integers.
Examples: √2, √3, π
Their decimal expansions are non-terminating and non-repeating.
7. Real Numbers (R)
Real numbers include both rational and irrational numbers.
Real Numbers = Rational Numbers ∪ Irrational Numbers
Every point on the number line represents a real number.
Number system relationship
REAL NUMBERS (R)
RATIONAL
Integers, fractions, terminating and repeating decimals
8. Prime Numbers
A prime number has exactly two distinct positive factors: 1 and itself.
2, 3, 5, 7, 11, 13, 17, 19...
Remember: 2 is the only even prime number.
9. Composite Numbers
A composite number has more than two positive factors.
4, 6, 8, 9, 10, 12, 14, 15...
Example: Factors of 12 are 1, 2, 3, 4, 6 and 12.
10. Even and Odd Numbers
Even Numbers
Divisible by 2 without a remainder.
2, 4, 6, 8, 10, 12...
Odd Numbers
Not divisible by 2 without a remainder.
1, 3, 5, 7, 9, 11...
11. Factors and Multiples
Factors: Numbers that divide a given number exactly.
Factors of 18: 1, 2, 3, 6, 9, 18.
Multiples: Products obtained by multiplying a number by whole numbers.
Multiples of 5: 5, 10, 15, 20, 25...
12. Place Value and Face Value
Place value is the value of a digit according to its position. Face value is the digit itself.
Number: 4,582
13. Number Line
A number line is a straight line on which numbers are represented at equal intervals.
Remember: Addition moves to the right for positive numbers. Subtraction moves to the left for positive numbers.
Multiplication can be shown as repeated jumps. Division can be shown by equal jumps and counting the groups.
14. Number Line Practice Problems
Problem 1: 2 + 4 = ?
Start at 2 and move four steps to the right.
Show Answer
Problem 2: 7 - 3 = ?
Start at 7 and move three steps to the left.
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Problem 3: 3 × 2 = ?
Make two jumps of three units each.
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Problem 4: 8 ÷ 2 = ?
Make equal jumps of two units from zero to eight.
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Problem 5: -3 + 5 = ?
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15. Introduction to Fractions
A fraction represents a part of a whole.
1/2 = One-half
16. Proper Fractions
A proper fraction has a numerator smaller than its denominator.
Examples: 1/2, 2/3, 3/4, 4/5.
17. Improper Fractions
An improper fraction has a numerator greater than or equal to its denominator.
Examples: 5/4, 7/3, 9/5.
18. Mixed Fractions
A mixed fraction contains a whole number and a proper fraction.
Example: 1 1/2 = 3/2
19. Unit Fractions
A unit fraction has 1 as its numerator.
Examples: 1/2, 1/3, 1/4, 1/5.
20. Like Fractions
Fractions having the same denominator are called like fractions.
Examples: 1/5, 2/5, 3/5.
21. Unlike Fractions
Fractions having different denominators are called unlike fractions.
Examples: 1/2, 2/3, 3/4.
22. Equivalent Fractions
Fractions representing the same value are called equivalent fractions.
1/2 = 2/4 = 3/6 = 4/8
24. Decimal Numbers
Decimals represent numbers using a decimal point.
0.5 = 5/10 = 1/2
25. Percentages
Percentage means per hundred.
50% = 50/100 = 1/2
26. Absolute Value
Absolute value is the distance of a number from zero on the number line.
|5| = 5 and |-5| = 5
27. Powers and Exponents
An exponent tells us how many times a number is multiplied by itself.
2³ = 2 × 2 × 2 = 8
28. Order of Operations (BODMAS)
BODMAS tells us the correct order for solving mathematical expressions.
B – Brackets
Example: 2 + 3 × 4 = 2 + 12 = 14.
29. HCF and LCM
HCF: Highest Common Factor.
LCM: Least Common Multiple.
HCF of 12 and 18 = 6
30. Square Roots and Cube Roots
√25 = 5 because 5 × 5 = 25
31. Four Fundamental Operations
Addition (+)
Combining two or more quantities.
25 + 15 = 40
Subtraction (−)
Finding the difference between quantities.
45 − 20 = 25
Multiplication (×)
Repeated addition of equal quantities.
6 × 4 = 24
Division (÷)
Sharing a quantity into equal groups.
24 ÷ 6 = 4
32. Number Systems – Assessment
Select the correct answer for each question.
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