Some basic mathematics

Foundations of Mathematics: Some basic mathematics

Zero is neither positive nor negative and is considered an even number.


  • Whole numbers initiate from zero.
  • Positive numbers are greater than zero, while negative numbers are less than zero.

Natural Numbers:

  • Natural numbers, also known as counting or cardinal numbers, commence from 1.

Number 1:

  • 1 is a natural and whole number.
  • Not prime, not composite; the only positive integer neither prime nor composite.


  • The smallest prime number is 2.
  • The smallest composite number is 4.
  • Integers encompass positives, negatives, and zero but exclude decimals and fractions.

Numeral and Place Value:

  • A numeral is a group of digits.
  • Place value indicates the local value of a digit based on its place.
  • Face value denotes the actual value of a digit.

Types of Numbers:

  • Natural numbers start from 1.
  • Ordinal numbers signify order (first, second, third, etc.).
  • Whole numbers include zero and all natural numbers.
  • Integers encompass natural, positive, negative numbers but exclude decimals and fractions.
  • Non-negative integers: 0, 1, 2, 3…
  • Non-positive integers: 0, -1, -2, -3…
  • Prime numbers have only two factors (1 and itself).
  • Composite numbers have more than two factors and are not prime.
  • Even numbers are divisible by 2.
  • Odd numbers are not divisible by 2.
  • Co-prime numbers share a highest common factor of 1.
Rational Numbers:
  • Expressible as P/Q, where P and Q (Q≠0) are integers.
  • Include perfect squares, terminating decimals, and repeating decimals.
Irrational Numbers:
  • Real numbers that cannot be expressed as a fraction of two integers.
  • Examples: √2 and π.

Real Numbers:

  • A combination of rational and irrational numbers.
  • A complete representation of the number system.

Angle Concepts:

  • A straight line angle measures 180 degrees.
  • The sum of all angles in a triangle is 180 degrees.
  • A circle has 360 degrees.
  • A rectangle also has 360 degrees.
  • A complete angle measures 360 degrees.

Types of Angles:

  • Acute: measures less than 90 degrees.
  • Right: measures exactly 90 degrees.
  • Obtuse: measures between 90 and 180 degrees.
  • Reflex: measures between 180 and 360 degrees.


  • The sum of all angles in a triangle is 180 degrees.

Types of Triangles (based on Side Length):

  • Equilateral: all sides are equal.
  • Isosceles: two sides are equal.
  • Scalene: all sides and angles are unequal.

Types of Triangles (based on Angle Measurement):

  • Acute: all angles measure less than 90 degrees.
  • Right: one angle measures exactly 90 degrees.
  • Obtuse: one angle measures greater than 90 degrees.
Angle Relationships:
  • Complementary angles sum up to 90 degrees.
  • Supplementary angles sum up to 180 degrees.
  • Adjacent angles share a vertex and a common arm.

Right Angles and Triangles:

  • A right angle measures 90 degrees.
  • A right triangle contains one right angle.

Lines and Line Segments:

  • A line consists of infinite points.
  • A line segment is part of a line with two endpoints.

Angle Vertex:

  • The vertex of an angle is the common endpoint of two rays forming the angle.

Circle Properties:

  • Circumference: distance around a circle.
  • Diameter: distance from one side to the other, passing through the center.
  • π (pi): ratio of the circumference to diameter, approximately 3.14.
  • A polygon with four sides and four vertices.
  • Can be regular or irregular.
  • Sum of interior angles is 360°.


  • A quadrilateral with all four sides equal, opposite sides parallel, and all angles equal to 90°.


  • A quadrilateral with all four sides equal, opposite sides parallel, and all angles equal to 90°.


  • Opposite sides equal and parallel.
  • Opposite angles equal.
  • No angle measures 90 degrees.


  • Four equal sides.
  • Opposite sides parallel.
  • Opposite angles equal.
  • No angle measures 90 degrees.


  • Only one pair of opposite sides parallel.


  • Two pairs of adjacent equal sides.
  • One pair of equal angles.

Perimeter and Area:

  • Perimeter is the boundary distance.
  • Area is measured in square units.


  • Perimeter: 2(length + width).
  • Area: length × width.


  • Perimeter: 4 × side or sum of all sides (a + a + a + a).
  • Area: side × side.


  • Circumference (Perimeter): π × diameter.
  • Area: π × radius².

Calculation Example:
Given length (L) and width (W) of a rectangle are 5.3 cm each:

  • Perimeter: 2(L + W) = 2(5.3 + 5.3) = 21.2 cm.
  • Area: L × W = 5.3 × 5.3 = 28.09 cm².

Conversion: Fahrenheit to Celsius:

  • C = (F – 32) × (5/9).

Conversion: Celsius to Fahrenheit:

  • F = (C × 9/5) + 32.

Part/Whole Percentage:

  • Percentage = (part/whole) × 100.

Cross Multiplying:

  • A method to find missing values in proportions.

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Some basic mathematics

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