Mathematical symbols are signs used to represent operations, relations, or quantities. They make mathematics easier to read and write.

Examples:

• + : Addition


• - : Subtraction


• × : Multiplication


• ÷ : Division


• = : Equal to


• ≠ : Not equal to


• > : Greater than


• < : Less than


• ≥ : Greater than or equal to


• ≤ : Less than or equal to


• % : Percent


• √ : Square root

An open sentence is a mathematical statement that contains a symbol, letter, or shape whose value is not yet known.

Examples :

1. x + 5 = 12 → x = 12 - 5 = 7


2. y - 7 = 3 → y = 3 + 7 = 10


3. 2 × a = 10 → a = 10 ÷ 2 = 5


4. b ÷ 4 = 3 → b = 3 × 4 = 12


5. c + 7 ≠ 12 → c ≠ 5 (any number except 5)


6. 5 × m - 8 = 12 → 5m = 20 → m = 20 ÷ 5 = 4

Letters (usually a, b, x, y) can represent numbers, symbols, or shapes. This allows writing general rules in algebra and geometry.

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Examples :

1. Let n represent the number of sides of a polygon. Sum of interior angles = (n-2) × 180. Example: n = 6 → (6-2) × 180 = 720°


2. Let s represent the side length of a square. Area = s². Example: s = 5 → 5² = 25


3. Let h be the height and b the base of a triangle. Area = 1/2 × b × h. Example: b = 8, h = 5 → 1/2 × 8 × 5 = 20


4. Let r represent the radius of a circle. Area = πr². Example: r = 7 → 3.14 × 7² = 153.86


5. Let x represent an unknown number. Equation: 3x + 4 = 19 → 3x = 15 → x = 5


6. Let p represent the perimeter of a rectangle. p = 2(l + w). Example: l = 6, w = 4 → p = 2(6+4) = 20

Polygon (Sum of Interior Angles)

Let n represent the number of sides of a polygon.

Formula: Sum = (n − 2) × 180

Example: Hexagon (6 sides)

     _______
    /       \
   /         \
  |           |
   \         /
    \_______/

n = 6
Sum = (6 − 2) × 180
     = 4 × 180
     = 720°

Square (Area)

Let s represent the side length. Area = s²

Example: s = 5

+-----+
|     |
|     |  <-- each side = 5 units
|     |
+-----+

Area = 5 × 5 = 25

Triangle (Area)

Let b = base, h = height. Area = 1/2 × b × h

Example: b = 8, h = 5

      /\
     /  \
    /    \  <-- height = 5
   /______\
      b = 8

Area = 1/2 × 8 × 5
     = 20

Circle (Area)

Let r = radius. Area = π × r²

Example: r = 7

      ****
   *        *
  *          *
  *    r=7   *
   *        *
      ****

Area = 3.14 × 7²
     = 3.14 × 49
     = 153.86

Unknown Number (Equation)

Let x represent unknown. Solve 3x + 4 = 19

3x + 4 = 19
3x     = 19 − 4
3x     = 15
x      = 15 ÷ 3
x      = 5

Rectangle Perimeter

Let p = perimeter. Formula: p = 2(l + w)

Example: l = 6, w = 4

+--------+
|        |  <-- height = 4
|        |
+--------+  <-- length = 6

p = 2 × (6 + 4)
  = 2 × 10
  = 20

1. Shopping: Price after discount = Original Price − Discount. Example: Original price ₦500, Discount ₦80 → Price = 420₦


2. Banking: Balance = Deposit − Withdrawal. Example: Deposit ₦2000, Withdrawal ₦750 → Balance = 1250₦


3. School: Average Score = Total Marks ÷ Number of Subjects. Example: Total marks = 360, Subjects = 5 → Average = 72


4. Geometry: Using letters to calculate areas, perimeters, or angles. Example: Square with side s = 9 → Area = s² = 81


5. Daily Life: Let t represent time in hours and d distance in km. Speed = Distance ÷ Time. Example: d = 120 km, t = 2 h → Speed = 60 km/h