Algebra is a branch of mathematics where we use letters and symbols to represent numbers. These letters, usually called variables, help us form general rules and solve problems without knowing all the values at once.
We use letters to represent unknown quantities, write rules or generalizations, and simplify long expressions. For example: Area = l × b
Variables: Symbols that represent unknown or changeable values (e.g., x, y, n).
Constants: Fixed numbers that do not change (e.g., 2, 5, 100).
Combinations of constants, variables, and operations. Examples: x + 5, 3y - 7.
| Verbal Statement | Algebraic Expression |
|---|---|
| Five more than a number x | x + 5 |
| Three times a number y | 3y |
| Ten less than a number a | a - 10 |
| n multiplied by 2 and then added 3 | 2n + 3 |
If x = 4, then 3x + 2 = 3(4) + 2 = 14
An equation states that two expressions are equal, e.g., x + 3 = 7. Solve by isolating the variable.
2n2n + 1n + (n + 1) = 2n + 14sl × bWrite formulas for shapes using variables:
2(l + b)s²e.g., Squares in a row:
Number of matchsticks = 3n + 1
x - 43pSolve 5x = 20 ⇒ x = 4
x + 63n - 22p - 7x + y = 53x − y = 7x² + y² = 13x − 4 = 6 ⇒ x = 102x = 10 ⇒ x = 5x/3 = 5 ⇒ x = 15The word "Algebra" comes from the Arabic word "Al-Jabr", introduced by Al-Khwarizmi in the 9th century.