Algebra Made Easy: The Best Student-Friendly Guide

Algebraic Techniques

• A pronumeral is a letter or symbol used to represent a number in algebra. For example, in x+5 the letter x is a pronumeral.
• When a pronumeral can take different values, it’s called a variable.
• If the value is fixed, it’s called a constant. Example : 5
• An algebraic expression is made up of numbers, pronumerals, and operations like addition, subtraction, multiplication, and division. Examples: 3x, 2a+5, x/2+4

• An expression does not have an equals sign — it’s different from an equation.

Algebra uses a neat way to write operations:

• ab means a × b
• xyz means x × y × z
• a² means a × a
• y³ means y × y × y
• a/b​ means a÷b
• Write 4x, and not 4 × x

Focus on English

Write algebraic expressions from everyday language and vice versa.

Examples:

• “Five more than a number” → x+5
• “A number divided by 3” → x/3​
• “Double a number and subtract 7” → 2x−7

Substitution means replacing the pronumeral with a number:

Example:

If x=3 then: 4x+1 = 4(3)+1 = 12 +1= 13

Algebra can describe patterns in numbers

Example: Pattern: 3, 5, 7, 9, 11; Expression: 2n+1 (where n is the position in the pattern)

Like and Unlike Terms

Like terms have the same variable and power.
You can add or subtract them.

Examples: 3x+4x = 7x; 5a−2a = 3a

If terms are not like terms, you cannot combine them.
For example: 2x+3y; 4a + 2b; stays the same.

Properties of Arithmetic in Algebra

• Commutative Property: Order doesn’t matter for addition or multiplication
  a+b = b+a & ab = ba
• Associative Property: Grouping doesn’t change the result: (a+b)+c = a+(b+c)
• Distributive Property: You multiply the number outside the brackets by each term inside: a(b+c) = ab+ac
• Factorizing: You factor out the common factor and put it back into brackets:

ab+ac = a(b+c)

Solve the following Questions on Basic Algebraic Operations:

1. Write the following using algebraic notation: “Multiply 6 by a number y, then divide the result by 3.”
2. The cost of x movie tickets is given by the expression 15x. If you buy 4 tickets, what is the total cost?
3. Use the algebraic expression 2n+1 to generate the first 4 numbers in the pattern when n=1,2,3,4.
4. Simplify the expression: 3x+5−2x+7
5. Expand and simplify: 3(x+4)
6. Factorize: 12x+12y

🔄 Answers:

• 6y/3 = 2y
• The total cost is 15×4 = 60
• 3, 5, 7, and 9
• 3x+5−2x+7 = x+12
• 3(x+4) = 3x+12
• 12x+12y = 12(x+y)