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Algebra - Using variables to represent unknowns

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

Definition of a Variable: A letter (like x,y,extornx, y, ext{ or } n) used to represent a number we do not know yet.

Algebraic Expression: A mathematical phrase that contains numbers, operators, and variables (e.g., n+5n + 5), but no equals sign.

Algebraic Equation: A mathematical statement that says two expressions are equal (e.g., x+2=10x + 2 = 10).

Substitution: The process of replacing a variable with a specific number to find the value of an expression.

Translating Words to Math: Turning phrases like '3 more than a number' into n+3n + 3 or 'twice a number' into 2n2n.

📐Formulae

x+ax + a (Addition: aa more than xx)

xax - a (Subtraction: aa less than xx)

axax (Multiplication: aa times xx)

xa\frac{x}{a} (Division: xx divided by aa)

💡Examples

Problem 1:

Write an algebraic expression for the following: 'Sarah has kk stickers and her friend gives her 12 more.'

Solution:

k+12k + 12

Explanation:

We start with the unknown number of stickers (kk) and add 12 to represent the stickers she received.

Problem 2:

Find the value of the expression 4n34n - 3 if n=5n = 5.

Solution:

17

Explanation:

Substitute 5 for nn: 4×534 \times 5 - 3. Following the order of operations, multiply first to get 2020, then subtract 3 to get 1717.

Problem 3:

Solve the simple equation: x+7=20x + 7 = 20.

Solution:

x=13x = 13

Explanation:

To find the unknown xx, we ask: 'What number added to 7 equals 20?' We can subtract 7 from 20 to find the answer (207=1320 - 7 = 13).