Chapter 3 · ICSE Class 6 Math

Algebra Basics

A letter can stand in for a number we don't know yet. Drag the slider and watch an algebraic expression evaluate live.

The Expression Evaluator

2 × 5 + 3 = 13

x = 5

Try it: as x grows, watch how much faster 2x + 3 grows compared to just x.

3.1

What is a variable?

A variable is a letter (like x, y, or n) that stands in for a number we don't know yet, or that can change. Variables let us write general rules instead of just single examples.

Everyday example — If a taxi charges ₹20 plus ₹10 per km, we can write the total cost as 20 + 10n, where n is the number of kilometres — the same rule works no matter how far you travel.

3.2

Writing algebraic expressions

"5 more than a number"

Written as: n + 5

"3 less than a number"

Written as: n − 3

"Twice a number"

Written as: 2n

"A number divided by 4"

Written as: n ÷ 4

1Combining operations

Write "twice a number, decreased by 3" as an expression. Twice a number is 2n, decreased by 3 means subtract 3: 2n − 3

3.3

What is an equation?

An equation is a statement that says two expressions are equal, using an equals sign (=). For example, x + 4 = 10 says "some number, plus 4, equals 10."

Watch out — An expression (like 2n + 3) has no equals sign and can't be "solved" — only an equation (like 2n + 3 = 11) can be solved for the variable.

3.4

Solving simple equations

1Using inverse operations

Solve: x + 7 = 15. To undo "+7", subtract 7 from both sides: x = 15 − 7 = 8

2Solving with multiplication

Solve: 3x = 21. To undo "×3", divide both sides by 3: x = 21 ÷ 3 = 7

3A two-step equation

Solve: 2x + 5 = 17. First subtract 5 from both sides: 2x = 12. Then divide by 2: x = 6

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