Chapter 2 · NCERT Ganita Prakash

Arithmetic
Expressions

Why is 2 + 3 × 4 equal to 14 and not 20? One small pair of brackets can flip an answer. Slide the numbers and watch the order of operations decide the result.

➗ 3 topics⏱ ~22 min📝 12-question quiz

Play with it

The expression lab

Move the sliders for a, b and c. The same three numbers give two different answers — because brackets change which operation happens first.

Explore · Order of operationsdrag a, b, c

a 2 b 3 c 4

2 + 3 × 4

3 × 4 = 12, then 2 + 12

no brackets · × before +

(2 + 3) × 4

(2 + 3) = 5, then 5 × 4

brackets first

Learn

The three big ideas

An arithmetic expression is numbers joined by operations (+ − × ÷). The parts added or subtracted are its terms.

In 2 + 3 × 4, the terms are 2 and 3 × 4 (a product counts as one term).
Reading well is half the battle: spot the terms before you calculate.

The rules of order:

Do × and ÷ before + and −.
Brackets override everything — do what's inside them first.

Worked example. Evaluate 5 + 6 × 2 and (5 + 6) × 2.

5 + 6 × 2 → × first → 5 + 12 = 17.

(5 + 6) × 2 → bracket first → 11 × 2 = 22. Same numbers, different answer.

Common mistake: working strictly left to right. 2 + 3 × 4 is 14, not 20 — the × happens before the +. Use the lab above to feel it.

Often you can compare expressions just by looking at their structure:

56 + 28 vs 56 + 25 → same first term, and 28 > 25, so the first is larger. No full sum needed.
The distributive idea: 3 × 5 + 3 × 2 = 3 × (5 + 2). Spotting this saves work.

Where you'll meet it

Expressions run the bill

Shopping totals

3 pens at ₹10 plus a ₹50 book is 3 × 10 + 50 = ₹80 — the × happens before the +, exactly the order your brain (and the shopkeeper) use.

Spreadsheets & code

Every formula in a spreadsheet or program follows these same rules. Putting brackets in the right place is the difference between a correct sheet and a wrong one.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

Score 0/12

ArithmeticExpressions