Chapter 2 — Arithmetic Expressions

Ganita Prakash • Grade 7 • Part I • 2026–27

🔢 From a situation to an expression

Suppose a school buys 8 packets at ₹35 each and then pays ₹60 for delivery. Instead of describing every calculation in words, we can represent it as 8 × 35 + 60. Such a combination of numbers and operations is an arithmetic expression.

1. Why order matters

The expression 8 + 3 × 4 has two operations. If we simply work from left to right, we get 44, but the standard order gives 8 + 12 = 20. Mathematics needs a common convention so that an expression has one unambiguous interpretation.

When operations have the same priority, work from left to right.

2. Brackets change meaning

The brackets tell us which part belongs together. This is why expressions must be written carefully.

3. Reading expressions in words

“Five added to twice a number” can be represented as 2 × number + 5. At this stage we focus on numerical expressions, but the same idea leads naturally into algebraic expressions later.

🧠 Worked Examples

1. 36 ÷ 6 + 7 × 2: 36 ÷ 6 = 6 and 7 × 2 = 14; therefore 6 + 14 = 20.
2. 48 − (12 + 8) ÷ 4: bracket = 20; 20 ÷ 4 = 5; 48 − 5 = 43.
3. 60 ÷ 5 × 2: division and multiplication have equal priority, so work left to right: 60 ÷ 5 = 12; 12 × 2 = 24.

🔍 Spot the Mistake

A student solves 50 − 12 ÷ 3 as (50 − 12) ÷ 3 = 12⅔. The mistake is treating subtraction before division. The correct calculation is 50 − 4 = 46.

🎯 Math Talk

1. Can two expressions contain exactly the same numbers and operations but have different answers? Use brackets to demonstrate.
2. Find a situation from shopping where a bracketed expression is useful.
3. Can you insert one pair of brackets in 6 + 4 × 5 to make the answer 50?

🧩 Concept MCQs

1. 18 + 4 × 5 = A. 110 B. 38 C. 70 D. 22
2. (18 + 4) × 5 = A. 38 B. 90 C. 110 D. 22
3. In 72 ÷ 8 × 3, after division we get: A. 3 B. 9 C. 24 D. 27
4. The main purpose of brackets is to — A. show grouping B. make numbers larger C. remove operations D. change place value

Answers: 1-B, 2-C, 3-B, 4-A

📌 Case-based Challenge

A family buys 3 notebooks at ₹45 each, 2 pens at ₹15 each and pays ₹20 for a cover.

1. Write one expression for the total cost.
2. Evaluate it.
3. Write a different grouping that would change the meaning and explain why it is wrong for this situation.

🔥 Challenge Corner

Use the numbers 2, 3, 4 and 5 exactly once with arithmetic operations and brackets to make 20. Find more than one solution if possible.

📝 Worksheet

1. Evaluate five mixed-operation expressions.
2. Write an expression for three real-life situations.
3. Insert brackets to reach given target values.
4. Find and correct two deliberately incorrect solutions.
5. Create one expression whose answer is 100.

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