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Arithmetic Expressions – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 2. Notes, key terms, important questions with answers and MCQs.

Chapter overview

An arithmetic expression combines numbers with +, −, × and ÷. The order of operations (brackets first, then × and ÷, then + and −) decides its value.

Order of operations

Brackets first, then multiplication and division (left to right), then addition and subtraction (left to right).
8 + 4 × 2 = 16, but (8 + 4) × 2 = 24.
Terms: an expression like 20 − 3 × 4 + 6 has terms 20, −3 × 4 and +6.

Properties

Commutative: a + b = b + a, a × b = b × a (not for − or ÷).
Associative: (a + b) + c = a + (b + c).
Distributive: a × (b + c) = a × b + a × c.

Key terms

Expression: numbers joined by operation signs
Term: a part of an expression separated by + or −
Brackets: symbols showing which part of an expression is calculated first

Formulas

BODMAS order
a(b + c) = ab + ac

Important questions with answers

Evaluate 18 + 6 × 2 − 4.2 marks

Multiply first: 6 × 2 = 12. Then 18 + 12 − 4 = 26.

Write an expression for: "Riya buys 3 pens at ₹12 each and pays with ₹50. How much change?" and evaluate it.3 marks

50 − 3 × 12 = 50 − 36 = ₹14.

Insert brackets to make each statement true: (i) 6 + 4 × 2 = 20, (ii) 24 − 8 ÷ 4 = 4, (iii) 3 × 5 + 2 × 4 = 84. Explain the order of operations.5 marks

(i) (6 + 4) × 2 = 20. (ii) (24 − 8) ÷ 4 = 4. (iii) 3 × (5 + 2) × 4 = 84. Order: brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.

Quick revision

Brackets first.
× and ÷ before + and −.
Subtraction is not commutative.

Exam tips

Remove brackets by distributing carefully, keeping the sign of each term.
Use properties to reorder for easy mental sums: 25 × 7 × 4 = 25 × 4 × 7 = 700.

Practice MCQs

6 + 3 × 2 equals
1. 12
2. 18
3. 11
4. 15
Show answer
Answer: (a) 12. 3 × 2 first.
(6 + 3) × 2 equals
1. 15
2. 12
3. 11
4. 18
Show answer
Answer: (d) 18. Brackets first.
40 − 12 ÷ 4 + 3 equals
1. 40
2. 10
3. 34
4. 37
Show answer
Answer: (a) 40. 12 ÷ 4 = 3; 40 − 3 = 37; 37 + 3 = 40.
Which property is used in 17 × 99 + 17 = 17 × 100?
1. commutative
2. distributive
3. associative
4. closure
Show answer
Answer: (b) distributive. a × b + a × c = a(b + c).
30 − 4 × 5 equals
1. 10
2. 130
3. 26
4. 50
Show answer
Answer: (a) 10. Multiply first: 30 − 20.
Value of 5 × (8 − 3) − 2 × (4 + 1) is
1. 15
2. 25
3. 35
4. 5
Show answer
Answer: (a) 15. 25 − 10.
Which is NOT true for all numbers?
1. a + b = b + a
2. a − b = b − a
3. a × b = b × a
4. a × 1 = a
Show answer
Answer: (b) a − b = b − a. Subtraction is not commutative.
(12 + 8) ÷ 4 − 2 × 3 equals
1. 14
2. 9
3. 2
4. −1
Show answer
Answer: (d) −1. 20 ÷ 4 = 5; 5 − 6 = −1.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.