Class 7 Maths Chapter 2 Arithmetic Expressions | NCERT Ganita Prakash Complete Explanation with Solutions

March 09, 2026

Class 7 Maths Chapter 2 Arithmetic Expressions | NCERT Ganita Prakash Complete Explanation with Solutions

Introduction

In everyday life we often perform calculations such as:

Total cost of items
Distance travelled
Total marks in exams

Mathematics represents these calculations using arithmetic expressions.

Examples:

13 + 2
20 − 4
12 × 5
18 ÷ 3

These are called Arithmetic Expressions.

An arithmetic expression is a mathematical phrase that contains:

Numbers
Operations (+, −, ×, ÷)

Each expression has a value, which we get after calculating it.

Example:

13 + 2 = 15

Here,

Expression → 13 + 2
Value → 15

1. Simple Arithmetic Expressions

Arithmetic expressions can represent real life situations.

Example

Mallika spends ₹25 every day for lunch.

She buys lunch for 5 days (Monday–Friday).

Expression:

5 × 25

Value:

5 × 25 = 125

Total money spent = ₹125

Multiple Expressions Can Have Same Value

Example for value 12

10 + 2 = 12
15 − 3 = 12
3 × 4 = 12
24 ÷ 2 = 12

So, different expressions can give the same value.

Comparing Arithmetic Expressions

Just like numbers, expressions can also be compared.

Example:

10 + 2 > 7 + 1

Because

10 + 2 = 12
7 + 1 = 8

12 > 8

Figure It Out (Page 25)

Question 1

Fill in the blanks.

a) 13 + 4 = ____ + 6
b) 22 + ____ = 6 × 5
c) 8 × ____ = 64 ÷ 2
d) 34 − ____ = 25

Solution

a) 13 + 4 = 17

17 = 11 + 6

Answer: 11

b) 6 × 5 = 30

22 + ___ = 30

Answer: 8

64 ÷ 2 = 32

8 × ___ = 32

Answer: 4

34 − ___ = 25

34 − 9 = 25

Answer: 9

Question 2

Arrange in ascending order

67 − 19
67 − 20
35 + 25
5 × 11
120 ÷ 3

Solution

Calculate values:

67 − 19 = 48
67 − 20 = 47
35 + 25 = 60
5 × 11 = 55
120 ÷ 3 = 40

Ascending order:

120 ÷ 3 < 67 − 20 < 67 − 19 < 5 × 11 < 35 + 25

2. Reading and Evaluating Complex Expressions

Some expressions can be interpreted in different ways.

Example:

30 + 5 × 4

Two possible answers:

(30 + 5) × 4 = 140 ❌
30 + (5 × 4) = 50 ✔

Correct answer:

30 + (5 × 4)

Step 1

5 × 4 = 20

Step 2

30 + 20 = 50

Brackets in Expressions

Brackets help remove confusion in expressions.

Rule:

Solve brackets first.

Example:

100 − (15 + 56)

Step 1

15 + 56 = 71

Step 2

100 − 71 = 29

Answer: ₹29

Terms in Expressions

Terms are the parts of an expression separated by + sign.

Example:

12 + 7

Terms:

12 and 7

Example

83 − 14

Rewrite as:

83 + (−14)

Terms:

83 and −14

Example

Expression:

2 − 10 + 4 × 6

Rewrite:

2 + (−10) + 4 × 6

Terms:

2, −10, 4 × 6

Properties of Addition

Two important properties apply to arithmetic expressions.

1. Commutative Property

Changing order does not change the sum.

Example:

6 + (−4) = 2

(−4) + 6 = 2

2. Associative Property

Grouping does not change the sum.

Example:

(2 + 3) + 4 = 9

2 + (3 + 4) = 9

Removing Brackets

Case 1: Bracket with negative sign

Example:

200 − (40 + 3)

Remove bracket:

200 − 40 − 3

= 157

Case 2

500 − (250 − 100)

Remove bracket:

500 − 250 + 100

= 350

Case 3

28 + (35 − 10)

Remove bracket:

28 + 35 − 10

= 53

Distributive Property

Multiplication can be distributed over addition.

Example:

2 × (43 + 24)

Step 1

43 + 24 = 67

Step 2

2 × 67 = 134

2 × 43 + 2 × 24

= 86 + 48
= 134

Both give same result.

Example: Scouts and Guides

4 rows of scouts with 5 students each.

3 rows of guides with 5 students each.

Expression:

4 × 5 + 3 × 5

Using distributive property:

(4 + 3) × 5

= 7 × 5
= 35 students

Example: Fast Multiplication

Calculate:

97 × 25

Rewrite:

(100 − 3) × 25

Using distributive property:

= 100 × 25 − 3 × 25

= 2500 − 75

= 2425

Figure It Out (Important Solutions)

28 − 7 + 8

Terms:

28, −7, 8

Solution:

28 − 7 + 8
= 21 + 8
= 29

39 − 2 × 6 + 11

Step 1

2 × 6 = 12

Step 2

39 − 12 + 11

= 27 + 11

= 38

40 − 10 + 10 + 10

= 30 + 10 + 10
= 50

48 − 10 × 2 + 16 ÷ 2

Step 1

10 × 2 = 20
16 ÷ 2 = 8

Step 2

48 − 20 + 8

= 28 + 8

= 36

Important Properties Learned in This Chapter

Students learn three major mathematical properties.

1. Commutative Property

a + b = b + a

2. Associative Property

(a + b) + c = a + (b + c)

3. Distributive Property

a × (b + c) = a × b + a × c

Chapter Summary

In this chapter students learned:

• Meaning of arithmetic expressions
• How to evaluate expressions
• Importance of brackets
• Concept of terms
• Commutative property of addition
• Associative property of addition
• Distributive property of multiplication
• Removing brackets in expressions

These concepts are very important because they form the foundation for Algebra in higher classes.