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Chapter 2

Arithmetic Expressions

Learn the basics of Arithmetic Expressions in an easy and interactive way with examples, activities and practice questions.

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Arithmetic Expressions

Class

7

Subject

Mathematics

Chapter

2

Difficulty

Easy

Contents

Introduction Definition Operations Examples Practice Quiz

Introduction

Arithmetic expressions are combinations of numbers and mathematical operations used to perform calculations. These expressions help us solve everyday mathematical problems such as shopping bills, distances, and scores.

Definition

Arithmetic Expression

An arithmetic expression is made using numbers together with addition (+), subtraction (-), multiplication (×), and division (÷). It does not contain an equals (=) sign.

Basic Operations

Operation Symbol Example
Addition + 8 + 6
Subtraction - 20 - 7
Multiplication × 9 × 4
Division ÷ 36 ÷ 6

Examples

Example 1

12 + 8 = 20

Example 2

24 - 9 = 15

Example 3

7 × 8 = 56

Example 4

48 ÷ 6 = 8

Quick Tip

Always solve expressions carefully and check the operation symbols before calculating.

Practice Questions

  1. 15 + 16 = ?
  2. 35 − 9 = ?
  3. 12 × 5 = ?
  4. 72 ÷ 8 = ?
  5. Write an arithmetic expression for "Seven added to twelve".

Quick Quiz

1. Which is an arithmetic expression?

A. 8 + 5 ✅
B. 8 = 5
C. x + 5
D. 8 > 5
2. 9 × 6 = ?

A. 45
B. 54 ✅
C. 56
D. 64

Chapter Summary

Frequently Asked Questions

What is an arithmetic expression?

It is a mathematical expression made with numbers and arithmetic operations.

Does an arithmetic expression contain "=" ?

No.

Congratulations 🎉

You have completed Part 1 of Chapter 2.

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Terms in Arithmetic Expressions

An arithmetic expression is made up of numbers and mathematical operations. Each number separated by an operation is called a term. Understanding terms helps us read and solve expressions correctly.

Definition

A term is a number or quantity connected with other numbers using addition, subtraction, multiplication, or division.

Examples of Terms

Example 1

15 + 8

Terms : 15 and 8

Example 2

24 − 9

Terms : 24 and 9

Example 3

7 × 6

Terms : 7 and 6

Example 4

42 ÷ 7

Terms : 42 and 7

Identify the Operation

Expression Operation Answer
16 + 9 Addition 25
40 − 13 Subtraction 27
9 × 8 Multiplication 72
56 ÷ 7 Division 8

Important Points

Daily Life Examples

Shopping

A pen costs ₹20. Buying 4 pens is represented by 20 × 4.

Travel

A bus ticket costs ₹35. For 3 passengers: 35 × 3.

School

Rahul scored 25 and 18 marks. Total marks = 25 + 18.

Practice Questions

  1. Identify the terms in 18 + 6.
  2. Identify the operation in 54 ÷ 9.
  3. Find the value of 25 − 14.
  4. Find the value of 11 × 8.
  5. Write an expression for "Nine added to twelve".

Quick Quiz

1. Which expression uses multiplication?

A. 12 + 8
B. 16 − 3
C. 7 × 5 ✅
D. 36 ÷ 6
2. How many terms are there in 18 + 7?

A. 1
B. 2 ✅
C. 3
D. 4
3. Which symbol represents division?

A. +
B. ×
C. ÷ ✅
D. −

Summary

Grouping Numbers in Arithmetic Expressions

Sometimes an arithmetic expression contains many numbers and more than one operation. To make the calculation easier, brackets are used to group numbers together. The grouped part is solved before the remaining operations.

Definition

Brackets are symbols used to group numbers or expressions. They help us know which calculation should be performed first.

Types of Brackets

Bracket Name Example
( ) Round Brackets (8 + 5)
[ ] Square Brackets [20 − 8]
{ } Curly Brackets {6 × 4}

Why Do We Use Brackets?

Easy Calculation

Brackets divide long expressions into smaller parts.

Correct Order

They tell us which operation should be performed first.

Avoid Mistakes

Grouping numbers reduces calculation errors.

Solved Examples

Example 1

(12 + 8) × 2

Step 1 : 12 + 8 = 20

Step 2 : 20 × 2 = 40

Example 2

30 − (10 + 5)

Step 1 : 10 + 5 = 15

Step 2 : 30 − 15 = 15

Example 3

(24 ÷ 6) + 8

Step 1 : 24 ÷ 6 = 4

Step 2 : 4 + 8 = 12

Rules for Solving Expressions

  1. Solve the expression inside brackets first.
  2. Perform multiplication and division.
  3. Perform addition and subtraction.
  4. Move from left to right if two operations have the same priority.

Real-Life Example

A family buys 5 notebooks costing ₹20 each and 3 pens costing ₹10 each.

Total Cost = (20 × 5) + (10 × 3)

= 100 + 30

= ₹130

Practice Questions

  1. (18 + 7) × 2
  2. 40 − (15 + 10)
  3. (36 ÷ 6) + 12
  4. 25 + (8 × 3)
  5. (50 − 20) ÷ 5

Quick Quiz

1. Which bracket is solved first?

A. ( ) ✅
B. [ ]
C. { }
D. None
2. What is the value of (8 + 4) × 2 ?

A. 16
B. 20
C. 24 ✅
D. 28
3. Which operation is performed first in an expression with brackets?

A. Addition
B. Multiplication
C. Bracket calculation ✅
D. Division

Summary

Using Brackets in Arithmetic Expressions

Some arithmetic expressions contain more than one set of brackets. To solve these expressions correctly, we follow a fixed order. Solving brackets in the correct sequence helps us get the right answer.

Remember

When different types of brackets appear together, always solve the innermost bracket first, then move outward step by step.

Order of Solving Brackets

Priority Bracket
1 ( ) Round Brackets
2 [ ] Square Brackets
3 { } Curly Brackets

Worked Examples

Example 1

{18 − (8 + 4)}

(8 + 4) = 12

18 − 12 = 6

Example 2

[24 + (12 ÷ 3)]

12 ÷ 3 = 4

24 + 4 = 28

Example 3

{40 − [15 − (5 + 2)]}

5 + 2 = 7

15 − 7 = 8

40 − 8 = 32

Useful Properties

Addition

The order of numbers can be changed without changing the answer.

Multiplication

Changing the order of factors does not change the product.

Subtraction & Division

Changing the order changes the answer.

Everyday Application

A shopkeeper sells:

6 notebooks × ₹25
4 pens × ₹10

Expression: (6 × 25) + (4 × 10)

= 150 + 40

= ₹190

Practice Questions

  1. {20 − (9 + 4)}
  2. [18 + (24 ÷ 6)]
  3. {50 − [18 − (6 + 3)]}
  4. (15 × 4) + (20 ÷ 5)
  5. {36 ÷ (8 − 2)}

Quick Quiz

1. Which bracket is solved first?

A. ( ) ✅
B. [ ]
C. { }
D. None
2. Value of (16 + 4) ÷ 5 is

A. 2
B. 4 ✅
C. 5
D. 20
3. Which operation does NOT satisfy the order property?

A. Addition
B. Multiplication
C. Subtraction ✅
D. None

Key Takeaways

Chapter Revision

In this lesson, you have learned how to identify arithmetic expressions, use brackets correctly, and evaluate expressions step by step. Now it is time to revise the important concepts before moving to the next chapter.

Quick Revision

Fill in the Blanks

  1. An arithmetic expression does not contain __________.
  2. The symbol × represents __________.
  3. Brackets are solved __________.
  4. 18 + 12 = __________.
  5. 48 ÷ 6 = __________.

True or False

  1. Arithmetic expressions always contain an equals sign.
  2. Multiplication is performed before addition.
  3. Brackets help group numbers.
  4. Division and multiplication have the same priority.
  5. Every arithmetic expression has a numerical value.

Match the Following

Column A Column B
Addition +
Subtraction -
Multiplication ×
Division ÷

Practice Exercise

  1. 25 + 16
  2. 60 − 18
  3. 9 × 12
  4. 84 ÷ 7
  5. (15 + 5) × 4
  6. 48 ÷ (8 − 2)
  7. 20 + 5 × 6
  8. (18 − 6) ÷ 3
  9. {30 − (8 + 7)}
  10. (25 × 2) + (18 ÷ 3)

Higher Order Thinking Skills (HOTS)

Riya buys 4 notebooks costing ₹25 each and 3 pens costing ₹10 each.

Write an arithmetic expression to find the total amount spent.

A shopkeeper sold 8 boxes containing 15 chocolates each. Write the expression and calculate the total number of chocolates.

Chapter Test

1. Which operation should be performed first?

A. Addition
B. Multiplication
C. Bracket ✅
D. Subtraction
2. Value of (12 + 8) × 3 =

A. 40
B. 50
C. 60 ✅
D. 36
3. Which of these is an arithmetic expression?

A. 15 = 10
B. 20 + 8 ✅
C. x + 5
D. 5 > 2

Chapter Summary

Brain Challenge 🧠

Using only the numbers 2, 4, 6, 8 exactly once and the operations +, −, ×, ÷, create three different arithmetic expressions whose value is 20.

Try solving this on your own before checking with your teacher or friends!

🎉 Congratulations!

You have successfully completed Class 7 Mathematics – Chapter 2: Arithmetic Expressions.

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