What this chapter is about
An arithmetic expression is a combination of numbers and operations like addition, subtraction, multiplication and division. For example, 5 + 3 × 2 is an arithmetic expression. In this chapter, you will learn how to read, write and evaluate such expressions correctly.
You already know the four basic operations. Now you will understand the rules that tell us which operation to do first when an expression has more than one operation. These rules are called the order of operations. Without these rules, the same expression could give different answers, which would cause confusion.
After studying this chapter, you should be able to write arithmetic expressions for real-life situations, evaluate them correctly using the order of operations, and use brackets to change the order when needed.
Key ideas
- An arithmetic expression contains numbers and operation symbols (+, −, ×, ÷) but no equals sign. Once you put an equals sign, it becomes an equation.
- When an expression has more than one operation, we follow a fixed order: first brackets, then multiplication and division (left to right), then addition and subtraction (left to right).
- Brackets tell us to do what is inside them first, before anything else.
- Multiplication and division have the same priority. We do them in the order they appear, moving from left to right.
- Addition and subtraction also share the same priority. We do them left to right after finishing multiplication and division.
- Writing a real-life problem as an arithmetic expression helps us solve it step by step without confusion.
- Two expressions that look different can still have the same value. For example, 2 × 6 and 4 + 8 both equal 12.
Formulas and facts to remember
Order of operations (BODMAS rule): B – Brackets first O – Orders (powers, but not in Class 7 scope here) D – Division (left to right) M – Multiplication (left to right) A – Addition (left to right) S – Subtraction (left to right)
Key fact: Multiplication and division are done before addition and subtraction.
Brackets change the order: The part inside brackets is always solved first.
No brackets and same priority: Work left to right.
Worked examples
Example 1: Evaluate 8 + 4 × 3
Step 1: Look for brackets. There are none. Step 2: Do multiplication first. 4 × 3 = 12. Step 3: Now do addition. 8 + 12 = 20.
Answer: 20
---
Example 2: Evaluate (7 + 5) × 2 − 6 ÷ 3
Step 1: Solve the bracket first. 7 + 5 = 12. The expression becomes 12 × 2 − 6 ÷ 3.
Step 2: Do multiplication and division left to right. 12 × 2 = 24. 6 ÷ 3 = 2. The expression becomes 24 − 2.
Step 3: Do subtraction. 24 − 2 = 22.
Answer: 22
---
Example 3: A shopkeeper sells 5 notebooks at ₹40 each and 3 pens at ₹15 each. Write an expression for the total cost and find its value.
Expression for total cost: 5 × 40 + 3 × 15
Step 1: Multiply first. 5 × 40 = 200. 3 × 15 = 45.
Step 2: Add the results. 200 + 45 = 245.
Answer: ₹245
Common mistakes
Doing addition before multiplication when there are no brackets → Remember: multiplication comes before addition unless brackets say otherwise.
Reading 12 ÷ 3 × 2 as 12 ÷ 6 (grouping 3 × 2 first) → Do division and multiplication left to right; here, 12 ÷ 3 = 4 first, then 4 × 2 = 8.
Ignoring brackets and solving left to right blindly → Always solve what is inside brackets before doing anything outside.
Writing 5 + 3 = 8 × 2 = 16 as a chain → This misuses the equals sign; instead write each step on a new line or rewrite the full expression after each step.
Forgetting that subtraction is not the same as adding a negative when grouping → Keep the sign attached to the number that follows it.
Quick revision
- An arithmetic expression has numbers and operations but no equals sign.
- BODMAS: Brackets, then Division/Multiplication (left to right), then Addition/Subtraction (left to right).
- Brackets let you control which part to solve first.
- Multiplication and division have higher priority than addition and subtraction.
- Always work left to right for operations at the same level.