Arithmetic Expressions
An arithmetic expression is a combination of numbers and operations that stands for a value. This Class 7 Ganita Prakash chapter shows how to read and build expressions, identify their terms, evaluate them using the correct order of operations, and compare expressions for equality.
Learning objectives
- Read and write arithmetic expressions.
- Identify the terms of an expression.
- Evaluate expressions in the correct order.
- Compare expressions for equality.
Key concepts
What is an arithmetic expression?
An arithmetic expression combines numbers using operations such as +, −, × and ÷, for example 3 + 4 × 2. Every expression has a single value once evaluated. Writing situations as expressions — like 'the cost of 3 pens at ₹5 and a ₹2 eraser' as 3 × 5 + 2 — turns words into maths.
Terms of an expression
The parts of an expression that are added or subtracted are called its terms. In 3 × 5 + 2, the terms are 3 × 5 and 2. Seeing the terms helps us evaluate and compare expressions, because the value is the sum of its terms.
Order of operations
When an expression has different operations, we follow an order: first brackets, then multiplication and division (left to right), then addition and subtraction. So 3 + 4 × 2 = 3 + 8 = 11, not 14. Brackets let us change the order on purpose: (3 + 4) × 2 = 14.
Comparing expressions
Two expressions are equal if they have the same value, even if they look different — for example 2 × 6 and 12 + 0 both equal 12. We can compare expressions using =, < or >, which is the first step towards algebra.
Important formulas
Order of operations
Brackets → × and ÷ (left to right) → + and − (left to right)
Key definitions
- Arithmetic expression
- A combination of numbers and operations standing for a value.
- Term
- A part of an expression that is added or subtracted.
- Brackets
- Symbols ( ) that group a part to be evaluated first.
- Evaluate
- To work out the single value of an expression.
Solved examples
Q1. Evaluate 3 + 4 × 2.
Solution: Multiply first: 4 × 2 = 8, then 3 + 8 = 11.
Q2. Evaluate (3 + 4) × 2.
Solution: Brackets first: 3 + 4 = 7, then 7 × 2 = 14.
Q3. Name the terms of 5 × 2 + 7.
Solution: The terms are 5 × 2 and 7.
Common mistakes to avoid
- Working strictly left to right and ignoring the order of operations.
- Forgetting that brackets must be evaluated first.
- Splitting a term like 3 × 5 across the + sign.
- Assuming two expressions are unequal just because they look different.
Arithmetic Expressions — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
In 6 + 3 × 2, which operation is done first?
Practice questions
Short answer
State the order of operations.
Brackets first, then × and ÷ (left to right), then + and − (left to right).
What are the terms of an expression?
The parts that are added or subtracted.
Evaluate 2 + 3 × 4.
3 × 4 = 12, then 2 + 12 = 14.
Long answer
Explain the order of operations with an example, and show how brackets change the result.
When an expression has several operations, we evaluate in a fixed order: anything inside brackets first, then multiplication and division from left to right, and finally addition and subtraction from left to right. For example, 3 + 4 × 2 means we multiply before adding, giving 3 + 8 = 11. Brackets let us override this order: (3 + 4) × 2 forces the addition first, giving 7 × 2 = 14. So the same numbers and operations can give different values depending on where the brackets are.
What does it mean for two expressions to be equal? Give examples.
Two expressions are equal when they have the same value after being evaluated, even if they are written differently. For example, 2 × 6 and 5 + 7 are both equal to 12, so 2 × 6 = 5 + 7. On the other hand, 3 + 4 × 2 = 11 while (3 + 4) × 2 = 14, so these two are not equal. Comparing expressions in this way — checking their values rather than their appearance — is the foundation of forming and solving equations later in algebra.
HOTS (Higher Order Thinking)
Place brackets in 8 − 3 + 1 to make the value 4.
8 − (3 + 1) = 8 − 4 = 4.
Without full calculation, which is larger: 12 × 0 + 9 or 12 + 0 × 9?
12 × 0 + 9 = 9, while 12 + 0 × 9 = 12; so the second is larger.
Quick revision
Revision notes
- Expression = numbers + operations standing for a value.
- Terms are separated by + and −.
- Order: brackets → × ÷ → + − (left to right).
- Equal expressions have the same value.
Key takeaways
- Order of operations decides an expression's value.
- Brackets are evaluated first.
- Different-looking expressions can be equal.
Frequently asked questions
What is done first, multiplication or addition?
Multiplication, unless addition is inside brackets.
What are terms?
The parts of an expression separated by + or − signs.
Can two different expressions be equal?
Yes, if they evaluate to the same value.