Arithmetic Expressions

Overview

An arithmetic expression combines numbers with operations like +, −, × and ÷. This chapter teaches how to read, write and evaluate such expressions correctly using order of operations and brackets.

Key concepts

• Terms are parts of an expression separated by + or − signs.
• Order of operations: brackets first, then × and ÷, then + and −.
• Brackets ( ) change the order in which we calculate.
• Expressions can represent real situations like total cost.

Important formulae

• a × (b + c) = a × b + a × c (distributive property)
• (a + b) + c = a + (b + c) (associative property)
• a + b = b + a (commutative property)

Solved example

1. Evaluate 5 + 3 × (8 − 2).
2. First the bracket: 8 − 2 = 6.
3. Then multiply: 3 × 6 = 18.
4. Then add: 5 + 18 = 23.

Important questions

1. Evaluate 24 ÷ (4 + 2) × 3.
2. Insert brackets in 6 + 4 × 2 to get 20.
3. Show that 7 × (10 + 5) equals 7 × 10 + 7 × 5.
4. Write an expression for the cost of 3 pens at ₹12 and 2 books at ₹40.

Quick revision

Always solve brackets first, then multiply/divide, then add/subtract. The distributive property lets us expand a × (b + c) easily.