Arithmetic Expressions

Chapter Overview

An arithmetic expression combines numbers, operation signs and brackets to represent a calculation. Clear conventions allow everyone to read and evaluate the same expression in the same way.

This chapter belongs to Ganita Prakash, Grade 7. Focus on explaining each step, checking whether an answer is reasonable, and comparing more than one solution method.

Learning Objectives

After studying this chapter, you should be able to:

• explain and apply terms and operations;
• explain and apply order of operations;
• explain and apply equivalent expressions;
• explain and apply forming expressions;
• communicate the reasoning behind a solution clearly;
• check answers using estimation, substitution, or a second method.

Key Concepts

| Concept | Meaning | |---|---| | Terms and operations | Addition, subtraction, multiplication and division connect numbers. An expression has a value but, unlike an equation, it does not state that two quantities are equal. | | Order of operations | Brackets are handled first, followed by division and multiplication from left to right, and then addition and subtraction from left to right. | | Equivalent expressions | Different-looking expressions may have the same value. Testing examples can suggest equivalence, but a logical argument explains why it always holds. | | Forming expressions | Words such as total, difference, groups of and shared equally help translate real situations into mathematical expressions. |

Detailed Explanation

Terms and operations

Addition, subtraction, multiplication and division connect numbers. An expression has a value but, unlike an equation, it does not state that two quantities are equal.

Order of operations

Brackets are handled first, followed by division and multiplication from left to right, and then addition and subtraction from left to right.

Equivalent expressions

Different-looking expressions may have the same value. Testing examples can suggest equivalence, but a logical argument explains why it always holds.

Forming expressions

Words such as total, difference, groups of and shared equally help translate real situations into mathematical expressions.

Important Rules and Formulae

• Evaluate operations at the same priority from left to right.
• Never assume multiplication always comes before division; they have equal priority.
• Use brackets when the intended order would otherwise be unclear.

Worked Examples

Example 1

Problem: Evaluate 36 ÷ 6 × 3 + 5.

Solution: Division and multiplication proceed left to right: 36 ÷ 6 = 6, then 6 × 3 = 18, and 18 + 5 = 23.

Example 2

Problem: A shop packs 8 boxes with 24 pencils each and gives away 35 pencils. Write and evaluate the expression.

Solution: 8 × 24 − 35 = 192 − 35 = 157 pencils remain.

Common Mistakes

• Working strictly from left to right without respecting operation priority.
• Doing multiplication before a bracket.
• Confusing an expression such as 3 + 5 with an equation such as 3 + 5 = 8.

Quick Revision

• Terms and operations: Addition, subtraction, multiplication and division connect numbers.
• Order of operations: Brackets are handled first, followed by division and multiplication from left to right, and then addition and subtraction from left to right.
• Equivalent expressions: Different-looking expressions may have the same value.
• Forming expressions: Words such as total, difference, groups of and shared equally help translate real situations into mathematical expressions.

Practice Questions

1. Evaluate 18 + 4 × 6.
2. Evaluate (18 + 4) × 6.
3. Insert brackets so 12 − 4 × 2 has value 16.
4. Write an expression for five packets of 12 biscuits plus 7 loose biscuits.

Answers and Explanations

3. (12 − 4) × 2 = 16.
4. 5 × 12 + 7.

Self-Check

Explain one rule from this chapter in your own words, create a fresh example, solve it, and verify the answer. If the explanation and verification agree, the concept is understood rather than merely memorised.