Comparing rational numbers

2026-11-08Numbers & Estimation Ms Lam

Compare fractions and decimals using common denominators or decimal form.

Key formulas

\text{Common denominator}

\text{Decimal comparison}

What this lesson covers

This lesson builds Secondary 2–3 skill in comparing rationals. Read the key formulas, study the worked example, then attempt the written practice and the four-question MCQ review.

Method

Write every step. Name the rule you use (comparing rationals) before substituting numbers. Keep units and signs visible until the final sentence.

Common mistakes

Students often rush the sign, use the wrong percentage base, or cancel terms instead of factors. Pause after each line and ask whether the step is reversible.

Exam habit

Underline the question verb (simplify, solve, factorise, find). Box the final answer and, where sensible, substitute back for a quick check.

Worked example

Worked example — comparing rationals

Problem. Apply the method for comparing rationals with the numbers 4 and 5.

Solution. Identify the rule for comparing rationals. Substitute 4 and 5 carefully with signs in brackets if needed. Complete each operation on a new line. State the final answer clearly and check by reversing one step.

Review quiz

1 / 4

Warm-up on comparing rationals: what is 9+3?

Practice questions

Practice 1 on comparing rationals: compute with the value 16.
Practice 2 on comparing rationals: change the numbers and repeat the same method.
Practice 3 on comparing rationals: write one sentence explaining the key rule.
Practice 4 on comparing rationals: invent a similar exam-style question and solve it.

Study notes

What is the main idea of comparing rationals?

Apply the stated formula or rule with clear steps, then check by reversing or substituting.

How should I revise this topic?

Cover the worked example, redo the practice without notes, then complete the MCQ set and log any wrong options.