WebLab STEM

Mathematics · 1. Number, ratio and numerical reasoning

Numerical foundations for problem solving

Build number sense, connect fractions–ratios–percentages and use factorisation instead of guesswork.

40 minutesContent version: 2.1
Start the interactive pathwayOpen the virtual experiment

Driving question

How can we recognise a numerical structure before choosing an operation?

Curriculum coverage

Vietnam Mathematics 6–9; Cambridge IGCSE Number.

Model scope and limitations

A calculator supports arithmetic but does not replace model choice, sign checks or order-of-magnitude estimates.

Learning objectives

  • Use prime factors to find HCF and LCM.
  • Convert accurately among fractions, decimals and percentages.
  • Solve direct/inverse proportion and estimate plausibly.

Prerequisite knowledge

  • Four operations and order of operations.

Core knowledge

Prime factors

Every integer above 1 has a unique prime factorisation apart from order.

Ratio

A ratio compares like quantities; convert to common units before simplifying.

Percentage change

% change = (new − original)/original × 100%; the denominator is the original value.

Worked example

84 = 2²×3×7 and 126 = 2×3²×7. HCF uses lower powers: 42; LCM uses higher powers: 252.

Misconceptions to avoid

  • A 20% rise followed by a 20% fall does not return to the start because the bases differ.
  • 1 is not prime because it has only one positive divisor.

Virtual experiment procedure: Number theory and factors

  1. Predict magnitude and sign before calculating.
  2. Represent the problem with a ratio diagram, table or factorisation.
  3. Calculate exactly, then verify using estimation.

Safety and cautions

  • Avoid intermediate rounding unless required; distinguish exact and approximate values.

Evidence to collect

  • A solution showing model, calculation, units and a plausibility check.
Open the virtual experiment

Diagnostic check

1. What is the HCF of 18 and 24?

  1. 6
  2. 72
  3. 3
Show answer and explanation

Correct answer: 6

18 = 2×3² and 24 = 2³×3, so the common part is 2×3 = 6.

2. 0.375 equals which simplest fraction?

  1. 3/8
  2. 37/5
  3. 3/5
Show answer and explanation

Correct answer: 3/8

0.375 = 375/1000 = 3/8.

Application practice

1. A price of 200 rises by 15% to?

  1. 230
  2. 215
  3. 170
Show answer and explanation

Correct answer: 230

200 × 1.15 = 230.

2. A 2:3 ratio totals 40. The smaller part is?

  1. 16
  2. 20
  3. 24
Show answer and explanation

Correct answer: 16

There are 5 parts of 8; the smaller is 2×8 = 16.

3. What is the LCM of 12 and 18?

  1. 36
  2. 6
  3. 216
Show answer and explanation

Correct answer: 36

12 = 2²×3 and 18 = 2×3², so LCM = 2²×3² = 36.

Academic references

  1. OpenStax Precalculus 2e — functions, geometry and probability

This lesson is maintained against the cited sources below. Simulations are learning models and do not replace supervised physical-laboratory safety procedures.

Content publisher
WebLab STEM
Technical maintainer
Đức Tiến — Control & Automation Engineer