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The real number system sheet
Structured-answer frame

Explain the real number system with examples, and find the HCF and LCM of 84 and 90.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Define real numbers. All numbers on the number line: the rationals and the irrationals together.
  2. 2 · Draw the nested sets. [Diagram: Natural inside Whole inside Integers inside Rationals; Irrationals beside Rationals; all inside Reals]
  3. 3 · Give the subsets with examples.
    • Natural: 1, 2, 3. Integers: −2, 0, 5.
    • Rational: 3/4, 0.25, 0.333…
    • Irrational: √2, π.
  4. 4 · Prime factorise. 84 = 2² × 3 × 7; 90 = 2 × 3² × 5.
  5. 5 · HCF and LCM. HCF = 2 × 3 = 6; LCM = 2² × 3² × 5 × 7 = 1,260. Check: 6 × 1,260 = 84 × 90 = 7,560.
  6. 6 · Business link. Six identical gift boxes, each with 14 tea and 15 biscuit packets.

Scoring tip: Write the prime factors in index form; the HCF and LCM then take one line each.