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Year 11 Maths — Real numbers

Use Euclid's division lemma and prime factorisation to find HCF and LCM, and tell a rational number from an irrational one.

Name: ________________________

Before you start

Move along this line between 1 and 2, a tenth at a time. Every tick you land on is a fraction — a whole number over a whole number.

1.01.11.21.31.41.51.61.71.81.92.0

√2 is about 1.414, so it hides between two of these ticks. Make the steps ten times finer and it hides between two of those instead. It never lands on one, and that is exactly what irrational means.

  1. 1.Euclid's division lemma says that for whole numbers a and b there are whole numbers q and r with a = bq + r, where r is smaller than b. Divide 455 by 42. What is the remainder?

  2. 2.Which of these numbers is irrational?

    • a) √2
    • b) 7/2
    • c) 0.25
    • d) √4

  3. 3.A number is written as 2³ × 3² × 5. What is the number?

  4. 4.Find the HCF of 6, 72 and 120.

  5. 5.Sort each number by whether it is rational or irrational.

    Groups: Rational · Irrational

    • 0.75
    • √3
    • √5
    • √7
    • 22/7
    • √9

  6. 6.Find the LCM of 12 and 18.

  7. 7.Find the HCF of 616 and 32 using Euclid's algorithm.

  8. 8.For any two numbers, HCF × LCM equals the product of the numbers. The HCF of two numbers is 9 and their LCM is 360. One of the numbers is 45. What is the other?

Answer key — Year 11 Maths — Real numbers

  1. 1. 35
  2. 2. a) √2
  3. 3. 360
  4. 4. 6
  5. 5. √9 → Rational; 0.75 → Rational; 22/7 → Rational; √5 → Irrational; √7 → Irrational; √3 → Irrational
  6. 6. 36
  7. 7. 8
  8. 8. 72