← Back to the activity

Year 9 Maths — Properties of rational numbers

Add, subtract, multiply and divide rational numbers, and use the properties that make the work shorter.

Name: ________________________

Before you start

Wander along this line in quarter steps. Nothing here is right or wrong — see how the numbers crowd together.

-2.00-1.000.001.002.00

The line only shows quarters, but between any two of them sits another rational number — an eighth, a sixteenth, and so on for ever. There is no 'next' rational number.

  1. 1.5/7 × 3/4 gives the same answer as 3/4 × 5/7. Which property is that?

    • a) Multiplication of rational numbers is associative
    • b) One is the multiplicative identity
    • c) Multiplication of rational numbers is commutative
    • d) Multiplication is distributive over addition

  2. 2.What is the reciprocal of -7/9? Write your answer as a fraction.

  3. 3.2/3 × 9/8 = ? Write your answer as a fraction in its simplest form.

  4. 4.Sort each statement by whether it is true for every choice of rational numbers a, b and c.

    Groups: Always true · Not always true

    • (a - b) - c = a - (b - c)
    • a - b = b - a
    • a + b = b + a
    • a ÷ b = b ÷ a
    • (a + b) + c = a + (b + c)
    • a × b = b × a

  5. 5.Write the rational number that lies exactly halfway between 1/3 and 1/2.

  6. 6.4/9 × 7/5 + 4/9 × 3/5 = ? Write your answer as a fraction.

  7. 7.Match each rational number to its additive inverse — the number you add to it to get zero.

    • 2/7
    • -5/9
    • 3/4
    • -11/6
    • 8/3
    • -2/7
    • -3/4
    • -8/3
    • 5/9
    • 11/6

  8. 8.-3/5 + 3/5 = ?

Answer key — Year 9 Maths — Properties of rational numbers

  1. 1. c) Multiplication of rational numbers is commutative
  2. 2. -9/7
  3. 3. 3/4
  4. 4. a + b = b + a → Always true; a - b = b - a → Not always true; a × b = b × a → Always true; a ÷ b = b ÷ a → Not always true; (a + b) + c = a + (b + c) → Always true; (a - b) - c = a - (b - c) → Not always true
  5. 5. 5/12
  6. 6. 8/9
  7. 7. 2/7 → -2/7; -5/9 → 5/9; 3/4 → -3/4; -11/6 → 11/6; 8/3 → -8/3
  8. 8. 0