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Year 8 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. 1.2/3 × 9/8 = ? Write your answer as a fraction in its simplest form.

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

  3. 3.4/9 × 7/5 + 4/9 × 3/5 = ? Write your answer as a fraction.

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

  5. 5.Put these rational numbers in order, smallest first.

    • 0
    • -1/4
    • 3/8
    • 7/6
    • -5/3
    • -1/2

  6. 6.Tap where -7/4 sits.

    Mark the line with an X.

    -3.00-2.00-1.000.001.002.003.00

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

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

Answer key — Year 8 Maths — Properties of rational numbers

  1. 1. 3/4
  2. 2. 5/12
  3. 3. 8/9
  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. 1. -5/3 2. -1/2 3. -1/4 4. 0 5. 3/8 6. 7/6
  6. 6. -1.75
  7. 7. -9/7
  8. 8. 2/7 → -2/7; -5/9 → 5/9; 3/4 → -3/4; -11/6 → 11/6; 8/3 → -8/3