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Class 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.Tap where -7/4 sits.

    Mark the line with an X.

    -3.00-2.00-1.000.001.002.003.00

  2. 2.-3/5 + 3/5 = ?

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

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

  4. 4.4/9 × 7/5 + 4/9 × 3/5 = ? Write your answer as a fraction.

  5. 5.1/2 ÷ -2/3 = ? Write your answer as a fraction.

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

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

  8. 8.Rational numbers are closed under addition, subtraction and multiplication. Which operation is the exception, because one case has no answer at all?

    • a) Division, when you divide by zero
    • b) Addition, when both numbers are negative
    • c) Subtraction, when the answer comes out negative
    • d) Multiplication, when one number is a fraction

Answer key — Class 8 Maths — Properties of rational numbers

  1. 1. -1.75
  2. 2. 0
  3. 3. 1. -5/3 2. -1/2 3. -1/4 4. 0 5. 3/8 6. 7/6
  4. 4. 8/9
  5. 5. -3/4
  6. 6. 2/7 → -2/7; -5/9 → 5/9; 3/4 → -3/4; -11/6 → 11/6; 8/3 → -8/3
  7. 7. 5/12
  8. 8. a) Division, when you divide by zero