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Year 8 Maths — The unitary method

Find the value of one thing first, then scale it to any number — and tell direct proportion from inverse.

Name: ________________________

  1. 1.A store of food lasts 20 cows for 6 days. How long would the same store last 15 cows, in days?

  2. 2.More workers finish the same job in less time. That relationship is called...

    • a) a ratio in its simplest form
    • b) inverse proportion
    • c) direct proportion
    • d) no proportion at all

  3. 3.If 5 notebooks cost £150, what does 1 notebook cost? Give just the number.

  4. 4.One pen costs £12. Match each number of pens to what they cost. Give the cost as a plain number.

    • 3 pens
    • 5 pens
    • 7 pens
    • 10 pens
    • 36
    • 60
    • 84
    • 120

  5. 5.A car travels 240 km in 4 hours. How far does it travel in 1 hour, in kilometres?

  6. 6.Sort each pair of quantities by the way they vary together.

    Groups: Direct proportion · Inverse proportion

    • Weight of rice bought and its cost
    • Speed of a car and the time for a fixed journey
    • Number of taps filling a tank and the time taken
    • Distance travelled and time taken at a steady speed
    • Number of workers and the days to finish a job
    • Number of books bought and the total cost

  7. 7.Which of these pairs are in direct proportion?

    • a) The speed of a car and the time it takes on a fixed journey
    • b) The number of taps filling a tank and the time it takes
    • c) The number of workers and the days needed to finish a job
    • d) The number of pens bought and the total cost

  8. 8.7 workers build a wall in 12 days. Working at the same rate, how long would 14 workers take, in days?

Answer key — Year 8 Maths — The unitary method

  1. 1. 8
  2. 2. b) inverse proportion
  3. 3. 30
  4. 4. 3 pens → 36; 5 pens → 60; 7 pens → 84; 10 pens → 120
  5. 5. 60
  6. 6. Number of books bought and the total cost → Direct proportion; Number of taps filling a tank and the time taken → Inverse proportion; Distance travelled and time taken at a steady speed → Direct proportion; Speed of a car and the time for a fixed journey → Inverse proportion; Number of workers and the days to finish a job → Inverse proportion; Weight of rice bought and its cost → Direct proportion
  7. 7. d) The number of pens bought and the total cost
  8. 8. 6