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Grade 8 Math — Direct and inverse proportion

Tell direct proportion from inverse proportion, and use each to find a missing quantity.

Name: ________________________

  1. 1.6 workers build a wall in 12 days. How many days would 8 workers take, working at the same rate?

  2. 2.A job takes 6 people 12 days. Put these teams in order by how long they would take, shortest first.

    • 6 people
    • 9 people
    • 4 people
    • 12 people
    • 18 people

  3. 3.A car travels 180 miles in 3 hours at a steady speed. How far does it go in 5 hours, in miles? Give just the number.

  4. 4.Sort each pair of quantities by how they vary together.

    Groups: Direct proportion · Inverse proportion

    • The amount of fuel bought and the price paid
    • The side of a square and its perimeter
    • Number of taps and the time to fill a tank
    • Speed and the time taken for a fixed journey
    • Number of identical tickets and the total cost
    • Number of workers and the days to finish a job

  5. 5.Which of these pairs is in direct proportion?

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

  6. 6.6 workers take 12 days to finish a job. Match each number of workers to the days they would take at the same rate.

    • 4 workers
    • 8 workers
    • 9 workers
    • 12 workers
    • 18 workers
    • 6 days
    • 18 days
    • 9 days
    • 8 days
    • 4 days

  7. 7.A journey takes 4 hours at 60 miles per hour. How many hours would it take at 80 miles per hour?

  8. 8.If 5 pens cost $60, what do 8 pens cost? Give just the number.

Answer key — Grade 8 Math — Direct and inverse proportion

  1. 1. 9
  2. 2. 1. 18 people 2. 12 people 3. 9 people 4. 6 people 5. 4 people
  3. 3. 300
  4. 4. The amount of fuel bought and the price paid → Direct proportion; Speed and the time taken for a fixed journey → Inverse proportion; Number of workers and the days to finish a job → Inverse proportion; Number of identical tickets and the total cost → Direct proportion; Number of taps and the time to fill a tank → Inverse proportion; The side of a square and its perimeter → Direct proportion
  5. 5. c) The number of identical books bought and the total cost
  6. 6. 4 workers → 18 days; 8 workers → 9 days; 9 workers → 8 days; 12 workers → 6 days; 18 workers → 4 days
  7. 7. 3
  8. 8. 96