When more means less

Mathematics · Ratio & Proportion · ages 14-15

Name ______________________ Date ____________

y is inversely proportional to x. When x is 3, y is 10. What is k, where y equals k over x?
Answer: ______________
Which table shows inverse proportion?
- x 1, y 6; x 2, y 12
- x 1, y 6; x 2, y 3
- x 1, y 6; x 2, y 8
- x 1, y 6; x 3, y 8
y is inversely proportional to x. When x = 3, y = 10. What is k, the constant, where y = k/x?
Answer: ______________
4 identical taps fill a tank in 6 hours. How long would 8 taps take?
- 12 hours
- 6 hours
- 3 hours
Which graph shows inverse proportion?
- A straight line through (0, 0)
- A flat horizontal line
- A curve falling steeply then flattening
- A straight line falling to zero
Noah says the graph of inverse proportion is a straight line through the origin. Is Noah right?
Circle one: True False
y = k/x with k = 30. What is y when x = 5?
Answer: ______________
Which graph shows inverse proportion?
- A straight line through (0, 0)
- A curve falling steeply then flattening
- A flat horizontal line
5 workers take 8 days to finish a job. How many days would 4 workers take?
- 5 days
- 8 days
- 10 days
12 machines take 5 days to finish a task. How many days would 8 machines take?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

30 · Multiply the pair: 3 times 10 is 30.
x 1, y 6; x 2, y 3 · Only x 1, y 6 with x 2, y 3 keeps x times y constant at 6.
30 · k = x times y = 3 x 10 = 30.
3 hours · Doubling the taps halves the time: 6 divided by 2 is 3.
A curve falling steeply then flattening · Inverse proportion follows y = k/x, a curve that drops fast then hugs the axes.
False · That line shows direct proportion, while inverse is a curve.
6 · y = 30/5 = 6.
A curve falling steeply then flattening · Inverse proportion follows a curve that drops fast then hugs the axes.
10 days · The job is 40 worker-days, and 40 divided by 4 is 10.
7.5 · The task is 12 x 5 = 60 machine-days, and 60/8 = 7.5 days.