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Inverse proportion
Dynamic inverse-proportion tables and word problems on speed, work time and fixed area. Includes recognizing relationships from text.
Questions: 10Estimated time: 20 minutes
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Question 1out of 10
A rectangle is 11 cm long and 6 cm wide. What must its width be if the length increases to 22 cm while the area stays constant?
The fixed area equals original length × original width. New width = that area ÷ new length. Increasing the length requires a smaller width.
Question 2out of 10
In the table, x and y are inversely proportional. Find the missing value.
For inversely proportional quantities, the product remains constant: x × y = k.
- Find the table column in which both x and y are known.
- Multiply them to obtain the constant product k.
- Divide the constant product by the x-value in the column where y is missing: y = k ÷ x.
The result is the missing value in the table.
Question 3out of 10
A car covers a route at 40 km/h in 5 h. How many hours will the same route take at 80 km/h?
First find the fixed route length: original speed × original time. New time = that distance ÷ new speed. Kilometres divided by km/h give hours.
Question 4out of 10
A rectangle is 11 cm long and 4 cm wide. What must its width be if the length increases to 22 cm while the area stays constant?
The fixed area equals original length × original width. New width = that area ÷ new length. Increasing the length requires a smaller width.
Question 5out of 10
The quantities x and y are inversely proportional. When x = 4, y = 8. Find y when x = 8.
When x and y are inversely proportional, their product is always the same: x × y = k.
- Multiply the original x- and y-values to find the constant product k.
- To find the new y-value, divide k by the new x-value.
- Choose the result that satisfies y = k ÷ x.
As x increases, y must decrease by the corresponding factor so that their product does not change.
Question 6out of 10
Which pair of ordered pairs can belong to the same inverse-proportion relationship?
Two ordered pairs can belong to the same inverse-proportion relationship only when the product of x and y is equal in both pairs.
- Multiply x and y in the first pair.
- Do the same for the second pair.
- Compare the two products.
Rule: choose the option for which x₁ × y₁ = x₂ × y₂. If the products are different, the pairs do not belong to the same relationship.
Question 7out of 10
If speed over the same distance becomes 3 times greater, how does travel time change? Choose the statement that uses “times” precisely.
Inversely proportional quantities have a constant product. For a fixed distance, speed × time = distance. Multiplying speed by k divides travel time by k, making it k times shorter.
Question 8out of 10
5 equally productive workers finish a job in 12 days. How many days will 15 such workers need?
For a fixed job with equally productive workers, worker count × days stays constant. New days = original workers × original days ÷ new workers.
Question 9out of 10
In which situation are the quantities inversely proportional?
Inversely proportional quantities have a constant product. For a fixed distance, speed × time = distance. Multiplying speed by k divides travel time by k, making it k times shorter.
Question 10out of 10
The quantities x and y are inversely proportional. When x = 9, y = 8. Find y when x = 18.
When x and y are inversely proportional, their product is always the same: x × y = k.
- Multiply the original x- and y-values to find the constant product k.
- To find the new y-value, divide k by the new x-value.
- Choose the result that satisfies y = k ÷ x.
As x increases, y must decrease by the corresponding factor so that their product does not change.
Time left: 00:00:00
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Sample questions
- In the table, x and y are inversely proportional. Find the missing value.___
- In which situation are the quantities inversely proportional?
- A car covers a route at ___ km/h in ___ h. How many hours will the same route take at ___ km/h?
- ___ equally productive workers finish a job in ___ days. How many days will ___ such workers need?
- A rectangle is ___ cm long and ___ cm wide. What must its width be if the length increases to ___ cm while the area stays constant?
Inverse proportion
Two quantities are inversely proportional when multiplying one by a factor divides the other by the same factor. Their product remains constant: x × y = k.
Recognition
A greater speed for a fixed distance means less time, and more workers for a fixed job means a shorter duration. Check products in a table; equal products indicate inverse proportion. Do not confuse it with direct proportion.
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