Inverse proportion

Question 1out of 10

In the table, x and y are inversely proportional. Find the missing value.

x	6	4
y	24	?

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 2out of 10

Which pair of ordered pairs can belong to the same inverse-proportion relationship?

(6; 18) and (3; 9)

(6; 18) and (12; 36)

(6; 18) and (12; 9)

(6; 18) and (7; 19)

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 3out of 10

The quantities x and y are inversely proportional. When x = 8, y = 10. Find y when x = 16.

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 4out of 10

5 equally productive workers finish a job in 12 days. How many days will 10 such workers need?

Question 5out of 10

A rectangle is 12 cm long and 6 cm wide. What must its width be if the length increases to 24 cm while the area stays constant?

1 cm

15 cm

11 cm

3 cm

13 cm

Question 6out of 10

A car covers a route at 50 km/h in 3 h. How many hours will the same route take at 100 km/h?

1.5 h

4 h

3 h

10 h

1 h

Question 7out of 10

In which situation are the quantities inversely proportional?

Item count and total price

Time worked and pay

Speed and travel time for a fixed distance

Side length and square perimeter

Question 8out of 10

A car covers a route at 100 km/h in 4 h. How many hours will the same route take at 300 km/h?

1.3333333333333 h

5 h

8 h

3 h

1 h

Question 9out of 10

If speed over the same distance becomes 4 times greater, how does travel time change? Choose the statement that uses “times” precisely.

4 hours shorter

4 times shorter

4 times longer

It does not change

Question 10out of 10

If speed over the same distance becomes 2 times greater, how does travel time change? Choose the statement that uses “times” precisely.

2 hours shorter

2 times longer

It does not change

2 times shorter

Time left: 00:00:00

Finish the test