Ratios

Inverse Proportion Calculator

Calculate unknown values using inverse proportion. As one quantity increases, the other decreases — ideal for speed/time, workers/days problems.

If x₁ corresponds to y₁, find y₂ when x = x₂ (inversely proportional).

x₁

y₁

x₂

y₂ (answer)

How it works

Identify the relationship (y = k/x)
$y = \frac{k}{x}$
In inverse proportion, as x increases, y decreases — their product is always constant.
Find the constant k
$k = x_1 \times y_1 = 4 \times 6 = 24$
Multiply the known x and y values: k = 4 × 6 = 24.
Result:k = 24
Calculate the unknown value
$y_2 = \frac{k}{x_2} = \frac{24}{3} = 8$
Divide k by x₂: 24 ÷ 3 = 8.
Result:8

y = \frac{k}{x} \qquad k = x_1 \times y_1 \qquad y_2 = \frac{k}{x_2}

k

Constant of proportionality (x × y)

x₁, y₁

Known pair of values

x₂

New x value (find the corresponding y)

Example substitution

k = 4 \times 6 = 24 \quad \Rightarrow \quad y_2 = \frac{24}{3} = 8

4 workers take 6 days: k = 24. For 3 workers: 24 ÷ 3 = 8 days.

6 workers build a wall in 8 days. How long would 4 workers take?

Answer: 4 workers take 12 days

Travelling at 60 mph, a journey takes 2 hours. How long at 80 mph?

Answer: 1.5 hours (1 hour 30 minutes)

What is inverse proportion?+

When one quantity increases and the other decreases by the same factor. Written as y ∝ 1/x, or y = k/x.

How do you solve an inverse proportion problem?+

Find the constant k = x × y, then use k to find the unknown.

If 4 workers take 6 days, how long for 3 workers?+

k = 4 × 6 = 24. For 3 workers: time = 24 / 3 = 8 days.

How do I know if it is direct or inverse proportion?+

Direct: more → more (more items, more cost). Inverse: more → less (more workers, fewer days).

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