Inverse Proportion Formula and Examples

Q: What does inversely proportional mean?

Two quantities are inversely proportional when multiplying one by a number divides the other by the same number. If one value doubles, the other halves; if one triples, the other becomes a third. Their product always stays the same, which is the key idea behind inverse proportion.

Q: What is the symbol for inverse proportion?

Inverse proportion uses the proportionality symbol ∝. You write y ∝ 1/x to show that y is inversely proportional to x. This relationship then becomes the working formula y = k ÷ x, where k is the constant that keeps the product x × y fixed.

Q: How do you find the constant of proportionality?

You find the constant of proportionality, k, by multiplying a known pair of x and y values. For example, if x = 6 when y = 8, then k = 6 × 8 = 48. Once you know k, you can write the formula y = k ÷ x for the relationship.

Key concept

Inverse proportion means as one value goes up, the other goes down, so their product xy = k stays constant. Multiply a known pair like 6 × 8 = 48 to find the constant k. Then write y = k ÷ x to work out any missing value.

Inverse Proportion Formula and Examples - introduction visual

Video Lesson

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Flashcards

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Inverse proportion with a definition, notation showing y is proportional to 1 divided by x, and the formula y = k divided by x.

Inverse proportion example y ∝ 1/x: x=6 gives y=8, so k=48 and y=12 when x=4.

Worked example of inverse proportion y ∝ 1/x²: x=3 gives y=8, so k=72 and y=2 when x=6.

Inverse proportion example n ∝ 1/√r: n=12 when r=9, so k=36 and n=9 when r=16.

What Is Inverse Proportion?

Inverse proportion means the product stays constant. For example, if x is doubled, y is halved, so xy stays the same.
In exams, multiply the variables together to get the constant k. For example, if $x = 3$ and $y = 8$ , then $k = 3 \times 8 = 24$ .

Practice Questions

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Q1Easy

$y$ is inversely proportional to $x$ , and when $x = 4$ , $y = 10$ . What is the formula connecting $y$ and $x$ ?

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Interactive Activity

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is inversely proportional to .

When , .

Find when .

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Step 1Find constant :

Substitute:

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What does inversely proportional mean?

Two quantities are inversely proportional when multiplying one by a number divides the other by the same number. If one value doubles, the other halves; if one triples, the other becomes a third. Their product always stays the same, which is the key idea behind inverse proportion.

What is the formula for inverse proportion?

The formula for inverse proportion is y = k ÷ x, where k is a constant. You can also write it as x × y = k, because the product of x and y always stays the same. You find the value of k from one known pair of values.

What is the symbol for inverse proportion?

Inverse proportion uses the proportionality symbol ∝. You write y ∝ 1/x to show that y is inversely proportional to x. This relationship then becomes the working formula y = k ÷ x, where k is the constant that keeps the product x × y fixed.

How do you find the constant of proportionality?

You find the constant of proportionality, k, by multiplying a known pair of x and y values. For example, if x = 6 when y = 8, then k = 6 × 8 = 48. Once you know k, you can write the formula y = k ÷ x for the relationship.

What if y is inversely proportional to x squared?

If y is inversely proportional to x squared, you use the formula y × x² = k. Find the constant k from a known pair, then write y = k ÷ x² and substitute the new value. The same method works for roots, such as the square root of x.

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