What is Proportion?

In science (and everyday life), we often need to describe how two quantities relate to each other. That's where proportion comes in.

Proportion

A proportion is a statement that two ratios or fractions are equal. When two quantities are in proportion, they increase or decrease at the same rate relative to each other.

For example, if you double the amount of ingredients in a recipe, you double the amount of food you make — the ingredients and the food produced are in proportion.

Analogy

Think of proportion like zooming in on a photo. When you zoom in, the image gets bigger, but everything stays in the same ratio — a person's head doesn't suddenly become twice as wide as their body. All the dimensions increase in proportion.

There are two main types of proportion you'll encounter:

Direct proportion — as one quantity increases, the other increases at the same rate
Inverse proportion — as one quantity increases, the other decreases at the same rate

In MYP 2 Sciences, we focus mainly on direct proportion and how to use percentages to describe changes.

Direct Proportion in Science

Two quantities are directly proportional when multiplying one by a certain factor causes the other to be multiplied by the same factor.

Direct Proportion

Two quantities are in direct proportion if, when one quantity is multiplied by a factor $k$ , the other quantity is also multiplied by the same factor $k$ . This can be written as $y = k x$ , where $k$ is the constant of proportionality.

The equation $y = k x$ tells us:

When $x = 0$ , then $y = 0$ (the graph passes through the origin)
The graph of two directly proportional quantities is always a straight line through the origin

Example

Mass and Volume of Water

The mass of pure water is directly proportional to its volume. If 1 cm³ of water has a mass of 1 g, then:

2 cm³ → 2 g
5 cm³ → 5 g
10 cm³ → 10 g

Here, the constant of proportionality $k = 1$ g/cm³ (which is the density of water).

The relationship is: $mass = density \times volume$ , or $m = ρ \times V$ .

Exam Tip

When you plot data from an experiment and get a straight line through the origin, that's strong evidence that your two variables are directly proportional.

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