Understanding Proportion Basics

What is Proportion?

A proportion is an equation that states two ratios are equal. It shows the relationship between two or more quantities. Proportions are often used to solve problems involving scaling, resizing, or comparing different quantities.

For example:

• If there are 2 apples for every 3 oranges, the ratio of apples to oranges is 2:3. If you have 4 apples, you would expect to have 6 oranges to maintain the same proportion.

How to Write Proportions

Proportions can be written in two ways:

• Using a colon: 2:3 = 4:6
• As a fraction: $\frac{2}{3} = \frac{4}{6}$

Solving Proportions

To solve proportions, you can use cross-multiplication. This involves multiplying the outer terms and setting them equal to the product of the inner terms.

For example, if $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$.

Examples of Proportions in Real Life

• Maps: Maps use scale to represent real distances. If 1 cm on a map equals 5 km in real life, this is a proportion.
• Recipes: Doubling a recipe involves maintaining the proportion of ingredients.
• Speed: If a car travels 60 km in 1 hour, it travels 120 km in 2 hours, maintaining the speed proportion.