Ratios and Proportions

What is a Ratio?

A ratio represents the relationship between two quantities. For Image A (Width 60, Height 40), the ratio is 60 : 40.

This means for every 60 units of width, there are 40 units of height.

Simplest Form

We can simplify ratios by dividing both terms by their Highest Common Factor (HCF).

• Ratio: $60 : 40$
• HCF of 60 and 40: 20
• Divide by 20: $3 : 2$

So, the fundamental relationship is 3 units of width for every 2 units of height.

Proportion

When two ratios reduce to the same simplest form, they are proportional. We write this as: $a : b :: c : d$

Example:

• Image A: $60 : 40 \rightarrow 3 : 2$
• Image D: $90 : 60 \rightarrow 3 : 2$

Since $3:2 = 3:2$, Image A and Image D are proportional ($60:40 :: 90:60$).