Understanding Ratios
Key Question: How do we compare two quantities mathematically?
1. What is a Ratio?
A ratio is a way to compare two quantities by division. It shows how many times one quantity contains another, or what part one quantity is of another.
Definition
The ratio of quantity a to quantity b is written as:
- a : b (with a colon)
- a/b (as a fraction)
- "a to b" (in words)
Example
If there are 3 apples and 5 oranges:
3 : 5
"The ratio of apples to oranges is 3 to 5"
Visual Representation of Ratio 3:5
Interactive visualization — available in the full lesson
2. Three Ways to Write Ratios
| Method | Example | How to Read |
|---|---|---|
| Colon notation (most common) | 3 : 4 | "three to four" |
| Fraction notation | 3/4 or 3/4 | "three to four" or "three fourths" |
| Word notation | 3 to 4 | "three to four" |
Remember: All three notations mean the same thing! The colon (:) is the most commonly used.
3. Order Matters in Ratios!
⚠️ Critical Point
"For every 2 boys there are 3 girls"
- Boys to Girls = 2 : 3
- Girls to Boys = 3 : 2
These are different ratios!
Interactive visualization — available in the full lesson
4. Finding the Ratio of Two Numbers
To find the ratio of two numbers, write them in order separated by a colon, then simplify if possible.
Steps to Find a Ratio:
- Write the first number
- Write a colon (:)
- Write the second number
- Simplify by dividing both by their GCD (Greatest Common Divisor)
5. Simplifying Ratios
Just like fractions, ratios can be simplified by dividing both terms by their Greatest Common Divisor (GCD).
Interactive visualization — available in the full lesson
Simplest Form: A ratio is in simplest form when the two terms have no common factors other than 1.