Ratio
Compares two quantities by division.
Formula
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Example
4:2 simplifies to 2:1
How it works
A ratio shows how one quantity compares to another by dividing one by the other, so the relationship can be written as a:b or as a fraction a/b. It works because division tells you how many times one amount fits into another, which is exactly what a comparison is measuring. Ratios can also be simplified by dividing both parts by the same number, just like fractions.
When to use it
Use ratios when comparing amounts such as ingredients in a recipe, parts in a mixture, or numbers in a class or survey. They are also useful for scaling drawings, splitting quantities, and checking whether two amounts are in the same proportion.
Worked example, step by step
Compare 6 apples to 3 oranges. Write the ratio: 6:3 Divide both numbers by 3: 6 ÷ 3 = 2 and 3 ÷ 3 = 1 Simplified ratio: 2:1 Check with division: 6/3 = 2, so there are 2 apples for every 1 orange.
Common mistakes to avoid
- Changing only one part of the ratio instead of dividing both parts by the same number
- Confusing a ratio with subtraction or adding the two quantities together
- Forgetting that the order matters, so a:b is not the same as b:a
Did You Know?
The golden ratio (≈1.618) appears so often in art and nature that Renaissance artists called it the "divine proportion".
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