📖Definition
A ratio is a comparison of two or more quantities showing the relative size of one quantity to another. It can be written as a:b, a/b, or "a to b" and tells you how many times one value contains another.
📐Formula
The ratio a:b means for every "a" units of one quantity, there are "b" units of another. For example, a ratio of 3:2 means for every 3 of one thing, there are 2 of another.
📝Step-by-Step Guide
Writing a Ratio
Identify the quantities being compared and write them in the correct order. Order matters in ratios!
Simplifying Ratios
Divide both parts of the ratio by their greatest common factor (GCF).
Using Equivalent Ratios
Multiply or divide both parts by the same number to find equivalent ratios.
Solving Ratio Problems
Set up a proportion (two equal ratios) and cross-multiply to find the unknown value.
⚠️Common Mistakes to Avoid
- Mixing up the order of quantities in a ratio
- Not simplifying ratios to lowest terms
- Adding instead of multiplying when finding equivalent ratios
- Confusing ratios with fractions (ratios compare parts, fractions show part of whole)
✏️Practice Problems
Simplify the ratio 15:20
Answer: 3:4
If the ratio of boys to girls is 3:5 and there are 24 boys, how many girls are there?
Answer: 40 girls
A recipe uses flour and sugar in the ratio 5:2. If you have 350g of flour, how much sugar do you need?
Answer: 140g
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