🔑 Key Concepts
- A ratio compares two quantities.
- The order of a ratio matters. If the question asks for girls to boys, write girls first and boys second.
- Ratios can be written with words, a colon, or as a fraction.
- A ratio is in simplest form when the two numbers have no common factor other than 1.
- You can simplify a ratio by dividing both numbers by their greatest common factor.
✏️ Worked Examples
🧠 Math Vocabulary
- Ratio: a comparison of two quantities.
- Simplest form: a ratio written so the two numbers have no common factor other than 1.
- Greatest common factor: the largest factor shared by two numbers.
- For every: ratio language that describes how two quantities are related.
- Order: the sequence of the two quantities in a ratio. The first quantity named must come first in the ratio.
💡 Main Idea
When writing a ratio, carefully count each group, place the numbers in the order asked by the question, and simplify if possible. A ratio such as \( 6:4 \) can be simplified to \( 3:2 \), which means there are 3 of the first quantity for every 2 of the second quantity.
📚 What You Should Already Know
Students should know how to count objects in a picture, compare two quantities, find common factors, and divide both parts of a ratio by the same number.
🚀 What Comes Next
After writing ratios in simplest form, students can use ratios to solve word problems, create equivalent ratios, complete ratio tables, and connect ratios to unit rates and proportional relationships.
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