Overview
This lecture covers how to write and simplify ratios in different forms using both visual and written examples, and distinguishes between part-to-part and part-to-whole ratios.
Writing Ratios from Pictures
- Ratios compare two amounts and order matters; the first term corresponds to the first group mentioned.
- Example: 4 strawberries and 2 oranges can be written as 4 to 2, 4:2, or 4/2.
- Ratios can be simplified like fractions by dividing both terms by their greatest common factor.
- Simplifying 4:2 gives 2:1, meaning 2 strawberries for every 1 orange.
- Part-to-part ratio compares two distinct parts within the whole group.
- Part-to-whole ratio compares one part to the total group (e.g., oranges to total fruit: 2:6 simplifies to 1:3).
Writing Ratios from Word Problems
- Identify and write the numbers in the order given by the problem statement.
- Sports to racing video games: 7 sports games to 3 racing games, or 7:3 (already simplest).
- Action to racing video games: 8 action games to 3 racing games, or 8:3 (already simplest).
Key Terms & Definitions
- Ratio — A comparison of two or more quantities, showing how many times one value contains or is contained within the other.
- Part-to-part ratio — Compares one part of a group to another distinct part.
- Part-to-whole ratio — Compares one part of a group to the entire group.
- Simplest form — A ratio in which the two numbers have no common factors other than 1.
Action Items / Next Steps
- Practice writing and simplifying ratios from both pictures and written scenarios.
- Identify whether each ratio is part-to-part or part-to-whole.