Understand the concept of a ratio

What you'll learn

1. Distinguish between an *additive* comparison ("4 more apples than oranges") and a *multiplicative* comparison ("3 apples for every 1 orange"), and identify the ratio as the multiplicative comparison.
2. Use **ratio language** -- *"for every ___ there are ___"* and *"the ratio of ___ to ___ is ___ to ___"* -- to describe a ratio relationship between two quantities.
3. Write a ratio in all three standard notations: *a* to *b*, *a:b*, and *a/b*, and translate among them.
4. Recognize that the order of a ratio matters -- *a:b* and *b:a* describe different relationships.
5. Classify a ratio as **part-to-part** (comparing two parts of a group) or **part-to-whole** (comparing a part to the total), and determine the whole when the ratio is part-to-whole.
6. Read a part-to-whole ratio as a fraction of the whole (boys are 2/5 of the class) while recognizing that this fraction-of-the-whole reading does not apply to part-to-part ratios.
7. Write a complete ratio statement for a real-world situation, including units, order, all three notations, ratio language, and part-to-part / part-to-whole classification.