M4.2.5 For the adult
Harder ratio problems
Mei and Ana share beads in the ratio 2 : 3. Ana and Tariq share beads in the ratio 4 : 5. What is the ratio of all three?
What this chapter teaches
Two ratios that share one quantity join into one ratio once that quantity is the same size in both. The lowest common multiple gives the matching size. When something is added, find the part that stayed the same, and use it to find the size of one part.
Three questions to ask
There is no one right wording. Listen for the idea.
- What must be true of the shared number before two ratios can be joined?
- How do you find a share when you know the total and the ratio a : b : c?
- In the goats and sheep problem, why do the goats stay 3 parts?
After the chapter, the learner can
- Combine two ratios into one, like a : b : c
- Solve a ratio problem that changes when some are added
What they copy into their notebook
To join a : b and b : c, make b the same in both with the lowest common multiple. When some are added, find what stayed the same, then the size of one part.