Study guide: Represent Proportional Quantities
Connect equivalent ratios, unit rates, percent parts, and ordered pairs in supplied models.
Ideas to explain in your own words
- Use equivalent ratios to scale a fictional mixture.
- Divide a paired amount to find a per-minute rate and scale it.
- Find the part of a batch represented by a percent.
- Build equivalent-ratio pairs and keep coordinate order clear.
Watch your reasoning
- 20 ÷ 5 = 4, so both amounts increase fourfold: 8 blue and 12 white. Equal quantities would change the ratio; reversing the amounts would reverse the recipe.
- 28 cups ÷ 4 minutes = 7 cups per minute. Multiplying 7 by the original four minutes returns 28 cups.
- 40% = 40/100 = 2/5. Two fifths of 30 is 30 ÷ 5 × 2 = 12 cups blue. The other 18 cups complete the 30-cup total.
- Scale 2 cups blue to 10 with factor 5. White becomes 3 × 5 = 15, so the ordered pair is (10,15). The batch total 25 is not the white coordinate.
A worked review example
Keep a mix in the same ratio: For 10 cups, the factor is 10 ÷ 5 = 2. Blue = 2 × 2 = 4 cups; white = 3 × 2 = 6 cups. The total is 10 and the ratio 4:6 simplifies to 2:3. Find a Rate for One Unit: 18 ÷ 3 = 6 cups per minute. Five minutes gives 6 × 5 = 30 cups. The rate stays 6 because 30 ÷ 5 = 6. Read a Percent as Parts per Hundred: 25% of 40 is (25/100) × 40 = 10 cups blue. The remaining 40 − 10 = 30 cups are nonblue, and 10 + 30 = 40. Connect a Ratio Table to Ordered Pairs: At x = 4, y = (3/2) × 4 = 6, so (4,6) means 4 cups blue and 6 cups white. Their total is 10 cups, but the y-coordinate is 6, not 10.
Make a practice plan
- Try the supplied lesson problems without looking at the answers.
- Compare your method with the worked examples and explain any correction.
- Use the new review cases, then complete the transfer task on paper or in your own document.