Ratios & Rates: Comparing Quantities
Week 4 · Ratios & Rates
Learn to write ratios three ways, find equivalent ratios, calculate unit rates, and solve ratio problems.
What is a Ratio?\nA **ratio** compares two quantities. If there are 3 red apples and 5 green apples, the ratio of red to green is **3 to 5**.\n\n## Three Ways to Write a Ratio\n- With a colon: **3:5**\n- With the word to: **3 to 5**\n- As a fraction: **3/5**\n\n**Order matters!** 3:5 is NOT the same as 5:3. Always list quantities in the order the problem asks.\n\n## Equivalent Ratios\nEquivalent ratios represent the same comparison. Multiply or divide BOTH parts by the same number.\n\n**2:3 = 4:6 = 6:9 = 10:15**\n\nThink of them just like equivalent fractions!\n\n## Unit Rate\nA **unit rate** tells you how much per 1 unit of another quantity.\n\nIf a car travels 150 miles in 3 hours:\nUnit rate = 150 / 3 = **50 miles per hour**\n\nDivide so the denominator becomes 1.\n\n## Solving Ratio Problems\nIf the ratio of cats to dogs is 2:3 and there are 12 dogs, how many cats?\n- Find the multiplier: 3 x ? = 12, so ? = 4\n- Cats = 2 x 4 = **8 cats**
Worked Examples
Example 1
📝 A recipe uses 3 cups of oats for every 2 cups of raisins. If you use 8 cups of raisins, how many cups of oats do you need?
✓ Answer: 12 cups of oats
Find the multiplier: 2 x ? = 8, so ? = 4. Oats = 3 x 4 = 12 cups.
Example 2
📝 A car travels 240 miles in 4 hours. What is the unit rate in miles per hour?
✓ Answer: 60 miles per hour
Unit rate = total distance / total time = 240 / 4 = 60 miles per hour.
Common Mistakes to Avoid
- ⚠️Writing the ratio in the wrong order — always list quantities in the order asked
- ⚠️Multiplying only one part when finding equivalent ratios — multiply BOTH parts
- ⚠️Confusing unit rate with the total — divide to get the rate per 1 unit