Ratios compare quantities, while rates compare quantities with different units. SAT problems often hide a simple unit rate inside a table, recipe, scale drawing, density, or travel context.
Essential concepts
\[ rac{a}{b}= rac{c}{d} qquad ext{unit rate}= rac{ ext{output quantity}}{ ext{input quantity}}\]
Label units before cross-multiplying so that the proportion compares corresponding quantities.
SAT strategy and application
Find and apply a unit rate
A car travels 180 miles in 3 hours at a constant rate. How far does it travel in 5 hours?
- Find miles per hour
\(180div3=60\) miles per hour.
- Scale to five hours
\(60 imes5=300\) miles.
Distance: \(300\) miles.
Mistakes and traps
Check your understanding
A recipe uses 6 cups of flour for 4 batches. How many cups are needed per batch?
- 1
- 1.5
- 2
- 2.5
Show answer and explanation
Answer: \(1.5\) cups per batch
\(6div4=1.5\). The requested unit is cups per batch.
Key takeaways
What to remember
- Preserve the order and units of every ratio.
- Reduce rates to a denominator of one when useful.
- Scale both parts of an equivalent ratio by the same factor.
- Use dimensional analysis to organize conversions.
Continue learning
Put these notes into practice
Apply the ideas with SAT-style questions, then reinforce key details with flashcards.