What this lesson covers
- Set up a proportion so units match, then cross-multiply (+ the scale shortcut)
- Unit rate: reduce to "per one" to find the better deal
- Convert units by canceling: 60 mph → 88 ft/s
- Practice: miles per gallon, and km/hr → m/s
- The three traps
Questions worked in the video
- 0:34A recipe uses 3 cups of flour for 12 cookies. How many cups for 36 cookies?
- 1:0812 oz for $3.00 or 20 oz for $4.60 — which is the better deal?
- 1:41Convert 60 miles per hour to feet per second.
- 2:15A car goes 150 miles on 5 gallons. How far on 8 gallons?
- 2:43Convert 90 km/hr to m/s.
Chapters
- 0:00The SAT's #1 setup
- 0:18Ratio · rate · proportion
- 0:34Set up a proportion
- 1:08Unit rate: the better deal
- 1:41Convert by canceling units
- 2:15Practice 1
- 2:43Practice 2
- 3:11Three traps
- 3:40Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:00The SAT's #1 setup
Welcome to SAT Climb. Ratios, rates, and proportions — the SAT's most common setup, hiding in word problems everywhere. Master one move: line up the units, then solve.
0:18Ratio · rate · proportion
Quick definitions. A ratio compares two quantities, 3 to 12. A rate is a ratio with different units, like miles per hour. A proportion sets two ratios equal — the key that cracks it.
0:34Set up a proportion
A recipe: 3 cups of flour makes 12 cookies. You want 36. Line up units: cups over cookies = cups over cookies. 3/12 = x/36. Cross-multiply: 12x = 108, so x = 9 cups. Shortcut: 12→36 is ×3, so 3 cups → 9.
1:08Unit rate: the better deal
Rates shine when you compare. Better deal — 12 oz for $3.00, or 20 oz for $4.60? Unit price: $3.00/12 = 25¢ an ounce; $4.60/20 = 23¢. The bigger bottle wins. Always get to per one.
1:41Convert by canceling units
Now converting units. 60 mph — how many feet per second? Multiply by conversion factors and cancel. 60 mi/hr × 5280 ft/mi × 1 hr/3600 s. Miles cancel, hours cancel — 88 feet per second.
2:15Practice 1
Your turn. A car goes 150 miles on 5 gallons. How far on 8? Find the rate first — miles per gallon — then scale up.
2:43Practice 2
One more. 90 km/hr — convert to m/s. Times 1000 m/km, over 3600 s.
3:11Three traps
Three traps. Flipping the proportion so units don't match across. Forgetting to convert before you compare. And comparing rates in different units — reduce both to per one first.
3:40Recap
Ratios: solved. Line up the units, and it falls right out. Start free at satclimb.com.
Read the written version: the Ratios, rates, proportions, units strategy guide, then try 25 hard Ratios, rates, proportions, units questions with full explanations. Both are free, no account needed.