SAT Problem Solving Framework • Topic 3 of 4

Unit Analysis

Tracking units (dimensional analysis) keeps multi-step problems honest and often reveals the path on its own. Treat units like factors that cancel: to convert 3 hours to minutes, multiply by 60 min/hour — the “hour” cancels, leaving minutes. To get a rate in the form the question wants, arrange the conversions so unwanted units cancel and the target unit survives. If your units don’t come out to what’s asked (you wanted miles but got miles per hour), the setup is wrong. Always end by checking that the leftover unit matches the question — it’s a fast, reliable error-catcher.

✅ Solved examples

1. Convert 3 hours to minutes.
3 h × 60 min/h = 180 min (the “h” cancels).
2. A car goes 60 miles in 2 hours. Speed in mph?
60 mi ÷ 2 h = 30 mi/h.
3. Convert 120 minutes to hours.
120 min ÷ 60 min/h = 2 h.
4. You want miles but your units came out as miles/hour. What’s wrong?
The setup — you must multiply by a time (hours) so the “/hour” cancels.

✏️ Practice — try these, take hints as needed

1. Convert 5 hours to minutes.
× 60.
—
—
300 minutes.
2. 150 miles in 3 hours is what speed?
mi ÷ h.
150/3.
—
50 mph.
3. Convert 180 minutes to hours.
÷ 60.
—
—
3 hours.
4. At 40 mph for 2 hours, distance =
mph × h → mi.
40 × 2.
—
80 miles.
5. You wanted dollars but got dollars/item. You forgot to multiply by:
Cancel “/item”.
—
—
The number of items.
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