Setting up a conversion fraction — what cancels what
Have
Want
Right fraction
Why
miles
feet
$\times \frac{5280 \text{ ft}}{1 \text{ mi}}$
miles cancels; feet remains
feet
miles
$\times \frac{1 \text{ mi}}{5280 \text{ ft}}$
feet cancels; miles remains
hours
minutes
$\times \frac{60 \text{ min}}{1 \text{ hr}}$
hr cancels; min remains
minutes
hours
$\times \frac{1 \text{ hr}}{60 \text{ min}}$
min cancels; hr remains
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Chaining a multi-step conversion
Is the conversion direct (one step), or do you need an intermediate unit?
Yes ↓
→ One fraction. Set it up so the unit you have cancels with the same unit on the bottom.
No ↓
Do you have a chain of facts (e.g., A→B and B→C)?
Yes ↓
→ Multiply both fractions in series: A → B → C. Each step cancels the previous unit.
No ↓
→ Re-read — find the conversion factor the SAT gave you
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Quick check
Try this SPR. Set up your conversion fractions so the unwanted units cancel. Multiply through; the leftover units should match the answer.
There are 5,280 feet in one mile. How many feet are in 5 miles?
Enter a whole number, fraction (e.g. 3/4), or decimal (e.g. .75).
Worked examples
Example 1
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Example 2
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Common pitfalls
Forgetting to square (or cube) the conversion factor for area / volume
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Multiplying when you should divide (or vice versa)
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Mixing units before converting
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Reading the conversion factor wrong
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Key takeaways
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Tracks your progress across lessons.
Checkpoint
10 questions on Ratios, Rates, Proportional Relationships, and Units, from our question bank. Score 70% or better across 10 answers to reach Silver and pass this step.
Converting units = multiplying by a conversion fraction equal to 1.
1 hour = 60 minutes, so 1 hr60 min=1 and 60 min1 hr=1. Multiplying by either doesn't change the value — but it does change the units.
The dimensional analysis technique — write everything as a chain of fractions, cancel the units you don't want.
Convert 5 miles to feet (5,280 feet per mile):
5 mi⋅1 mi5280 ft=26,400 ft
The miles cancel; feet remain. The numerical answer is 5×5280=26,400.
Multi-step conversions. Chain the fractions.
Convert 90 km/h to m/s:
1 hr90 km⋅1 km1000 m⋅3600 s1 hr=360090⋅1000=25 m/s
The km cancels with km; hr cancels with hr. We're left with m/s.
SAT-typical setups:
Time conversions: 1 hr = 60 min = 3,600 s. 1 day = 24 hr = 1,440 min.
Length: 1 mile = 5,280 ft = 1,609 m. 1 km = 1,000 m. 1 m = 100 cm.
Volume: 1 gallon ≈ 3.785 L. 1 L = 1,000 mL.
Mass / weight: 1 kg = 1,000 g = 2.205 lb (often approximated).
The SAT often gives you the conversion factor in the problem — you don't need to memorize obscure ones. Read the problem carefully.
Square / cubic units. Converting square or cubic units requires squaring or cubing the linear factor.
1 m = 100 cm. So 1 m² = (100)² cm² = 10,000 cm². NOT 100 cm².
1 ft = 12 in. So 1 ft³ = 12³ in³ = 1,728 in³.
Word-problem unit traps:
Speed × time = distance — make sure all in matching units. 60 mph × 30 min doesn't equal 1,800 miles; convert minutes to hours first: 60⋅0.5=30 miles.
Density × volume = mass — units must match.
A bakery uses 24 cups of flour each day. How many gallons of flour does it use in 30 days, given that 16 cups = 1 gallon?
A rectangular field measures 20 m by 30 m. What is its area in square feet, given that 1 m ≈ 3.28 ft?
1 m=100 cm doesn't mean 1 m2=100 cm2. It's (100)2=10,000 cm2. For volume: (100)3. Square the linear factor for square units; cube it for cubic units.
Going from a bigger unit to a smaller unit (miles → feet), multiply. From smaller to bigger (feet → miles), divide. Or just write the fraction and cancel — let the units guide you.
60 mph × 30 min doesn't directly give you a distance — the 60 is per hour, but you have minutes. Convert one to match: 30 min = 0.5 hr, so 60⋅0.5=30 miles.
1 mile = 5,280 feet means there are 5,280 feet IN 1 mile. To convert miles to feet, multiply by 5,280. To convert feet to miles, divide. Don't mix it up.
Multiply by a conversion fraction equal to 1 (e.g., 1 hr60 min). Choose the orientation that cancels the unit you don't want.
Chain fractions for multi-step conversions. Cancel as you go.
Square units need the conversion factor SQUARED. Cubic units cubed.
Always check that your units cancel correctly — the result should leave the desired unit.
Match all units before doing arithmetic in word problems (e.g., convert minutes to hours if speed is in mph).