SAT Ratios, Rates & Unit Conversions: Complete Guide

Ratios and rates appear throughout SAT Problem-Solving and Data Analysis.

The biggest skill is keeping track of what each number means.

Ratio

If a class has:

• 12 juniors;
• 18 seniors;

junior : senior:

[ 12:18=2:3 ]

Part-to-whole

Total students:

[ 12+18=30 ]

Fraction who are juniors:

[ 12/30=2/5 ]

Do not confuse part-to-part with part-to-whole.

Rate

A rate compares quantities with different units.

Example:

180 miles in 3 hours:

[ 180/3=60 ]

miles per hour. Rate problems like this are really linear equations in disguise — see the linear equations guide for the underlying setup.

Proportion

If 5 notebooks cost $12.50:

[ \frac{12.50}{5}=2.50 ]

per notebook.

Eight notebooks:

[ 8(2.50)=20 ]

If you'd rather solve proportions graphically, the Desmos on the Digital SAT guide shows how to set that up.

Unit conversion

Suppose:

[ 1\text{ hour}=60\text{ minutes} ]

Convert 2.5 hours:

[ 2.5\times60=150 ]

minutes.

Dimensional analysis

Convert 72 kilometers per hour to kilometers per minute:

[ 72\frac{\text{km}}{\text{hr}}\times\frac{1\text{ hr}}{60\text{ min}} =1.2\frac{\text{km}}{\text{min}} ]

Units cancel.

That is the safest way to avoid inversion mistakes.

Density

[ \text{density}=\frac{\text{mass}}{\text{volume}} ]

If density = 4 g/cm³ and volume = 15 cm³:

[ \text{mass}=4(15)=60\text{ g} ]

See more SAT Math guides for related skills.

Scale

A map uses:

1 cm = 8 km

Distance on map: 5.5 cm

Actual distance:

[ 5.5(8)=44\text{ km} ]

Original practice

1

Ratio of 15 red to 25 blue?

2

A car travels 210 miles in 3.5 hours. Average speed?

3

Convert 4.2 hours to minutes.

4

A recipe uses 3 cups of flour for 8 servings. How many cups for 20 servings?

5

A model scale is 1 cm = 2.5 m. What actual length is represented by 7 cm?

Answers

1. 3:5
2. 60 mph
3. 252 minutes
4. 7.5 cups
5. 17.5 m

Common traps

• reversing a ratio;
• mixing units;
• using part-to-part when part-to-whole is needed;
• multiplying when you should divide;
• forgetting to label units.

Once ratios feel automatic, the quadratic equations guide tackles the next major Algebra skill.

Bottom line

When a ratio/rate question feels confusing, write the units next to every number.

Units often tell you the entire setup.

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