Ratios, rates, proportions and units · SAT · Courselo

Lesson 1 of 6 · Problem-solving and data analysis

Ratios, rates, proportions and units

6 min read · about 1 h 10 min with practice3 quick checks≈2% of the testFoundational

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Ratio, rate and unit questions are the easiest points in Problem-Solving and Data Analysis to secure, and they also come back inside other topics: in geometry (scale factors), in science contexts (density) and in data questions (rates per person). The math is arithmetic. The points are lost in the setup: a flipped ratio, a part mistaken for the whole, a square unit converted like a length, or an answer left in the wrong unit.

By the end you’ll be able to

Solve problems with ratios, rates and proportional relationships
Convert units, including multistep, squared-unit and cubic-unit conversions
Apply unit-rate, speed and density reasoning
Use scale factors from maps and scale drawings

What the exam asks

Typical stem	What you must do
The ratio of A to B is 4 to 5, and there are 36 in all. How many are B?	Turn a part-to-part ratio into a fraction of the whole
At this rate, how many ... in 25 seconds?	Find a unit rate and convert the time units
What is the speed in meters per second?	Convert two units at once
Carpet costs $28 per square yard...	Convert square units with the squared factor
How many minutes to fill the tank?	Convert cubic units, then divide by a rate
What is the population density of Town B?	Use density = amount ÷ area (or volume)
On a map, 1 inch represents 25 miles...	Use scale factors (for area, the factor squared)
Which expression represents the number of hours...?	Unit conversion with variables; plug in numbers to check

Most items are in context and many are SPR. The hard ones chain three conversions or hide a whole-number rounding step.

Core ideas

Ratios: part-to-part and part-to-whole

A ratio $a : b$ splits the whole into equal parts.

Check your understanding

3 questions on ratios, rates, proportions and units. Every option is explained once you answer.

Answers are checked on our side, every option is explained, and your result feeds your mastery for this topic. It’s free.

Flashcards

The first 3 of 9 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.

PromptCard 1 of 3

The ratio of part A to part B is $a : b$ and the total is $T$ . How big is part A?

a + b

Length	Area	Volume
1 yd = 3 ft	1 yd² = 9 ft²	1 yd³ = 27 ft³
1 ft = 12 in	1 ft² = 144 in²	1 ft³ = 1,728 in³
1 m = 100 cm	1 m² = 10,000 cm²	1 m³ = 1,000,000 cm³ = 1,000 L

Ratios, rates, proportions and units

By the end you’ll be able to

What the exam asks

Core ideas

Ratios: part-to-part and part-to-whole

Check your understanding

Flashcards

Proportions

Rates and unit rates

Unit conversion by multiplying by 1

Square and cubic units

Density

Scale drawings and maps

Worked examples

Exam technique

Common mistakes

Quick recap

By the end you’ll be able to

What the exam asks

Core ideas

Ratios: part-to-part and part-to-whole

vii.Check your understanding

viii.Flashcards

Proportions

Rates and unit rates

Unit conversion by multiplying by 1

Square and cubic units

Density

Scale drawings and maps

Worked examples

Exam technique

Common mistakes

Quick recap

Check your understanding

Flashcards