SAT Math: Ratios, rates and units

Ratios, rates, proportional relationships and units.

Problem-Solving and Data Analysis · Ratios, rates, proportional relationships, and units
Both modules
12 practice questions · 3 with free solutions
Calculator allowed (Desmos)

Practise ratios, rates and units →Adaptive SAT module

What the test covers

Unit conversion chains
Direct proportion and scaling

Key ideas

Unit rate = amount $\div$ time (or per item). Scale it to the new time.
Convert units by multiplying by a fraction equal to 1, e.g. $\frac{1 mile}{1.6 km}$ .
Proportional: $y = k x$ ; doubling $x$ doubles $y$ .

Common mistakes

Divide or multiply by the conversion factor? Check whether the answer should get bigger or smaller.
Keep track of per-minute versus per-hour.

Do it in Desmos

The calculator is fine for the arithmetic; set the ratio up on paper first.

Worked example

A printer prints 45 pages in 1.5 minutes. At this rate, how many pages does it print in 8 minutes?

$240$
$180$
$360$
$270$

Answer: A: $240$

Rate $= 45 / 1.5 = 30$ pages per minute; $30 \times 8 = 240$ .

Practice questions

Try each question before opening the solution. Desmos or your own calculator is allowed on every SAT Math question. Solutions to the first 2 are open to everyone; the rest need only a free account. Every answer here was checked independently before it was published.

Question 1

A machine fills 60 bottles in 4 minutes. At this rate, how many bottles does it fill in 6 minutes?

$150$
$90$
$180$
$360$

Show the answer and solution

Answer: B: $90$

Rate $= 60 \div 4 = 15$ bottles per minute; $\times 6 = 90$ .

Question 2

Use 1 mile = 1.6 kilometers. A car travels at 88 kilometers per hour. What is its speed in miles per hour?

Student-produced response: type your answer.

Show the answer and solution

Answer: 55

$88 \div 1.6 = 55$ miles per hour.

Question 3

Use 1 mile = 1.6 kilometers. A train travels at 72 kilometers per hour. What is its speed in miles per hour?

Student-produced response: type your answer.