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Digital SAT · Solve it in Desmos

How to Solve Rates and Unit Conversion on Desmos (Digital SAT)

Once the fraction and the direction are set, the calculator is there to keep a grid-in clean. Everything that decides the answer, the setup and the units, happens before you type.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for rates and unit conversion

The Desmos steps

  1. 1

    Punch in the arithmetic

    Type it as written, like 180/3 for a speed, and read the number.

  2. 2

    String the conversions together

    Multiply by each conversion factor on one line so the units cancel down the chain.

  3. 3

    Label the result

    Desmos gives the number; you supply and check the units before answering.

Open a real question in the same Desmos calculator you get on Perfect1600, with the setup already typed in:

Worked in Desmos

Easy example
A car travels 180180 miles in 33 hours at a constant speed. What is its speed, in miles per hour?
6060
B
9090
C
177177
D
540540

A: Correct. Speed is distance over time: 180÷3=60180\div3=60 miles per hour.

B: Incorrect. 9090 divides by 2 instead of the 3 hours given.

C: Incorrect. 177177 subtracts 33 from 180180; rate is a quotient, not a difference.

D: Incorrect. 540540 multiplies 180×3180\times3 instead of dividing.

Explanation

Speed = distance / time = 180 / 3 = 60 mph.

Medium example
A train travels 9090 kilometers in 1.51.5 hours at a constant speed. What is its speed, in kilometers per hour?
A
4545
6060
C
135135
D
150150

A: Incorrect. 4545 divides by 22; the time is 1.51.5 hours.

B: Correct. 90÷1.5=6090\div1.5=60 kilometers per hour.

C: Incorrect. 135135 multiplies 90×1.590\times1.5 instead of dividing.

D: Incorrect. 150150 adds distance and a scaled time; rate is a quotient.

Explanation

Speed = 90 / 1.5 = 60 km/h.

Hard example
A recipe uses 33 cups of flour for 1212 cookies. At the same rate, how many cups of flour are needed for 4040 cookies?
A
33
B
55
C
99
1010

A: Incorrect. 33 cups makes only 1212 cookies, not 4040.

B: Incorrect. 55 cups corresponds to 2020 cookies.

C: Incorrect. 99 cups corresponds to 3636 cookies.

D: Correct. The rate is 3÷12=0.253\div12=0.25 cup per cookie, so 0.25×40=100.25\times40=10 cups.

Explanation

Rate 3/12 = 0.25 cup/cookie; 0.25 x 40 = 10 cups.

Try it with the calculator

Question 1easy

A cyclist travels at a constant speed of 8 meters per second. What is the cyclist's speed, in meters per minute?

Question 2easy

A city has a population density of 320 people per square mile and a total population of 96,000 people. What is the area, in square miles, of the city?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

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Desmos questions

Can Desmos solve rates and unit conversion questions on the SAT?

Once the fraction and the direction are set, the calculator is there to keep a grid-in clean. Everything that decides the answer, the setup and the units, happens before you type.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master rates and unit conversion, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

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