Word problem: compound units by dimensional analysis

Every ratio is offered both ways up. Only one orientation cancels the unit you are trying to lose, and picking wrong is the whole trap.

01 Worked Example Video

Every step of Word problem: compound units by dimensional analysis explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE

02 Recognize the Question

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Kroner

Petrol costs 2.98 dollars per gallon. 1 krone is worth 0.075 dollars. 1 gal = 3.79 L.

What is the cost in kroner per litre? Round to the nearest hundredth.

A tiny unit

Petrol costs 4.20 dollars per gallon. 1 yen is worth 0.011 dollars. 1 gal = 3.79 L.

Cost in yen per litre, to the nearest hundredth?

Spot the flip

Petrol at 3.10 dollars per gallon, 1 real is worth 0.26 dollars, 1 gal = 3.79 L.

A student answered 3.06 reais per litre. What is the correct answer, to the nearest hundredth?

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 The Rule

to cancel a unit on TOP, put it on the BOTTOM of the next ratio

to cancel a unit on the BOTTOM, put it on TOP same rule, other direction

A conversion factor is just the number 1 written awkwardly. 1 gal = 3.79 L, so both 1 gal / 3.79 L and 3.79 L / 1 gal equal 1, and multiplying by either leaves the value unchanged. Only one of them cancels the unit you want gone, which is how you choose.

Common slips

(1) Flipping a ratio. The answer comes out wrong by a factor of that number squared, so it is usually wildly off rather than slightly. (2) Cancelling the wrong unit first. Order does not matter mathematically, but it does for keeping track. (3) Forgetting to round. This question type asks for the nearest hundredth.

04 Practice — Step by Step

Two ratios, four ways up

A tourist from Mexico is vacationing in the U.S. One day, he notices that gasoline costs 3.45 dollars per gallon. On that same day, 1 peso is worth 0.058 dollars. How much does the gas cost in pesos per liter?

Fill the two blanks using two of the ratios, then give the answer rounded to the nearest hundredth. Use 1 gal = 3.79 L.

Ratios: 0.058 dollars / 1 peso 1 peso / 0.058 dollars 1 gal / 3.79 L 3.79 L / 1 gal

3.45 dollars / 1 gal × [ ? ] × [ ? ] = ? pesos / L

Step 1

Cancel the dollars

Dollars sit on top of 3.45 dollars / 1 gal, and you want pesos there instead. Which ratio does that?

Step 2

Cancel the gallons

Gallons sit on the bottom, and you want litres there. Which ratio does that?

Step 3

Now compute it

3.45 ÷ (0.058 × 3.79). Round to the nearest hundredth.

Step 4

Does it look right?

A peso is worth about six cents, and a litre is about a quarter of a gallon. Is 15.69 pesos per litre believable?

Q14 Q16

Word problem: compound units by dimensional analysis

Both wrong ways are obvious once you look