EASA / CAR Part-66 · Module 1 · 1.1 Arithmetic · Cat A

Ratio & Proportion

Objective: a ratio shares a total out in fixed proportions. Set the ratio and the total, and watch the split, then use the same idea on a gear pair where the ratio decides speed and torque.

The split

Use

First part 3

Second part 5

Total to share 240

First share

Second share

One part is worth

Ratio, simplified

share = (part / total parts) × total · gear: speed ∝ 1/teeth, torque ∝ teeth

Add the parts first. A ratio of 3 : 5 means the total is divided into 3 + 5 = 8 parts, not 3 or 5. Find what one part is worth by dividing the total by 8, then multiply back up. Forgetting to add the parts is the classic error.

Ratios simplify like fractions. 6 : 10 is the same split as 3 : 5, because dividing both sides by the same number leaves the proportion unchanged. Give answers in the simplest whole-number form.

Gears turn a ratio into speed and torque. A gear with more teeth turns more slowly but delivers more torque, in exactly the same proportion, which is why the ratio idea from arithmetic shows up again in Module 6 and in engine systems.

Try this: Split 240 in the ratio 3 : 5. What is one part worth, and do the two shares add back to 240?
Try this: Change the ratio to 6 : 10. Do the shares change? What does that tell you?
Try this: Switch to the gear view. If the driver has 12 teeth and the driven has 36, how many turns of the driver make one turn of the driven?