A pinion with 14 teeth drives a gear with 42 teeth. What is the simplest form of the teeth ratio?

A pinion with 14 teeth drives a gear with 42 teeth. What is the simplest form of the teeth ratio?

• A. 2:3
• B. 3:4
• C. 1:3
• D. 3:1

Answer: (C)

Think of the ratio as pinion teeth to gear teeth. The numbers are 14 and 42, which share a common divisor of 14. Dividing both by 14 gives 1 and 3, so the simplest form is 1:3. This means for every turn of the pinion, the gear has three teeth more, and the gear rotates more slowly overall. If you expressed the gear-to-pinion relationship, it would be 3:1, but the question is asking for the pinion-to-gear form, which is 1:3.

Think of the ratio as pinion teeth to gear teeth. The numbers are 14 and 42, which share a common divisor of 14. Dividing both by 14 gives 1 and 3, so the simplest form is 1:3. This means for every turn of the pinion, the gear has three teeth more, and the gear rotates more slowly overall. If you expressed the gear-to-pinion relationship, it would be 3:1, but the question is asking for the pinion-to-gear form, which is 1:3.