# Hands-On Exercises to Understand Gear Ratios

Practicing with hands-on exercises is one of the most effective ways to grasp the concept of gear ratios. In this tutorial, we'll present several problems and work through the solutions step-by-step.

## Exercise 1: Bicycle Gear Ratios

Consider a bicycle with a front chainring of 48 teeth and a rear sprocket of 12 teeth. What's the gear ratio?

The gear ratio is calculated as the number of teeth on the chainring divided by the number of teeth on the sprocket.

= 48 / 12

= 4:1

So, for every rotation of the pedals, the rear wheel rotates four times.

## Exercise 2: Gear Ratios in a Car Transmission

A car has a five-speed transmission. The gear ratios for first and fifth gears are 3.5:1 and 0.8:1, respectively. What does this mean in terms of the engine's rotations versus the wheel's rotations?

In first gear, for every 3.5 rotations of the engine's crankshaft, the wheels rotate once. Conversely, in fifth gear, for every rotation of the engine's crankshaft, the wheels rotate 1.25 times (since 1 divided by 0.8 equals 1.25).

## Exercise 3: Gear Ratios in Clocks

Given that the minute hand of a clock moves 12 times faster than the hour hand, what is the gear ratio?

= 12 / 1

= 12:1

So, the gear ratio of the minute hand to the hour hand is 12:1.

## Exercise 4: Overall Gear Ratios

Consider a gear train with three gears: Gear A with 12 teeth, Gear B with 18 teeth, and Gear C with 24 teeth. Gear A is the driving gear, and Gear C is the driven gear. What is the overall gear ratio?

The overall gear ratio is the product of the individual gear ratios of A to B and B to C.

= (18 / 12) × (24 / 18)

= 1.5 × 1.33

= 2:1

This means that for every two rotations of Gear A, Gear C makes one rotation.

By working through these exercises, you should now have a better understanding of how gear ratios work in various real-life situations. Continue practicing with different scenarios and gear teeth counts to solidify your understanding.

## Gear Ratios Tutorials

If you found this ratio information useful then you will likely enjoy the other ratio lessons and tutorials in this section: