To determine the gear ratio for a bike with 45 front teeth and 18 rear sprocket teeth, we'll use the following steps:
1. Understand Gear Ratio: The gear ratio is determined by dividing the number of teeth on the front chainring (front sprocket) by the number of teeth on the rear sprocket.
2. Identify the Number of Teeth:
- Front chainring (front sprocket): 45 teeth
- Rear sprocket: 18 teeth
3. Calculate the Gear Ratio:
The formula for the gear ratio is:
[tex]\[
\text{Gear Ratio} = \frac{\text{Number of front teeth}}{\text{Number of rear teeth}}
\][/tex]
Substituting the known values:
[tex]\[
\text{Gear Ratio} = \frac{45}{18}
\][/tex]
4. Simplify the Fraction:
Simplifying the fraction [tex]\( \frac{45}{18} \)[/tex]:
[tex]\[
\frac{45}{18} = 2.5
\][/tex]
Therefore, the gear ratio for the bike, where the front sprocket has 45 teeth and the rear sprocket has 18 teeth, is [tex]\( 2.5 \)[/tex].
Hence, the gear ratio is 2.5.
