91Ó°ÊÓ

Ratios are a way of comparing two quantities. In this exercise, we are comparing the number of revolutions to the amount of time in seconds.
To set up a ratio, think of it as creating a fraction where one quantity is the numerator (top part) and the other is the denominator (bottom part).
For example, if we have 800 revolutions and 10 seconds, our ratio would be written as \( \frac{800 \text{ revolutions}}{10 \text{ sec}} \).
This is the first step in solving many problems involving rates and can be applied to other scenarios like miles per hour or cost per item.
Ratios help us understand relationships between different quantities and make comparisons easier.

Simplifying fractions is about making the numbers in the fraction smaller and easier to work with, while keeping the same value.
For our example, we have the ratio \( \frac{800 \text{ revolutions}}{10 \text{ sec}} \).
To simplify this fraction, we look for the greatest common divisor (GCD) of the numerator and the denominator.
In this case, both 800 and 10 can be divided by 10.
When we divide the numerator and the denominator by 10, we get: \( \frac{800 \text{ revolutions}}{10 \text{ sec}} = \frac{80 \text{ revolutions}}{1 \text{ sec}} \).
The fraction \( \frac{80 \text{ revolutions}}{1 \text{ sec}} \) is in its simplest form because 80 and 1 have no common divisor other than 1.
Simplifying fractions makes it easier to understand and use the information given.

Revolutions per second is a unit of measure that tells us how many complete turns or revolutions occur in one second.
This is useful in describing the speed of rotating objects like wheels, gears, or engines.
In our problem, after simplifying the ratio, we found that the unit rate is 80 revolutions per second.
This means that for every second, the object completes 80 full revolutions.
Understanding revolutions per second helps in various practical applications like understanding the performance of mechanical systems and optimizing their efficiency.