A ratio is a comparison of two quantities. If we consider two quantities a and b, the ratio a:b indicates that there are a units of the first quantity for every b units of the second quantity.
a/b or a:b
Ratios occur in everyday life in countless scenarios. Let's see a few examples!
Scenario
Ratio Notation
Gasoline consumption when traveling by car
Miles per gallon = Miles traveled/Gallons of gasoline
Types of fruit in a bowl
Apples : Bananas
Rate of travel, according to the distance formula
Rate = Distance/Time
Demographics of a school classroom
Students who take the bus:Students who walk
We are kayaking at a pace of 63 feet every 12 seconds and our friend's pace is 21 feet every 3 seconds. We want to know if we are kayaking at the same pace. To do so, we can start by rewriting each pace as a ratio.
63 feet every 12 seconds → 63:12
21 feet every 3 seconds → 21:3
Now we need to determine whether the ratios are equivalent. Recall that two ratios are equivalent when we can multiply each quantity in one ratio by the same positive number to obtain the second. Let's see an example!
We can use this information to see if the given ratios are equivalent.
There is no number that we can multiply one ratio by to get the other. This emans that we are not kayaking at the same pace. To determine who is faster, we can use an equivalent ratio to compare our pace to our friend's pace. Let's multiply our friend's ratio by 3.
This means that our friend travels 63 feet every 9 seconds. It takes us 12 seconds to travel the same distance. Therefore, our friend is faster than we are.
