A ratio is a comparison of two quantities. If we consider two quantitites 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
Consider that to win a relay race we must swim 200 yards before our opponent swims 190 yards. We want to determine who will win the race if we are swimming at a pace of 50 yards every 40 seconds and our opponent's pace is 10 yards every 8.5 seconds. Let's start by rewriting each pace as a ratio.
50 yard every 40 seconds → 50:40
10 yard every 8.5seconds → 10:8.5
Now we will calculate the total time required for each swimmer to complete their respective distances by using equivalent ratios. Let's multiply our ratio by 4.
It takes us 160 seconds to travel 200 yards. Now let's multiply our opponent's ratio by 19.
Our friend travels 190 yards in 161.5 seconds. Since our time is less than our opponent's time, we finish the race first. Therefore, we win the race.
