Ratio and rates are frequently used together in everyday life to compare two quantities. While calculating the amount to be paid to shopkeepers to the changes, we will get back; all involve calculating rates of quantities in the form of a ratio.
They also calculate a population’s birth, mortality, or death rate. The incidence of COVID-19 over a region, district, or state and its death rate in a country are all calculated based on ratios and rates.
Ratio
A ratio compares two quantities having the same units. It is written using a colon ‘:’, for example, 2:3, and is also written in fraction form as ${\dfrac{2}{3}}$.
For example, the expression between 20kg of sugar and 14 kg of wheat represents a ratio.
Rates
A rate is a unique ratio that compares 2 quantities with different units.
For example, if a man covers 3 km in 30 minutes, it is written as 3 km/30 minutes.
A unit rate is a rate with a denominator of 1.
Let us use the concept of ratios and rates to solve some problems.
Solved Examples
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A frog limps 180 times in 10 seconds. Write the rate as a fraction in the lowest terms.
Solution:
![]()
${\dfrac{180 \ times}{10 \ seconds}}$
= ${\dfrac{180}{10}=\dfrac{18}{1}}$
So, the rate is 18 limps per second.
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A swimmer swims 30 laps in 60 minutes. Find the time it takes the swimmer to cover one lap.
Solution:
![]()
${\dfrac{60 \ laps}{30 \ minutes}}$
= ${\dfrac{60}{30}=\dfrac{2}{1}}$
= 2 minutes
Thus, the time taken by the swimmer to cover one lap is 2 minutes
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If a truck travels 24 miles in 2 hours, calculate the average speed of the truck.
Solution:
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= ${\dfrac{24 \ miles}{2 \ hours}}$
= ${\dfrac{24}{2}=\dfrac{12}{1}}$
= 12 miles/hour
Thus, the average speed of the truck is 12 miles/hour.
Ratio and rates are frequently used together in our everyday life for comparing two quantities. Calculating the amount to be paid to a shopkeeper and the amount of return we will get back involves finding rates of quantities in the form of ratios.
They are also used to calculate a population’s birth, mortality, or death rate.
Ratio
A ratio is a comparison of two quantities having the same units. It is written using a colon ‘:’, for example, 2:3, and is also written in fraction form as ${\dfrac{2}{3}}$.
For example, the expression between 20kg of sugar and 14 kg of wheat is an example of a ratio.
Rates
A rate is a special kind of ratio that compares between 2 quantities having different units.
For example, if a man covers 3 km in 30 minutes, it is written as 3 km/30 minutes as an example of the rate.
A unit rate is a rate with a denominator of 1.
Let us use the concept of ratios and rates to solve some problems.
Solved Examples
![]()
A frog limps 180 times in 10 seconds. Write the rate as a fraction in the lowest terms.
Solution:
![]()
${\dfrac{180 \ times}{10 \ seconds}}$
= ${\dfrac{180}{10}=\dfrac{18}{1}}$
So, the rate is 18 limps per second.
![]()
If a car travels 24 miles in 2 hours, calculate the average speed of the car.
Solution:
![]()
= ${\dfrac{24 \ miles}{2 \ hours}}$
= ${\dfrac{24}{2}=\dfrac{12}{1}}$
= 12 miles/hour
Thus, the average speed of the car is 12 miles/hour
This helped me alot