Ratios and Rates

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

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.

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

If a truck travels 24 miles in 2 hours, calculate the average speed of the truck.

Solution:

= ${\dfrac{24 \ miles}{2 \ hours}}$
= ${\dfrac{24}{2}=\dfrac{12}{1}}$
= 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