# 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 recent incidence of Covid 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 amount of time taken by the swimmer to cover one lap.

Solution:

${\dfrac{30 laps}{60 minutes}}$
= ${\dfrac{30}{60}=\dfrac{1}{2}}$
= 0.5 minutes
Thus, the time taken by the swimmer to cover one lap is 0.5 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. While calculating the amount to be paid to a shopkeeper to the amount of return we will get back, all involves calculating rates of quantities in the form of ratio.

They are also used to calculate the birth, mortality or death rate of a population. The recent incidence of Covid over a region, district, or a state and its death rate in a country are all calculated based on the concept of ratios and rates.

## Ratio

A ratio is a comparison of two quantities having 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 with 14 kg of wheat is an example of 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 is an example of 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 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 taken by the swimmer to cover one lap.

Solution:

${\dfrac{30 laps}{60 minutes}}$
= ${\dfrac{30}{60}=\dfrac{1}{2}}$
= 0.5 minutes
Thus, the time taken by the swimmer to cover one lap is 0.5 minutes

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