# Part to Part Ratio || Definition, property and examples

In this post we will learn concept of “Part to Part Ratio” with examples.

We will also solve some of the questions related to the concept.

## What is Part to Part Ratio?

The ratio basically do the comparison between two entities.

For Example;
In a room, three boys and two girls are present.

Here the given entities are boys and girls.

Given below are three ways in which ratios can be expressed.

Here the ratio 3 : 2 mean that for every 3 boys, there are 2 girls present in the class. Hence it gives the ratio of number of boys to girls.

You can also reverse the order and express the ratio of girls to boys.

Swapping the position of boys and girls in the below image.

The ratio of girls to boys can be expressed in following three ways:

### Multiplication/Division of ratios

The ratio can be multiplied or divided on both sides without change in its character.

For example;
You hosted a party in the evening and you bought 5 big chocolates and 11 small candies for your guest.

Ratio of chocolate and candies is 5 : 11.

Shockingly some people get in uninvited and the number of people get doubled.

In this case, the number of chocolates and candies required also get doubled.

The quantities of sweet is now given as:

So we need 10 chocolate and 22 candies for the total guest attending the party.

Conclusion:
The point is you can multiply any number with the ratio with out changing its underlying characteristics.
However, multiply the ratio on both sides otherwise the math will go wrong.

## Examples of Part to Part Ratio

Example 01
There are three pencils and one pen in the box.
Find the ratio of pen to pencil.

Solution
Here pencils and pens are two entities.
We have to form the relationship with the help of ratios.

Number of Pencil = 3
Number of pen = 1

Ratio of Pen to Pencil = 1 : 3

It means that for every pen, there are three pencils present.

Example 02
The ratio of red to yellow rose is 5 : 7. Find the number of red rose, if there are 21 yellow rose present.

Solution
The ratio of red to yellow rose is 5 : 7

It means that for every 5 red roses, there are 7 yellow roses present.

The ratio can be expressed in form of fraction as 5/7.

Since there are 21 yellow roses, we have to do something to make denominator 21.

Multiply numerator and denominator by 3.

\mathtt{\frac{5}{7} \Longrightarrow \ \frac{5\ \times \ 3}{7\ \times \ 3} \ \Longrightarrow \frac{15}{21}}

Now the ratio becomes 15 : 21.

Hence for 21 yellow roses, there are 15 red roses present.

Example 03
There are 6 dogs and 5 cats present in the house. Find the ratio of dogs to cats.

Solution
There are two entity present; dogs and cats.
We have to form relationship between the entity using ratios.

Number of dogs = 6
Number of cats = 5

Ratio of dogs to cats = 6 : 5

Hence, 6 : 5 is the required ratio.

Example 04
In a box, the red balls and blue balls are present in the ratio 2 : 3. Find the number of blue balls, if the number of red ball is 10.

Solution
Ratio of red & blue balls = 2 : 3

It means for every 2 red balls there are 3 blue balls.

The ratio can be written in form of fraction as 2/3.

Now the number of red balls is 2.
We have to make the numerator 10.

Multiply numerator and denominator by 5, we get;

\mathtt{\frac{2\ \times \ 5}{3\ \times \ 5} \ \Longrightarrow \frac{10}{15}}

Now the fraction becomes 10 : 15.

Hence, the number of blue balls will be 15.

Example 05
The number of badminton and cricket player is 5 & 13 respectively.
Find the ratio of cricket to badminton player.

Solution
The two entities are badminton and cricket players.
We have to form relationship using ratios.

Number of badminton player = 5
Number of cricket players = 13

Ratio of cricket to badminton player = 13 : 5

Hence for every 13 cricket players, there are 5 badminton players present.