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**.