In this post we will learn the concept of **part to whole ratio** with examples.

Some questions are also solved at the end.

**What is Part to whole ratio?**

The **ratio form the relationship between one entity and the total entity present**.

**For Example**

There are** 2 basketballs and 5 tennis balls** in the box.

Here the two entities are basketballs and tennis balls.

The **total number of balls** are ⟹ 2 + 5 = 7

The ratio of basketball to total balls are expressed as:

The ratio says that out of given seven balls, there are two basket balls.

Given below is the **ratio between tennis balls and total number of balls**.

Out of given seven balls, there are five tennis balls.

**Note:**Here the relationship is formed with total number of entities.

When the ratio is formed between two entities ( basketball & tennis ball) it is known as Part to Part ratio.

**Multiplication and division of Ratios**

**One can multiply or divide both side of ratios without affecting its inherent property**.

**For Example;**

Consider a bucket of 3 liter in which 2 liter is water and 1 liter is oil.

The ratio of water to total quantity is 2 : 3.

Hence, for every 3 liter capacity, there are 2 liters of water.

Now, suppose you doubled the quantity of bucket to 6 liter. What will now be the quantity of water?

Multiply the ratio 2 : 3 with 2

⟹ 2 ( 2 : 3 )

⟹ 2 x 2 : 2 x 3

⟹ 4 : 6

Hence, for 6 liter quantity there is 4 liter of water.

Note that with multiplication, we have not changed the characteristics of the ratio. We just have doubled the quantity of the entity involved.

Hence, both the following ratios are same, just quantity is altered.

Ratio 2 : 3 ⟹ 2 liter of water in 3 liter capacity

Ration 4 : 6 ⟹ 4 liter of water is 6 liter capacity

**Conclusion**

Multiplication/Division of ratios on both sides do not change the basic characteristics of the ratio.

**Examples of Part to Whole Ratio**

(01) In a class, there are 3 boys and 7 girls. Find the ratio of number of girls to total students in class.

**Solution**

Number of girls = 7

Total students = 3 + 7 = 10

**Ratio of girls to total students = 7 : 10**

(02) The ratio of apples to total fruits is 2 : 5. Find the number of apples, if there are total of 20 fruits available.

**Solution**

Ratio of apples to total fruits = 2 : 5

It means that for every 5 fruits, 2 of them are apples.

The ratio 2: 5 can be written in form of fraction as 2/5.

Since there are 20 fruits available, we have to make denominator 20.

Multiply numerator and denominator by 4.

\mathtt{\Longrightarrow \frac{2\ \times \ 4}{5\ \times \ 4} \ =\ \frac{8}{20}}

So we get the ration 8 : 20.**It means that out of 20 fruits available, 8 of them are apples.**

**Examples 03**

In sport complex, there are 15 players present out of which 6 are swimmers. Find the ratio of swimmers to total players.

**Solution**Number of swimmers = 6

Number of athletes = 15

**Ratio of swimmer to total athlete = 6 : 15**

**Example 04**

The ratio of tulips to total flower is given as 2 : 11. Find the number of tulips if the total flower available is 55.

**Solution**Ratio of tulip to total flower is 2 : 11

It means that if 11 flowers are available, there will be 2 tulip flowers in it.

The ratio can be written in form of fraction as 2/11.

Now there are 55 flowers available.

We have to make the denominator of fraction 55.

Multiply numerator and denominator by 55.

\mathtt{\Longrightarrow \frac{2\ \times \ 5}{11\ \times \ 5} \ =\ \frac{10}{55}}

Hence, we get the ration 10 : 55.

**It means that out of 55 flowers, there are 10 tulips in it.**

**Example 05**

There are 50 students who took the Math test. The ratio of students passed to failed is given as 2 : 3. Find the number of students passed.

**Solution**

Ratio of passing to failing is 2 : 3

It means that for every 2 student passed, there are 3 students who failed the test.

Hence student passed = 2

Student failed = 3

Total student considered in ratio = 2 + 3 = 5

So the ratio of student passed to total student is 2 : 5

It means that for every 5 students, there are 2 students who passed the exam.

The ratio can be expressed in fraction as 2/5.

Now there are 50 students in the class.

So we have to make denominator 50.

Multiply numerator and denominator by 10.

\mathtt{\Longrightarrow \frac{2\ \times \ 10}{5\ \times \ 10} \ =\ \frac{20}{50}}

Hence, we get the **ratio 20 : 50.**

**It means that out of 50 students who gave the test, only 20 of them passed**.