Ratio in Math || Definition of Ratio with examples

In this post we will learn about the concept of ratios, its properties and some questions with examples.

What is Ratio?

Ratio is used to form comparison between two entities.

Consider the above image.
The image has 3 yellow box and 2 blue box.

The relationship between the yellow and blue box as be established with the help of ratio as:

The above ratio means that for every 2 blue box there are 3 yellow boxes.

How to represent ratios?

Suppose there is some value a to value b.

The ratios can be expressed in three ways:

(a) Using the symbol ” : “

(b) Using the word ” to “

(c) Using the fraction symbol (also called “a by b”)

Note: Since the ratios can be represented as fraction, they can also be divided as fractions.

Manipulating Ratio Numbers

Suppose you want to prepare fish for dinner and the recipe asks you to put salt and turmeric in the ratio 5 : 2 for 100 gram of fish.

Hence, for fish preparation, you have to put 2 gram of turmeric and 5 gm of black salt.

But what if a guest come to your house for dinner and you have to prepare 200 gram of fish.

You need to put larger quantity of salt and turmeric.

To find accurate measurement, multiply the ratio with 2.

Now we have to put 10 grams of salt and 4 grams of turmeric.

Note that the ratio is still the same, we have just increased the quantity to accommodate our guest.

Conclusion
The ratio can be multiplied or divided by any number without any change its underlying relationship.

Types of Ratios

There are mainly two types of ratios:

(a) Part to Part Ratio
(b) Part to Whole Ratio

We will learn both the ratios step by step.

Part To Part Ratio

This ratio basically tells the relationship between two entities.

Suppose there are 3 cats and 5 dogs.

Here the two entities are cats and dogs, and Part to Part ratio tells the relationship between number of cats and dogs.

Given below is the ratio of number of cats to dogs:

3 : 5 ( expressed using symbol ” : ” )

3 to 5 ( ratio expressed using word “to”)

3/5 (ratio expressed using fraction)

Now let us change the order of ratio.
I mean, find the ratio of number of dogs to number of cats.

Here the word “dog” comes first. It means that in ratio, the number of dogs will be expressed first, followed by number of cats.

Given below is ratio of dogs to cats;

5 : 3 ( expressed using symbol ” : ” )

5 to 3 ( ratio expressed using word “to”)

5/3 (ratio expressed using fraction)

I hope the concept is clear. Let us now move to understand Part to Whole ratio.

Part to Whole ratio

Part to whole ratio tell the relationship between one entity to the total number of entity present.

To understand the concept, let’s refer to above example.
Suppose there are 3 cats and 5 dogs.

Here total entity is = 3 + 5 = 8

(i) Ratio of cats to total animal is expressed as:

3 : 8 ( expressed using symbol ” : ” )

3 to 8 ( ratio expressed using word “to”)

3/8 (ratio expressed using fraction)

(ii) Ratio of total animal to cat is expressed as:

8 : 3 ( expressed using symbol ” : ” )

8 to 3 ( ratio expressed using word “to”)

8/3 (ratio expressed using fraction)

(iii) Ratio of dog to total animal is expressed as:

5 : 8 ( expressed using symbol ” : ” )

5 to 8 ( ratio expressed using word “to”)

5/8 (ratio expressed using fraction)

(iv) Ratio of total animal to dog is expressed as:

8 : 5 ( expressed using symbol ” : ” )

8 to 5 ( ratio expressed using word “to”)

8/5 (ratio expressed using fraction)

Solved Examples of Ratios

(01) The ratio of carrot to rabbit is in the ratio 2 : 1. If there are 10 carrots available, find the number of rabbits.

Solution
Ratio of carrot to rabbit = 2 : 1

It means that for every 2 carrots, there is 1 rabbit.

Now, there are 10 carrots available.
How can we make the ratio available from 2 carrots to 10 carrots.

Multiply the ratio by 5.

Hence, for 10 carrots, there are 5 rabbits present in the garden.

(02) The ratio of boys and girls present in the classroom is in the ratio 3 : 5. Find the number of girls, if 12 boys are present.

Solution
Ratio of boys and girls present is 3 : 5.

It means that for every 3 boys, there are 5 girls present in the classroom.

Now there are 12 boys present.
How can we convert the boys number from 3 to 12?

Multiply the ratio with 4

Hence, for 12 boys there are 20 girls present.

(03) The number of cats and dogs present are in the ratio 3 : 7. Find the number of cats if total of 20 animals are present.

Solution
This question involves the concept of “Part to Whole ratio”.

Ratio of cats & dogs = 3 : 7

The ratio mean that for every 3 cats, there are 7 dogs present.

Total number of animals = 3 + 7 = 10

Ratio of cats & total animals = 3 : 10

Now we have 10 animals present.
How to convert the animal number from 10 to 20?

Multiply the ratio by 2.

Hence, for 20 animals present, there are 6 cats available.

(04) The ratio of basketball & football players is 5 : 8. Find the number of football players if there are 39 number of players in the campus.

Solution
Ratio of basketball player to football player = 5 : 8

It means for every 5 basketball players, there are 8 football players available in court.

Total number of players = 5 + 8 = 13 players.

Ratio of football to total players = 8 : 13

Its given that there are 39 total players in court.
How to convert total players from 13 to 39?

Multiply the ratio with 3.

Hence, out of 39 players, 24 players play football.

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