How To Find Ratio: Tutorial, Examples, And More

In this class, we going to focus on providing information about how to find ratios.

The term ratio can be described as a mathematical expressions that compare two or more quantities and numbers.

Ratio can compare absolute amounts and quantities, and can also be used to compare portions of a larger whole. Ratios can be written and calculated in fractions and in percentages.

However, the basic principles governing the use of ratios are universally the same.

Uses Of Ratios

Ratios can be used in both real world and in school settings to compare the differences between two or more quantities.

The simplest form of ratio compare only two numbers or quantities.

However, ratios can also be used to compare more than 3 quantities and numbers.

For example:

In a basket containing different types of vegetables and fruits such as spinach, apricot, cabbage, carrot, avocado, apple, and oranges. All these can be expressed in form of a ratio.

Ratio is only used when two or more numbers and quantities are compared.

By describing numbers and quantities in relation to one another that will give you clue on how to find a perfect proportion and a percentage of a given quantities.

Ratio is widely used in the manufacturing industries such as pharmaceutical industries and soapmaking industries to formulate the amount of ingredients in a product.

Describing Ratios

Ratios are described by comparing the relationship between two or more numbers.

For example:

If in a class , there are four boys and 3 girls, then if you are to describe this information in form of ratio, you are going to say that the ratios of boys to girls in the class is 4:3.

Note that you can't interchange the quantity of a ratio. Each quantity is independent of one another.

For example:

You can't say the ratio of boys to girls in the class is 3:4.

Because, that is mathematically wrong.

Different Ways In Which Ratios Can Be Expressed

Ratios can be expressed both in written and numerical form.

Here are the most common ways in which ratios are expressed:

1. Ratios can be expressed using an everyday language

For example:

If you want to compare two fruits, let say apples and oranges.

You will do it like this:

In a basket, there are 12 apples and 14 oranges.

Then, the ratio of apples to oranges in the basket is 12 to 14 .

2. Ratios can also be expressed in form of colon.

For example:

When it happens you will compare more than two numbers, then use colon between every set of numbers in succession.

For example:


3. Ratios can also be expressed in form of fractions

For example:

From the above examples that we give, the ratios can be changed to fractions.

In practice:

13:14 = 12/14
3:4 = 3/4

Problems Involving Ratios

When using ratios be sure to simplify the quantities and numbers to lowest forms.

Know that the units of the quantities remain the same or unchanged.

For example:

Assuming there are 12 boys and 4 girls in your house, when simplifying a ratio like this, the units of the quantities, that is both boys and girls will remained unchanged.

In practice:

12 boys: 4 girls = 12/4

From the above fraction, 4 can go into itself one time and can go into 12 3 times.

Therefore, you can simplify the ratio as follows:

12/4 = 3/1
     = 3:1

Therefore, there are 3 boys for every  one girl.

But, if the quantities or numbers to be compared contain the same units, then the individual unit cancel out each other.

For example:

If Amina has 4 bags in her rooms and in every two bags, there are 3 lip balms. Then, how many lip balms Amina has in her room?

Let's do the math together:

Total number of bags in Amina's room = 4

But, in every two bags there are 3 lip balms.


4 bags × 3 lips/2 bags = 2 × 3 lip balms
                     = 6 lip balms

The bag units from the above example cancel out each other.

Another case is when both the denominator and numerator have no common factor, which means the ratio can't be simplified.

For example:

4:13 = 4/13

From the above example, it is clear that 4 can't enter 13, and also there is no any common factor to divide them.

Therefore, we just leave the ratio without simplifying.

Multiplication Involving Ratios

Ratios can be used to determine the outcome of a something.

For example:

In the manufacturing industry, at a normal scale, they used to producing 20kg coconut oil and 30kg olive oil.

One day, the company decide to scale up their output by 4 times the original output (20:30).

From the above example of ratio, you can easily find the new output by simply multiplying the original output with 4.

In practice:

4(20:30) = 80kg:120kg

Therefore, the company wants to scale up their output from 20kg coconut oil and 30kg olive oil to 80kg coconut oil and 120kg oil olive oil.

How To Find The Unknow Variables Using  Ratios

You can use ratios to find unknown variables in a given problems.

For example:

A woman decides to craft her own homemade body moisturizer. The original recipes is the ratio of 2ml Rose flower oil and 3ml lavender essential oil.

If the woman wants to use 4ml Rose flower oil, how many ml of lavender essential oil is now needed by the woman to make up  the formula?

This problem is going to be solved as follows:


Original formula = 2ml:3ml
New formula = 4ml:x ml

For 2ml of Rose flower essential oil she needs 3ml of lavender essential oil, and for 4ml of Rose flower essential oil, the woman needs x ml of lavender essential oil.

In practice:

2:3 = 4:x
2/3 = 4/x

Cross multiply the equation.


2 × x = 4 × 3
   2x = 12
   x = 6

Therefore, the woman needs 6ml of lavender essential oil to make up the formula.


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