Ratio Formula: Calculation, Properties & Table

Ratio formula is predominantly used in cases where there is a requirement to compare the relationship between two numbers of a similar kind. In other words, the ratio formula is referred to as a separation between the numbers which is represented by a colon (:). Other than colon, division sign (/) is also used to express the ratios between the two numbers. 

Key Takeaways: Ratio, Ratio Formula, Equivalent Ratios, Greatest Common Factor, Antecedent, Consequent, Number, Colon, Division, Fraction

---

What is Ratio?

[Click Here for Sample Questions]

Ratio is used to compare two quantities which are of similar kind in order to compare them with ease. This ratio can also be expressed as a fraction wherein the numerator is compared to the denominator.

Ratios can be further divided into two types: 

• Part Ratio 
• Whole Ratio

In part ratio, it denotes how two distinct groups or numbers or entities are related to each other. For instance, in the case of a class, the ratio between boys and girls is 4:10.

In whole ratio, it denotes the relationship which exists between a specific group as compared to the whole. For instance, in a generalized case, out of 20 people, 10 of them are interested in books and like to read. Thus, the whole ratio becomes 10:20, which infers that every 10 people from a group of 20 people like to read books.

Also Read:

---

Ratio Formula

[Click Here for Sample Questions]

Ratio formula is used to express relation between two numbers or quantities. In order to express ratios between two quantities, for instance ‘a’ and ‘b’, it can be represented as ‘a:b’, which is generally read as ‘a is to b’. Furthermore, the fraction form for the same is represented as ‘a/b’. Here, ‘a’ can also be called as the antecedent or the numerator and ‘b’ can be called as the consequent or the denominator.

---

Calculation of Ratios

[Click Here for Sample Questions]

The following steps can be used to calculate the ratio of the two said quantities. This can be elaborated using an example. For instance, if 20 cups of flour and 25 cups of sugar are required to prepare sponge cake, the ratio of the flour and sugar utilized in the recipe can be calculated as follows:

Step 1: Finding the quantities of both the items for which the ratio has to be determined. In

this scenario, it is 20 and 25.

Step 2: Writing these quantities in a fraction form of ‘a/b’. Thus, the quantities can be written

as 20/25.

Step 3: Simplifying the fraction even further, if it is possible, in order to give the final ratio. 

Thus, for the quantities, 20/25 can be simplified further as 4/5.

Step 4: Thus, the ratio of the flour to the sugar can be expressed as 4:5.

Also Read: Sequence and Series

---

Simplification of Ratios

[Click Here for Sample Questions]

In order to express how much of one entity or quantity is required in comparison to the other, the two terms in the ratio can be further classified and expressed in their lowest forms. This is done because ratios when expressed in their lowest forms are easier to understand.

The following steps can be followed to simplify a ratio using an example of ratio 18:10.

Step 1: Writing of the provided ratio ‘a:b’ as fraction ‘a/b’. On writing as such, the fraction form will be 18/10.

Step 2: Finding the greatest common factor (GCF) of both ‘a’ and ‘b’. Here, it will be 2 in case of 18 and 10.

Step 3: Dividing the numerator as well as the denominator of the fraction with the GCF in order to obtain a more simplified fraction. Here, dividing the numerator and the denominator by 2, we get 9/5.

Also, the fraction obtained can be represented in a ratio form as 9:5.

Also Read: Complex numbers and Quadratic equations

---

Properties of Ratios

[Click Here for Sample Questions]

The main properties of ratios are as follows:

• If a < b in the ratio a : b, then a : b < 1.
• In case both the numbers 'a' and 'b' are equal in the ratio a: b, then a: b = 1
• If a > b in the ratio a : b, then a : b > 1.

---

Equivalent Ratio

[Click Here for Sample Questions]

In the case of equivalent ratios, they are almost similar to the equivalent fractions. Here, if the antecedent (numerator) and the consequent (denominator) of any given ratio is either multiplied or divided by the same number (any number other than zero), it then gives an equivalent ratio. For instance, when the antecedent and the consequent of the ratio 2:4 are multiplied by 2, we get, (2x2) : (4x2) or 4:8. Here, 2:4 and 4:8 are the equivalent ratios. Similarly, when both the terms of the ratio 30:20 are divided by 10, it gives 3:2. Here, 30:20 and 3:2 are equivalent ratios.

Thus, an infinite number of equivalent ratios of any given ratio can be found by multiplying the antecedent and the consequent by a positive integer.

Read Also: Class 12 Differential Equation

---

Ratio Table

[Click Here for Sample Questions]

Ratio table refers to a list containing the equivalent ratios of any particular given ratio in a structured manner. The following ratio table gives the relation between the ratio 1:4 and four of its equivalent ratios. 

For instance, by taking the ratio 1:4 and finding its four equivalent ratios, by multiplying both the terms of the ratio by 2, 3, 6 and 9, we get 2:8, 3:12, 6:24, and 9:36. 

---

Things to Remember 

• Ratio is used to find relations between two or more quantities with respect to each other.
• In a ratio, the dividend is called the 'antecedent' and the divisor is called the 'consequent'.
• The symbol ‘:’ is used to denote ratio.
• A ratio table refers to a list of equivalent ratios that are obtained either by multiplying or dividing both antecedent and consequent by the same value.
• Two ratios are equivalent, if the fractions corresponding to them are equivalent.

Also Read: