Ratio: Meaning, Formula, Simplification, Ratio Table & Solved Examples

Ratio is a mathematical concept that refers to the comparison of two or more numbers. It is used to express the relative size of one quantity when compared to another. in our daily lives, for example, in business when dealing with money or while making any meal. When comparing the relationship between two numbers or quantities, we implement the ratio formula. A ratio between two quantities say 'a' and 'b', is generally expressed as a: b, which is read as 'a is to b'. In ratio, two quantities are compared using the division operation. In this case, the dividend is called the 'antecedent' and the divisor is known as the 'consequent'.

Read Also: Ratio to Percentage Formula & Conversion

Key Terms: Ratio, Division, Comparison, Ratio Formula, Arithmetic Operations, Antecedent, Consequent, Fractions, Notation

---

What Does Ratio Mean?

[Click Here for Sample Questions]

In Mathematics, a ratio is a word for comparing two or more numbers together. It is used to compare the size of one object to another. The ratio is defined as the proportion of two components of the same unit that reflects how much of one element is included in the other. 

Two distinct sorts of ratios exist. There are two types of ratios that exist- part to part and portion to the whole. The part-to-part ratio indicates the degree of correspondence between two distinct elements or groups. 

For instance, the ratio of boys to girls in a class is 12: 15, but the part-to-whole ratio indicates the interaction between two distinct groups. Also if five people out of every ten people enjoy reading. As a result, the ratio of part to total is 5: 10, which suggests that every five people out of ten enjoy reading.

Check More: Angle of Depression

---

Ratio Formula

[Click Here for Sample Questions]

The ratio formula is used in order to compare the relationship between two numbers or quantities provided. The general form for representing a ratio of between two quantities/numbers (For instance a and b) is a: b, which is read as 'a is to b'. The sign ':' is used to represent a ratio.

For example, a ratio can be expressed as a fraction, such as 5/4, or as 5: 4 and read as "5 is to 4."

The ratio of any two identical quantities, p and q, can be written as p/q or p:q. Here, p is referred to as the 'antecedent' and q is referred to as the 'consequent'. Ratios are used to correlate many variables such as length, height, and width. 

Ratios are denoted by two distinct notations.

• Type 1: Odds Notation
• Type 2: Fractional Notation

In odds notation, the expression begins with ':', i.e. " is to ". For instance, 2:3. Fractional notation represents ratios in fraction form. For instance, 2/3.

In ratios, the order of the values is critical. When we declare that there are four red marbles and seven blue marbles, the ratio of red to blue marbles must be 4:7 or 4/7, not 7:4 or 7/4.

Also Read:

Example: In a classroom of 50 students, 23 are female and the remaining are male. Determine the gender ratio.

The total number of students is 50; the total number of female students is 23.

Total boys = Total students - Total girls = 50 - 23 = 27

As a result, the desired ratio is (Boys: Girls), which is 27:23.

Check Important Difference Between Fraction and Rational Numbers

---

Calculation of Ratios

[Click Here for Sample Questions]

We can use the following steps to determine the ratio of two quantities. This can be illustrated with an example. For instance, if 15 cups of flour and 20 cups of sugar are required to make fluffy pancakes, we may determine the flour-to-sugar ratio in the recipe.

• Step 1: Determine the quantities for both scenarios for which the ratio is to be determined. It is 15 and 20 in this instance.
• Step 2: Express it as a fraction a/b. As a result, we write it 15/20.
• Step 3: If possible, simplify the fraction more. The final ratio will be determined by the simplified fraction. Now, 15/20 can be reduced to 3/4.
• Step 4: Thus, as a result, the flour-to-sugar ratio is 3: 4.

Also Read:

---

How to Simplify Ratios?

[Click Here for Sample Questions]

A ratio denotes the quantity of one quantity required in relation to another quantity. The ratio's two terms can be simplified and reduced to their simplest form. When presented in their simplest form, ratios are simple to comprehend and can be modified in the same way that fractions can be simplified. The following steps are used to simplify a ratio. Consider the ratio 18:10 as an example.

• Step 1: Express the supplied ratio a:b as a fraction a/b. When we convert the ratio to fraction form, we obtain 18/10.
• Step 2: Determine the largest common factor between the variables 'a' and 'b'. The Greatest Common Factor (GCF) of 10 and 18 is 2 in this situation.
• Step 3: Divide the fraction's numerator and denominator by the GCF to acquire the simplified fraction. Divide both the numerator and denominator by two to obtain (18÷2)/(10÷2) = 9/5.
• Step 4: To obtain the result, convert this fraction to the ratio form. As a result, the simplified ratio equals 9:5.

Check Also: Reducing Equation To Simpler Form

---

Tips and Tricks on Ratios

[Click Here for Sample Questions]

Here are some important tips for the concept of ratio: 

• If both 'a' and 'b' have the same value in the ratio a: b, then a: b = 1.
• If a exceeds b in a:b ratio, then a:b > 1.
• If a is less than b in the ratio a: b, then a: b < 1
• Prior to comparing two quantities, it is necessary to check that their units are identical.

Also Check:

---

Equivalent Ratios

[Click Here for Sample Questions]

Equivalent ratios and equivalent fractions are similar. When the antecedent (first term) and consequent (second term) of a given ratio are multiplied or divided by a non-zero quantity, an analogous ratio is obtained. 

For instance, multiplying the antecedent and consequent of the ratio 1:3 by three results in (1 × 3) : (3 × 3) or 3: 9. In this case, the ratios 1:3 and 3:9 are comparable. Similarly, dividing both components in the ratio 20:10 by ten equals 2:1. In this case, the ratios 20:10 and 2:1 are equivalent. By multiplying the antecedent and consequent by a positive integer, an indefinite number of equivalent ratios of any given ratio can be found.

---

Ratio Table

[Click Here for Sample Questions]

A ratio table is a structured list of the equivalent ratios of each given ratio. The following table compares the ratio 1:4 to four of its equivalent ratios. Equivalent ratios are related to one another by multiplication. Equivalent ratios are calculated by multiplying or dividing a ratio's two terms by the same amount. 

Let us take the ratio 1:4 and determine four equivalent ratios by multiplying both ratio terms by 2, 3, 6, and 9. As a result, 2:8, 3:12, 6:24, and 9:36 are obtained.

Read More: Multiplication and Division of Integers

---

How To Solve Ratio Equations?

[Click Here for Sample Questions]

Here, the concept of the calculation of ratios can be understood with the help of an example. Consider the following example.

If Ram and Shyam earn Rs. 7000 and Rs. 9000 each month, respectively. Then we might argue that their salaries are paid in a 7:9 ratio. Here, 7 and 9 are a reduced depiction of the original values 7000 and 9000, or the relatively prime integers 7 and 9. That is, we cannot further simplify these numbers into integers.

In reverse, if the ratio of Ram's and Shyam's salaries is 7:9, this does not suggest that Ram's and Shyam's incomes are 7 and 9 rupees, respectively. Rather than that, their salaries are a multiple of 7 and 9. As a result of the data provided, we can express Ram and Shyam's salary as follows:

Ram's salary is 7x. Shyam's annual salary is equal to 9x, where x is a positive integer number. And the variable 'x' is referred to as the 'Multiplicative Constant'.

Also Check:

---

Things to Remember

[Click Here for Sample Questions]

• Ratio refers to the comparison of two or more numbers and is used to express the relative size of one quantity when compared to another. 
• There should be a ratio between quantities of the same type. 
• A ratio of two quantities 'a' and 'b', can be expressed as a: b, which is read as 'a is to b'.
• The two quantities are compared using the division operation in ratios. 
• The order of the values/quantities is important in ratios. 
• A ratio table is defined as a structured list of the equivalent ratios of each given ratio. 

Read Further: Multiplicative Inverse

---