Table of Contents

**Ratio Formula**

**Introduction**

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the ‘antecedent’ and the divisor is called the ‘consequent’.

**Ratio Formula**

The ratio formula is used to compare quantities or values in terms of their relative sizes or proportions. The general formula for a ratio between two quantities, A and B, is:

Ratio = A : B = A / B

This formula represents the division of A by B to determine the ratio between them. Ratios can be expressed in various ways, such as in fraction form (A:B), using a colon (A to B), or as a decimal or percentage.

For example, if there are 4 red balls and 6 blue balls, the ratio of red to blue balls can be calculated as:

Ratio of red to blue balls = 4 / 6 = 2/3 or 2:3

This ratio indicates that for every 2 red balls, there are 3 blue balls. The ratio formula is fundamental in comparing and analyzing relationships between quantities or values in various fields, including finance, statistics, and mathematics.

**Solved Examples on Ratio Formula:**

**Example 1:** In a class of 30 students, the ratio of boys to girls is 2:3. How many boys are there?

Solution:

Let’s represent the number of boys as B and the number of girls as G.

According to the given ratio, B/G = 2/3.

Since the total number of students is 30, we have B + G = 30.

From the ratio, we can rewrite B = (2/3)G.

Substituting this into the second equation, we get (2/3)G + G = 30.

Combining like terms, we have (5/3)G = 30.

Simplifying, we find G = 18.

Substituting G = 18 into the equation B = (2/3)G, we get B = (2/3)x18 = 12.

Therefore, there are 12 boys in the class.

**Example 2: **The ratio of the lengths of two sides of a rectangle is 4:7. If the shorter side has a length of 12 cm, what is the length of the longer side?

Solution:

Let’s represent the length of the shorter side as L1 and the length of the longer side as L2.

According to the given ratio, L1/L2 = 4/7.

Since we know L1 = 12 cm, we can substitute this into the ratio equation: 12/L2 = 4/7.

Cross-multiplying, we have 4L2 = 7 x 12.

Simplifying, we get 4L2 = 84.

Dividing both sides by 4, we find L2 = 21.

Therefore, the length of the longer side is 21 cm.

**Example 3: **A recipe calls for a ratio of 3 cups of flour to 2 cups of sugar. If you want to make a batch with 6 cups of flour, how many cups of sugar should you use?

Solution:

Let’s represent the number of cups of flour as F and the number of cups of sugar as S.

According to the given ratio, F/S = 3/2.

Since we want to use 6 cups of flour (F = 6), we can substitute this into the ratio equation: 6/S = 3/2.

Cross-multiplying, we have 3S = 2 x 6.

Simplifying, we get 3S = 12.

Dividing both sides by 3, we find S = 4.

Therefore, you should use 4 cups of sugar to make the batch with 6 cups of flour.

**Frequently Asked Questions on Ratio Formula: **

1: What is ratio?

Answer: A ratio is a mathematical concept that compares the relative sizes or quantities of two or more values. It is expressed as a comparison of two numbers or quantities using a colon, a fraction, or a division symbol. The formula for a ratio is Ratio = Quantity A / Quantity B, where Quantity A and Quantity B represent the values being compared. Ratios are used to represent and analyze proportions, relationships, and comparisons between different quantities or values in various fields such as mathematics, finance, and statistics.

2: How to solve a ratio question?

Answer: To solve a ratio question, follow these steps:

- Identify the quantities or values being compared in the ratio.

- Write the ratio using the appropriate notation (e.g., A:B or A/B).

- Determine the known quantities and the unknown quantity.

- Set up a proportion or equation using the ratio formula.

- Solve the proportion or equation to find the value of the unknown quantity.

- Check your answer and ensure it makes sense in the context of the problem.

3: How do you solve 3 ratios?

Answer:

- Write down the given ratios in the proper notation (e.g., A:B, C:D, E:F).

- Determine the missing value(s) in each ratio.

- Choose a common factor or multiplier to make the ratios consistent.

- Multiply each term of the ratios by the chosen factor.

- Simplify the ratios if necessary.

- Use the resulting ratios to compare quantities or solve related problems, depending on the specific context of the question.

4: How do I interpret a ratio?

Answer: When interpreting a ratio, it represents the relationship or proportion between two quantities. For example, a ratio of 3:2 means that there are three units of one quantity for every two units of the other quantity.

5: How can I simplify a ratio?

Answer: To simplify a ratio, divide both quantities by their greatest common divisor until they cannot be divided further. This results in the simplest form of the ratio.

6: What are the Ways of Writing a Ratio?

Answer: A ratio can be written by separating the two quantities using a colon (:) or it can be written in the fractional form. For example, if there are 4 apples and 8 melons, then the ratio of apples to melons can be written as 4:8 or 4/8, which can be further simplified as 1:2.

7: How to Find Equivalent Ratios?

Answer: Two ratios are said to be equivalent if they represent the same value when simplified. This concept is similar to equivalent fractions. For example, when the ratio 1: 4 is multiplied by 2, it means multiplying both the terms in the ratio by 2. So, we get, (1 × 2)/ (4 × 2) = 2/8 or 2: 8. Here, 1:4 and 2:8 are equivalent ratios. Similarly, the ratio 30: 10, when divided by 10, gives the ratio as 3:1. Here, 30:10 and 3:1 are equivalent ratios. So, equivalent ratios can be found by using the multiplication or division operation depending on the numbers.

8: Why are Ratios Important?

Answer: Ratios are important because they allow us to express quantities in such a way that they are easier to interpret. It is a tool that is used to compare the size of two or more quantities with respect to each other. For example, if there are 30 girls and 20 boys in a class. We can represent the number of girls to the number of boys with the help of the ratio which is 3: 2 in this case.