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.
