Understanding the Concepts of Ratio and Proportion
You can now understand the fundamental concepts of Ratio and Proportion.
Listed below are the different concepts of the topic
1. Ratio
A ratio is a comparison of two quantities obtained by dividing the first by the second.
Ratio can be properly represented using the diagram below.
If a and b are two values of the same kind and with the same units, and b is not equal to zero, then the quotient a/b is known as the ratio between a and b.
The colon sign is used to denote ratios (:). This means that the ratio a/b has no unit and can be expressed as a: b.
2. Proportion
The equality of two ratios is referred to as proportion. Two equal ratios are always proportional. Proportions are represented by the symbol (::) and assist us in solving for unknown quantities.
To put it another way, proportion is an equation or statement that shows that two ratios or fractions are equivalent.
If a: b = c: d, four non-zero values, a, b, c, and d, are said to be in proportion.
For Example
3 : 5 and 15 : 25
In this case,
- 3:5 can be written as 3:5 = 3/5 = 0.6, and
- 15:25 can be written as 15:25 = 15/25 = 3/5 = 0.6.
Because both ratios are equal, we can conclude that they are proportional.
3. Concept of Proportionality
To address problems faster, we must also comprehend the concept of proportionality between these elements.
1. Direct Proportion
The term 'direct proportion' refers to the direct link between two quantities. When one quantity rises, the other rises as well, and vise - versa. As a result, a direct proportion is expressed as y ∝ x.
For Example
When the speed of a car is raised, it travels a greater distance in a given amount of time.
- Time & Distance are directly proportional
- Speed & Distance are directly proportional
2. Inverse Proportion
Inverse proportion explains the connection between two quantities in which one rises while the other falls and vise - versa. As a result, an inverse proportion is expressed as y ∝ 1/x.
For Example
If the speed of a vehicle is increased, it will cover a fixed distance in less time.
- Time & Speed are Inversely proportional
FAQsFAQs
Why is understanding the concepts of Ratio and Proportion important?
Understanding the concepts of Ratio and Proportion assists in:
Understanding how Ratio and Proportion formulas are derived
Addressing the Ratio and Proportion problems promptly and accurately.
Resolving each of the various forms of questions on Ratio and Proportion topic
Developing your unique shortcuts
Is it possible to solve Ratio and Proportion problems without knowing the concepts?
Yes, it's possible to solve Ratio and Proportion questions without understanding what they entail. However, experts advise that comprehending the fundamentals is essential to address the Ratio and Proportion problems effectively.
What is the right way to learn Ratio and Proportion concepts?
The foundation of mathematics is concepts, and understanding them is critical to boosting your performance in the Quantitative Aptitude section. Visualising the Ratio and Proportion concepts using real-life examples is the best approach to learn the Ratio and Proportion concepts.
