Ratio and Proportion
The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:
The concept of ratio and proportion are used in day-to-day life, from calculating the speed of a motorcycle to knowing the price difference of vegetables in your local market and a supermarket. Therefore, knowing about them is important.
A ratio is defined as the relation between two quantities that are usually denoted in numbers. It allows you to compare or contrast two numbers of the same kind. In the above examples, we calculated the ratio of pencils owned by different people. So, basically, ratio gives you an idea as to how many times a specific event or a quantity is equal to the same event or quantity owned by someone else.
You should keep in mind that a ratio can only be calculated if the quantities being compared are:
- Of the same kind
- Measured in the same unit
A ratio is denoted by the symbol “:” (colon).
Proportion is defined as the comparison of two ratios. As seen in the above examples, proportion gives you the equivalence of two ratios. This can help to decide similarities and differences in events. For example, you can use the concept of proportion to compare the vegetable price differences in your city and your cousin’s city (if they are different).
Proportion is usually denoted using the symbols “::” (two colons) and “=” (equal to).
The magic of proportion can be described by its properties. For example, if A:B = C:D, then:
- A+B = C+D
- A-C = B-D
- B:A = D:C
- A-B:B = C-D:D
- A+B:B = C+D:D
There are many more such properties that you can learn. You can also learn about the unitary method, which you can use to calculate the value of a single unit from multiple values.
The formula of a ratio is given as A:B
(assuming A and B are two quantities of a similar kind.)
The formula of proportion is given as A:B = C:D
(assuming A:B and C:D are ratios of two similar quantities.)
These two concepts of comparison and relationship between numbers are known as ratio and proportion. They are an integral part of mathematics and lay a foundation for advanced concepts, such as probability and statistics.
- What is the formula of ratio and proportion?
The formula of a ratio is given as A:B. The formula of proportion is given as A:B = C:D.
- What is the concept of ratios?
A ratio is a mathematical tool used to compare or find the relationship between two different quantities. It helps you compare two quantities in its own unit and format.
- What is the ratio formula?
The formula for ratio is given as A:B where A and B are quantities of a similar kind. For example, A and B can be the number of tennis balls that you and your friend own, respectively.
- How do you solve a ratio?
A ratio can be solved by dividing the two numbers or quantities with each other.
- How do you solve ratio and proportion word problems?
You can solve ratio and proportion word problems by first assigning the quantities to the formulae. Read the word problems carefully and extract the numbers as A, B, C, and D (individual quantities). First, calculate the ratios separately and then compare them to check if they are in proportion or not.
- What is a proportion (with an example)?
A proportion is a comparison between two ratios. For example, consider 1:2 and 1:3 as two ratios. When you compare these ratios, you can deduce that they are not equal. This means that the ratios are not in proportion, i.e., they are not equal.