Proportion | Definition of proportion | Equality of two ratios |

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#Proportion |
Definition of proportion |
#Equality of two ratios |
#Equivalency of two ratios |
#Proportion with examples |
#Product of extreme = Product of mean |
Class 10th topic on proportion |
Lecture on topic proportion |
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Definition of #Proportion
#Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

For example, the time taken by train to cover 100km per hour is equal to the time taken by it to cover the distance of 500km for 5 hours. Such as 100km/hr = 500km/5hrs.

Ratio and proportions are said to be faces of the same coin. When two ratios are equal in value, then they are said to be in proportion. In simple words, it compares two ratios. Proportions are denoted by the symbol ‘::’ or ‘=’.

The proportion can be classified into the following categories, such as:

#Direct Proportion
#Inverse Proportion
#Continued Proportion
Now, let us discuss all these methods in brief:

#Direct Proportion
The direct proportion describes the relationship between two quantities, in which the increases in one quantity, there is an increase in the other quantity also. Similarly, if one quantity decreases, the other quantity also decreases. Hence, if “a” and “b” are two quantities, then the direction proportion is written as a∝b.

#Inverse Proportion
The inverse proportion describes the relationship between two quantities in which an increase in one quantity leads to a decrease in the other quantity. Similarly, if there is a decrease in one quantity, there is an increase in the other quantity. Therefore, the inverse proportion of two quantities, say “a” and “b” is represented by a∝(1/b).

#Continued Proportion
Consider two ratios to be a: b and c: d.

Then in order to find the continued proportion for the two given ratio terms, we convert the means to a single term/number. This would, in general, be the LCM of means.

For the given ratio, the LCM of b & c will be bc.

Thus, multiplying the first ratio by c and the second ratio by b, we have

First ratio- ca:bc

Second ratio- bc: bd

Thus, the continued proportion can be written in the form of ca: bc: bd

Also, read:
Direct And Inverse Proportion
#Ratio To Percentage

Ratio and Proportion Formula
Now, let us learn the Maths ratio and proportion formulas here.

#Ratio Formula
Assume that, we have two quantities (or two numbers or two entities) and we have to find the ratio of these two, then the formula for ratio is defined as;

a: b ⇒ a/b

where a and b could be any two quantities.

Here, “a” is called the first term or antecedent, and “b” is called the second term or consequent.

Example: In ratio 4:9, is represented by 4/9, where 4 is antecedent and 9 is consequent.

If we multiply and divide each term of ratio by the same number (non-zero), it doesn’t affect the ratio.

Example: 4:9 = 8:18 = 12:27

Also, read: Ratio Formula

Proportion Formula
Now, let us assume that, in proportion, the two ratios are a:b & c:d. The two terms ‘b’ and ‘c’ are called ‘means or mean term,’ whereas the terms ‘a’ and ‘d’ are known as ‘extremes or extreme terms.’

a/b = c/d or a : b :: c : d
Example: Let us consider one more example of a number of students in a classroom. Our first ratio of the number of girls to boys is 3:5 and that of the other is 4:8, then the proportion can be written as:

3 : 5 :: 4 : 8 or 3/5 = 4/8

Here, 3 & 8 are the extremes, while 5 & 4 are the means.

Note: The ratio value does not affect when the same non-zero number is multiplied or divided on each term.

Important Properties of Proportion
The following are the important properties of proportion:

#Addendo – If a : b = c : d, then a + c : b + d
#Subtrahendo – If a : b = c : d, then a – c : b – d
#Dividendo – If a : b = c : d, then a – b : b = c – d : d
#Componendo – If a : b = c : d, then a + b : b = c+d : d
#Alternendo – If a : b = c : d, then a : c = b: d
#Invertendo – If a : b = c : d, then b : a = d : c
#Componendo and dividendo – If a : b = c : d, then a + b : a – b = c + d : c – d