Introduction to proportions with definition, characteristics and examples > Consider a class of school. Let’s imagine there are 50 pupils, 30 of whom are girls and 20 of whom are boys. . Could you explain how you differentiate between guys and girls in your class? If not, then notion of proportion is introduced into your maths.
Here, the proportion of boys is 20 out of 50 (two out of five), whereas the proportion of girls is 30 out of 50. (3 out of 5). If you wish to raise the strength proportionally, you must admit two boys and three girls for every five new students.
A proportion is simply the amount or quantity of one thing present in another as a total. In the financial industry, it is utilised for comparative analysis. It is useful in everyday life when purchasing products that are denoted by numbers [mass, volume, etc. In this article we will exclusively describe the concept of proportion.
What is proportion?
“Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion.”
Or
“A proportion is made up of two ratios that have been established to be equal, implying that proportions may be solved.”
Formula
Let say we have four quantities l, m, n and p such that the ration l : m is equal to ratio n : p then we can write these four quantities in proportion such as:
l: m :: n : p
This is the mathematical representation of proportion. We can use the equality sign for the proportion. That is, the first and fourth components in a proportion are known as extremes, whereas the second and third terms are known as means.
l: m = n : p
We may substitute ration indications with divide signs to get the value of any unknown quantity, such as m.
l / m = n / p
The above phrase is the final formula of proportion. We can reform above phrase to calculate the value of any proportion member like l, n and p.
The most general formula used to calculate the proportion is given as:
Extreme products = Mean products
Proportional Characteristics
The proportional relationships are as follows:
Addendo
If l : m = n : p, then value of each ratio is l + n : m + p
Subtrahendo
If l : m = n : p, then value of each ratio is l – n : m – p
Dividendo
If l : m = n : p, then l – m : m = n – p : p
Componendo
If l : m = n : p, then l + m : m = n + p : p
Alternendo
If l : m = n : p, then l : n = m : p
Invertendo
If l : m = n : p, then m : l = p : n
Componendo and dividendo
If l : m = n : p, then l + m : l – m = m + p : m – p
Proportional Tips & Tricks
- l/m = n/p ⇒ lp = mn
- a/b = c/d ⇒ m/l = p/m
- a/b = c/d ⇒ l/n = m/p
- a/b = c/d ⇒ (l + m)/m = (n + p)/p
- a/b = c/d ⇒ (l – m)/m = (n – p)/p
- l/(m + n) = m/(n + l) = n/(l + m) and l + m + n ≠0, then l = m = n.
- l/m = n/p ⇒ (l + m)/(l – m) = (n + p)/(n – p), which is known as componendo -dividendo rule.
Examples of proportions:
Below are some of the solved example of proportions.
Example 1:
The price of 50 notebooks is 1600. How many such notebooks can be bought by 6400?
Step 1: write given data values
Let X be the unknown number of notebooks then proportion is direct.
50 : 1600 :: X :6400
Step 2: write its general formula
Extreme products = Mean products
Step 3: Now solve by putting mean and extreme values
Here the extreme value are 50 and 6400 while X and 1600 are mean values. Hence by applying formula we get:
Since proportion is direct so
50 / X = 1600 / 6400
Or
50 × 6400 = X × 1600s
320000 = X × 1600s
Reform the above phrase.
X = 320000 / 1600
X = 200
As a result, the total number of unidentified notebooks has been determined.
The Proportion calculator can also be used to determine the value of unknown notebooks in above problem. Any other unknown quantity can also be determined using power calculator. Follow the procedures outlined below to compute with a proportion solver.
Step 1: Put the given value according to formula and click on calculate button.
Step 2: You can also see how it was solved by clicking the display steps button.
Hence, your desired results have been calculated using a very easy procedure.
Example 2:
On two liters of gasoline, a car may go 90 kilometers. To go 225 kilometers, how many litters of gasoline will be required?
Step 1: write given data values
Let X be the unknown number of liters then proportion is direct.
90: 225:: 2 :X
Step 2: write its general formula
Extreme products = Mean products
Step 3: Now solve by putting mean and extreme values
Here the extreme value are 90 and X while 225 and 2 are mean values. Hence by applying formula we get:
90 / 225 = 2 / X
Or
90 × X = 225 × 2
90 × X = 450
Reform the above phrase.
X = 450 / 90
X = 5l
As a result the car will use 5 liters of gasoline to travel 225km.
Summary:
A proportion is simply the entire amount or quantity of one item in another. A proportion, by definition, is not an absolute number, but rather the amount of one item in relation to another. Males, for example, account for around half of the total population.
It has vast advantages in financial and banking industry. To make its calculations fast proportion calculator must be used to avoid time taking calculations.
