Learn the Concept of Proportion in our Maths Tution
Proportion is a mathematical concept that is an essential part of Maths tuition. The concept is used when a change in a value or quantity ‘A’ affects a value or quantity B in any way. If this happens, the two quantities; quantity A and quantity B, are said to be proportional. This means if quantity A or quantity B increases or decreases the other quantity will either increase or decrease.
There are two types of proportion namely; Direct proportion and Inverse proportion. The main difference between these two is that, in direct proportion, as one quantity increase, the other quantity decreases. On the other hand, in inverse proportionality, while one quantity increases, the other quantity will decrease. Let’s take a closer look at each of these two;
- Direct proportion
In direct proportion, the increase in quantity A results in an increase in quantity B in an identical ratio. This means one of the quantities will be a multiple of the other and this will help us in our calculations in later topics.
Example 1: Let us say for that quantity A is directly proportional to quantity B, the expression for this scenario can be written as;
A ∝ B OR A = kB
In the equation, k is a constant. It is referred to as the constant of proportionality. It is a constant number that does not change when the quantities in the expression, A and B, change. The constant ensures that the ratio of multiplication is constant in the expression.
Calculating the constant: The constant can be calculated very easily when we are given the two quantities in in a given expression.
Example 2: The quantity of A is 60 and the quantity of B is 30. Quantity A is directly proportional to quantity B.
To calculate the value of constant K, write the expression down;
A = kB
Now, substitute our values in the expression;
To get k, we divide both sides by 30
As such, k = 2
Therefore, our constant of proportionality in the above expression is 2.
Example 3: Calculating a proportional quantity after its counterpart changes value.
Quantity A is 60 and the constant of proportionality is 3. Calculate the quantity B if quantity A is directly proportional to quantity B.
We first make sure that we establish the quantities involved in the expression. After that, the expression should be written.
Now, substitute for the information given in the question;
60 = 3B
To calculate our unknown we divide both sides with 3
B = 20
- Inverse Proportion
In this proportion, one value decreases as one increases.
If A is inversely proportional to B, the relationship can be expressed as;
A ∝ 1/B OR A = k/B, where k is the constant of proportionality.
The rest of the calculation remains the same as before.
Example 4: If A = 5, B =8, then
5 = k/8
Multiply both sides by 8 to remove the denominator,
k = 40
The Calculation Process
Questions in direct proportion usually have a single unknown and there is a set of sequential steps that can be used to calculate the proportion.
Step 1: Analyze and fully understand the proportional relationship between the quantities in the question
Step 2: Write down the proportional relationship between the quantities in the question
Step 3: Include the constant of proportionality in the proportionality relationship statement
Step 4: Calculate the constant of proportionality if it is not given, using the given data
Step 5: Substitute the constant of proportionality that you have calculated or that was given in the question
Step 5: Solve the problem.