Change of subject of formula is a very important aspect of mathematics that must be understood by everyone. Its application is broad and goes beyond mathematics to engineering and statistics. Understanding the subject very well is crucial to solving any mathematics where some formulas are involved.
With regards to change of subject of formula, we will cover the following:
- Understanding Change of subject of formula
- Tips on how to change the subject
- Working with examples
We want to start with the first item on the list.
Understanding Change of subject of formula
In mathematics, formulas are used to solve for the value of unknown items. However, a formula might contain more than one variable. If the unknown variable is not isolated, then it becomes difficult to find its value. In order to isolate it from the rest of the expression, you make it the subject of the formula.
Basically, change of subject of formula is a way to separate an unknown variable from the rest of the mathematical expression or formula. The subject of any formula is usually placed alone on the left side of the equals sign, while the rest of variables and constants are kept together on the right side of the equals sign.
Tips on how to change the subject
There is no universal method of changing the subject of any expression. The most important activities or steps involved is usually normal math executions like addition, division, subtraction and the rest. Take note of the following though:
- When + crosses an equals sign (=), it becomes - and vice versa
- If the subject carries a square sign, the square root sign would be introduced to the other side of the equation to cancel the square sign, and vice versa
- If the subject carries a cube sign, cube root will be introduced to the other side to cancel it
- If there is a bracket containing variables and needs to be expanded, the expansion needs to be done too
- If values are given to solve for the subject after working on the formula, you need to substitute those values.
Working with examples
Example 1: If x = 2y + 5z, make y the subject of the formula.
Our job is to rearrange the expression such that y takes the position of x. So..
(Next step: first, we need to send 5z to the other side of the equation to isolate the subject. The positive sign changes to - as it crosses the = sign)
(Next step: Move 2 to the other side of the equation. As multiplication sign crosses the = signs, it turns to division)
We have successfully made y the subject of the formula of expression. If we wish, we can change their order for easy calculation. Thus...
Example 2: Express s in terms of m, r and T in the following expression: T = m/2(5r + [m-3] s)
Solution: To express s in terms of m,r and T is another way of saying: make s the subject of the formula. So we go again....
(Next step: Move 2 to the other side of the equation to remove the fraction part. As division crosses equals sign, it becomes multiplication)
(Next step: Expand the bracket on the right side)
(Next step: Collect like terms in variables containing s, means that 5mr will need to be moved to the other side of the equation, thus..)
(Next step: Factorize s which is common to the expressions on the right, we have..)
(Isolating s means we have to move all of the expression on the right to the left. When that happens, multiplication sign crossing over equals sign turns to division. We then have)
Now we have made s the subject of this formula. To make it look nice, lets swap the positions of the variables. We then have
Conclusion
Subject of the formula is an important aspect of solving any arithmetic's. Whether you were asked to make any variable the subject of an expression or not, it usually comes up any time you are solving expressions using a stated formula. Learning how to solve this is crucial.
The examples above will go a long way in helping you learn how to make any variable the subject. In our next class, we will see tougher examples of this topic and try to find their solution.
Use the comment section to ask questions on things that are not clear.