In this section we’re going to be looking at rearranging equations. We shall explore how to arrange linear equations, brackets, fractions and quadratics. This entry explores the basic ideas of rearranging equations, more harder examples of rearranging equations can be found here
What is the subject?
Consider the following SUVAT formula. The following formula is used to find the velocity of an object over time. In the formula V (velocity) is known as the subject of the formula. That is; VELOCITY is the subject we’re trying to solve or find.
The above formula is used to find velocity over time. Suppose we wanted to find time (t) in the formula, we would have to know what the value of v is.
Let’s rearrange the formula below to make t the subject.
First move u to the other side to leave the time (t) with the other letter a, we’re trying to make t the subject to do this we’ll have to make sure that t is on its own.
Now to leave t on its own we must divide both sides by a.
Now we have;
Lastly we rewrite the equation in a more easy readable form.
Rearranging equations with brackets
Here we’re going to be looking at how to rearrange equations which involve brackets. Suppose we have an equation shown below and we wanted to make y the subject.
Here we can see a multiplication on one side of the equation. Since y is on the other side we have to find a way to leave it on its own. To get rid of k on the other side we must divide both sides by k.
We have y one the other side but with another term or letter which we have to get rid of. To get rid of this we must subtract z from both sides.
We rewrite it in an easy to approach form;
We have managed to make y the subject
Rearranging equations with fractions
In the following example we’re going to look at rearranging equations with fractions. Suppose we have the following equation and are asked to make x the subject.
Here we have to get rid of the fraction; we do this by dividing both sides by x or cross multiplying.
…we multiply 5b with x and a+4 with 1 which results in;
Since we’re trying to make x the subject we have to get rid of 5b, we do this by dividing both sides by 5b.
Rewrite it as;
We have managed to make x the subject.
Rearranging equations with quadratics
The following shows an equation which involves quadratics;
Make x the subject…
In the above example we have a square. First we have to get rid of the fraction as we did before. We do this by dividing both sides by e or cross multipliying.
We multiply e with b and ax2 + f with 1 to get the following result.
Now we must leave x2 on its own since we’re trying to make x the subject. First we subtract f from both sides.
Now we divide both sides by a as shown below;
To make x2 x we must square root it, this means we must square root both sides if they’re to remain equal.
This results in;
That concludes this section on rearranging equations. If you would like to explore further with much harder examples click here.