# data[].attributes.attachment_link.title
BBC Bitesize - GCSE Maths - Algebraic formulae - Edexcel - Test

# data[].attributes.attachment_link.description
Learn about and revise formulae and how to apply skills in substituting, creating and rearranging formulae with BBC Bitesize GCSE Maths Edexcel guide.

# data[].attributes.attachment_link.readable_text
A formula is a mathematical relationship between different quantities that is expressed with algebra. For example, one formula for speed is distance divided by t ime, which we express like

In this case, we say s (speed) is the subject of the formula. This is because s sits on its own one side of the equation and doesn't appear at all on the other. We can change the subject of the formula, for example by multiplying both sides by t the equation becomes

So now, d (distance) sits on its own on one side of the equation and thus is the new subject. Rearranging formulae in order to change the subject is the focus of this topic, and we do it by applying the core principle of: an equation remains unchanged as long as you do the same thing to both sides.

We will go through a series of (sometimes subtly) different examples to see how sometimes it can take several steps and a bit of ingenuity to get the subject that you desire.

Example: Rearrange the formula F=\dfrac{mv}{t} to make m the subject.

As a rule of thumb, it's good to try to get rid of any algebraic fractions as soon as you can. This is to say that if the thing that you want to make the subject is part of a fraction (especially if it's in the denominator) , then it's generally a good idea to multiply up by the denominator of that fraction as a first step. It's worth keeping in mind and is precisely what we're going to do here. So, to kick off making m the subject, we will multiply both sides by t and get

Then, if we divide both sides of the equation by v, we get

Now m is on its own on one side, and thus we have made it the subject of the formula.

Example: Rearrange the formula for the area of a circle to make r the subject.

Firstly, recall that the formula for the area of a circle is

Now, the square in there makes the situation slightly different, and we're going to make sure that the square is the last thing that we deal with (this is another good rule of thumb to follow). So, dividing both sides of the equation by \pi, we get

\dfrac{A}{\pi}=r^2

Now, r is on its own on one side but it's not technically the subject, since it is being squared. So, if we now square root both sides of the equation, we get

\sqrt{\dfrac{A}{\pi}}=r

This completes the process of making r the subject of the formula.

Example: Rearrange the formula H=2R-gR to make R the subject.

This is different to what we've seen so far in that there are two instances of R - the thing we want to make the subject. This is not helpful, obviously, since we need there to be only one R, but there is a nice way out of this conundrum, and that is to factorise the terms involving an R.

Both of the terms on the right-hand side of the equation have a R in them, so if we take out a factor of R from them both, we get

Now, there's only one R. Much better. Then, if we divide by (2-g) (and yes, we divide by the whole thing in one go, since it's the whole that is being multiplied by R), we get

Thus, we have made R the subject of the equation.

We've gone through a few typical examples, now you can have a go at the questions below for a few more.

# data[].attributes.attachment_link.title
Rearranging Formulas - GCSE Maths Revision | GCSE Maths Worksheets

# data[].attributes.attachment_link.description
A formula is a mathematical relationship between different quantities that is expressed with algebra. For example, one formula for speed is distance divided by t ime, which we express like In this case, we say s (speed) is the subject of the formula.

# data[].attributes.attachment_link.readable_text
What is an Equation?

An equation says that two things are equal. It will have an equals sign "=" like this:

That equations says: what is on the left (x + 2) is equal to what is on the right (6)

So an equation is like a statement " this equals that"
(Note: this equation has the solution x=4, read how to solve equations.
What is a Formula?

A formula is a fact or rule that uses mathematical symbols.

It will usually have:

an equals sign (=)

two or more variables (x, y, etc) that stand in for values we don't know yet

It shows us how things are related to each other.

Example: The formula for finding the volume of a box is:

V = lwh

V stands for volume, l for length, w for width, and h for height.

When l=10, w=4, and h=5, then:

V = 10 × 4 × 5 = 200

These are all equations, but only some are formulas:

Without the Equals

Sometimes a formula is written without the "=":

Example: The formula for the volume of a box is:
lwh
But in a way the "=" is still there, because we can write V = lwh if we want to.

Subject of a Formula

The "subject" of a formula is the single variable (usually on the left of the "=") that everything else is equal to.

Example: in the formula

"s" is the subject of the formula

Changing the Subject

A very powerful thing that Algebra can do is to "rearrange" a formula so that another variable is the subject.

Example: Rearrange the volume of a box formula (V = lwh) so that the width is the subject

So if we want a box with a volume of 12, a length of 2, and a height of 2, we can calculate its width:

# data[].attributes.attachment_link.description
An equation says that two things are equal. It will have an equals sign "=" like this: That equations says: what is on the left (x + 2) is equal to what is on the right (6) So an equation is like a statement " this equals that" (Note: this equation has the solution x=4, read how to solve equations.

# data[].attributes.attachment_link.title
BBC Bitesize - KS3 Maths - Formulae - Revision 1

# data[].attributes.attachment_link.description
Learn and revise algebraic terms and constructing formulae with BBC Bitesize KS3 Maths

# data[].attributes.attachment_link.title
GCSE Maths - Using Formulae (Substituting into and writing formula) Algebra Higher and Foundation

# data[].attributes.attachment_link.description
All videos can be found at www.m4ths.com and www.astarmaths.com These videos were donated to the channel by Steve Blades of maths247 'fame'. Please share via twitter or facebook if you find them helpful. Designed for the Edexcel spec but applicable to AQA, OCR,MEI and WJEC.