Using simple formulae

Key vocabulary:

Formula - In mathematics, a formula is a fact, rule, or principle that is expressed in terms of mathematical symbols. 

We use formulae in our day to day lives without even realising It sometimes.

For example:

This is an advert for a taxi company. The cost of the taxi is £1.50 for a pickup and then £2 per mile of the journey.

We can represent this with an algebraic formula

The ‘cost’ we will label C

The amount of miles we drive we will label M

The fee will be labelled F

Therefore our Formula would look like this:

C (cost) = F (fee) + 2 x M (miles driven)

So the formula without the words would be:

C=F+2m

We can then use this formula to help us solve how much a journey will cost.

For example:

John wants to get a taxi from Manchester to Leeds. The total distance is 36 miles.

John wants to use this formula to help him find out how much it will cost

We will start with the formula

C=F+2m

Now we can start to input some information

F (fee) is £1.50 – we can put this into our formula

C=1.50 + 2m

We have replaced the F with the value 1.50

We can then replace the M with the amount of miles John will travel, 36

C=1.50 + 2 x 36

Now we are ready to solve this formula

First lets multiply 2 x 36 = 72 so our formula now looks like:

C=1.50 + 72

Our final step is to simply add 1.50 to 72 which is = 73.50

So...

C=73.50

C = £73.50

Johns total cost for this journey would be £73.50

Example 2

Here we have a rectangle

The length of the rectangle is 7cm and the width is 3cm

Tony wants to find the area of this rectangle.

He knows that to find the area he must multiply the length by the width

Tony thinks that he can make a formular that will work with any rectangle

First, he wants to swap the numbers with algebraic letters, like this:

Then, he decides to label the ‘area’ as C

Tony thinks that if you multiply the value of A by B you will always get C

Let's check this formula with another rectangle to see if Tony is right:

In this rectangle we can see that A has a value of 5cm and B has a value of 4.

Let’s use Tony’s formula to solve it:

A x B = C

First lets swap A with the value 5

5 x B = C

Then, let’s swap B with the value 4

5 x 4 = C

Now, let’s solve the question to find C

20 = C

So, the area is 20! It works!

These are both examples of simple formulae. Now watch the video to see how we can solve even more! Once you have watched the video have a go at the questions on the worksheet.