Åk 6–9

4.1 Calculating with Formulas and Functions
It is important to be able to figure out the unknown variable in a function if you know the others. This you do by taking out the unknown variable.

We will look at two examples of formulas where you can do a little different calculation depending on which variables you know:

This is a well known formula which you use to calculate speed.

v: speed (v comes from the word velocity.)
d: distance
t: time

The formula looks like this:

 v = d t

If you know the distance and the time, then it is not a problem to calculate the speed.

Example:

d = 240 km
t = 3 h

 v = 240 = 80 km/h 3

If you know the speed and the time, then it is not a problem to calculate the distance.

v = 70 km/h
t = 2.5 h

The variable that you don’t know is d (the distance).  How do you calculate the distance?

We begin by taking out the distance from the formula:

 d · t v · t = We multiply both sides with t. t

d
= v · t

Then we get:
d =
70 · 2.5
d = 175 km  A formula we often use in geometry is the formula for the rectangle’s perimeter.

 h: height b: base P: perimeter P = 2h + 2b If you know the base and the height of the rectangle, it is no problem to calculate the perimeter.  But how do you do it if you only know the perimeter and the base and want to calculate the rectangle’s height?  We take an example:

P = 38 cm
b = 9 cm

We put these in the formula:

38 = 2h + 2 · 9
38 = 2h + 18
38 - 18 = 2h + 18 - 18
20 = 2h
h = 10 cm

Answer: The rectangle’s height is 10 cm.  