1.04 Formulas

Changing the subject of a formula is an important skill to learn. It can come in handy when you know the value of one algebraic symbol but not another. The subject of an equation is the pronumeral that is by itself on one side on the equals sign and it usually is at the start of the formula.

For example, in the formula A=pb+y, A is the subject because it is by itself on the left hand side of the equals sign.

We have been changing the subject of equations when we learnt to solve equations because we took steps to get the pronumeral by itself, for example we made x the subject of equations. We can make any term in an equation the subject, even if it starts off as the denominator of a fraction. When we're changing the subject of a formula, we often have more than one pronumeral but we still use a similar process.

• Group any like terms

• Simplify using the inverse of addition or subtraction

• Simplify further by using the inverse of multiplication or division

• Other inverse operations might be needed like square and square root

Examples

Out in the real world all sorts of amazing relationships play out every day: Air temperatures change with ocean temperatures; Populations of species rise and fall depending on seasons, food availability and the number of predators; The surface area of a human body can even be measured fairly accurately according to your height and weight.

One of the most powerful things about mathematics is its ability to describe and measure these patterns and relationships exactly. Given a mathematical formula for the relationship between, say, the weight of a patient and how much medication they should be given, we can find one quantity by substituting a value for the other.

We have come across so many different formulas in mathematics that allow us to measure quantities such as area, volume, speed, etc. Let's have a look at the process of substituting values into these formulas to find a particular unknown.

Examples