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# 2.11.1 Manipulation of formulae

Manipulating or rearranging formulae involves the same process as manipulating or rearranging equations.

In the formula S = D / T, S is the subject of the formula. (This simply means that S stands on its own and is determined by the other parts of the formula. By convention the subject is always placed on the left-hand side of the equal sign, although S = D / T means the same as D / T = S)

To rearrange or manipulate an equation, the formula S = D / T can also be manipulated to make D or T the subject.

S = D / T

D / T = S (turning the formula around)

D = S x T (multiplying both sides of the formula by T)

Or, from D = S x T

D / S = T (dividing both sides of the formula by S)

T = D / S (turning the formula around)

## Box 6 An important note about formulae

A formula is simply an equation that states a fact or rule, such as S = D / T or Speed is equal to Distance divided by Time. The accounting equation you will learn about in Week 3, although always described as an ‘equation’ by convention, could be more accurately described as the ‘accounting formula.’

## Activity 10 Use of equations and formulae

### Part A

Solve the following algebraic equations:

1. c + 9 = 11

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c = 2

1. a - 15 = 21

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a = 36

1. d x 7 = 63

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d = 9

1. b / 13 = 13

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b = 169

### Part B

Rearrange the formula h = 3dy - r to make:

1. r the subject

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h = 3dy - r

h + r = 3dy

r = 3dy – h

1. y the subject

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