Gcse Maths - Changing the branch of a formula

Homeschool Math Worksheets Printable - Gcse Maths - Changing the branch of a formula

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Rearranging Formulae

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Homeschool Math Worksheets Printable

Why rearrange formulae?

The recipe d = st expresses length (d), in terms of speed (s) and time (t).

It is sometimes critical to write a recipe in a different, but equivalent form.

e.g. S = d/t

What is the 'subject' of a formula?

In formulae, a single changeable appears on the Lhs of the equation.

This is called the field of the formula.

In the recipe d = st , d is the field of the formula,

whereas in s = d/t, s is the field of the formula.

The process of expressing (s) in terms of (d) and (t) is known as

rearranging or changing the field of the formula.

Example 1

Make n the field of the formula:

m = 3 n + 5

Method

Subtract 5 from both sides.

m - 5 = 3 n

Divide both sides by 3:

1/3 ( m - 5 ) = n

Rearrange so that field is on Lhs:

Solution

n = 1/3 ( m - 5 )

Exercise

1. Make t the field of the formula:

(i) y = 3 t + 5x

.........................................................

.........................................................

t =.................................

(ii) v = 3 x - 4 tz

.........................................................

.........................................................

t =.................................

(iii) s = (t/p) - 2r

.........................................................

.........................................................

t =.................................

Solutions

1. (i) t = (1/3) (y - 5x )

(ii) t = (3x - v) / 4z

(iii) t = p (s + 2r )

Required field Occurs more than Once

If the required field appears more than once in the primary formula,

we need first to accumulate the terms with the new field and then factorise.

Example

Make p the field of the formula:

r = 3 p s - 2 p

Method

Factorise the expression on the Rhs:

r = p ( 3 s - 2 )

Isolate the subject:

divide both sides of the equation by ( 3 s - 2 )

Solution

p = r /( 3 s - 2 )

Exercise

1. Make x the field of the formula:

(i) t = x y + 3 x

......................................................

...................................................

x =.....................................

(ii) u = x - 4 x z

...................................................

...................................................

x =.....................................

(iii) w = 2x - x y ^2

....................................................

...................................................

x =.....................................

2. Make m the field of the formula:

E = m v ^2 + m g h

.......................................................

m =..................................................

Solutions

1. (i) x = t / ( y + 3 )

(ii) x = u / ( 1 - 4z )

(iii) x = w / ( 2 - y^2 )

2. E = m ( 1/2 v^2 + gh )

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