Rearranging Or Transposing Formulae

Rearranging or transposing formulae
BTEOTSSSBAT:

Write down the integers which satisfy the following:
0 < x < 3
1 < x < 5
-1 < x < 2
-1 < x 2
-1 < x 2

Key terms
Equation
Expression
Formula
Rearrange
Transpose
Subject
Balance
Flow diagram

There are different ways of doing this:
balance method
flow diagram method
cross method
Look at the examples to find which method you think is the best and then use whichever method you are happiest with.

The balance method

We can think of an equation as a balance. We can do whatever we want to one side, provided we do the same to the other side.

7a + b = c

7a + b (- b) = c (- b)
7a = c – b

Cancelling the 7s on the LHS gives:

which gives us our answer!

The flow diagram method

Make a the subject 7a + b = c

To make a the ‘subject’ we have to look at a and see what happens to it: first it is multiplied by 7 and then b is added to it.

This can be drawn as a flow diagram

To rewrite the expression as a = … we can reverse the diagram and do the ‘inverse’ (opposite) operations:

Reading from the right to left we have:

c subtract b divided by 7

This can then be written in mathematical language as:

a = c – b
7

Cross method
In the cross method, every time we take something over the equals symbol we ‘reverse’ its operation (+ becomes -, - becomes +;  becomes , and  becomes  etc.)
Example: Make a the subject of 7a + b = c
So
7a + b = c take the b over and change its sign to become – b
7a = c - b
take the 7 over and change its sign to become  7
7a = c - b
a = c - bthis then gives us our answer
7

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Rearranging Or Transposing Formulae

by Steve Bishop on Jan 19, 2010

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Rearranging Or Transposing Formulae — Presentation Transcript