The document discusses the "onion skin" method for transposing (rearranging) algebra formula equations. It explains that with this method, you draw concentric "skins" or circles around the equation, starting with the variable you want to isolate. You then work inward by applying the opposite operations to each term or part of the equation until the desired variable is alone on one side. It provides examples of using this method to transpose different types of equations, including ones with fractions, exponents, multiple variables, and square roots.

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2. In a previous lesson we showed how to
Solve Equations using the work down
through the “Onion Skins” Method.
In this lesson we will review the use of the
“Onion Skin” method, and show how it can
be applied to Transposing (or rearranging)
Algebra Formula Equations.

3. • Turn the whole equation into an “onion”, building skins
outwards from the letter variable in the center.
• These onion skins are created by first drawing a centre
skin around the letter variable we are solving for.
• We then create skins outwards from here, following the
BODMAS/PEMDAS order of operations.
• The outermost skin should enclose the entire equation.
• Now “Peel” inwards doing opposite operations.
• Apply these opposites, starting from the single number
item which is contained in the outermost onion skin.
• Keep applying opposites until we reach the letter
variable, that is in the center of the Onion.

4. Solving Equations Using Onion Skins
Solve the Equation : n + 5 = 7
To solve the Equation work from the biggest outer
skin, inwards through the smaller skins, applying
opposites, until we reach the letter variable center.
n + 5 = 7
Solution for n is: n = 7 - 5 = 2 n = 2
Draw the first skin around “n”,
and then draw more skins
radiating outwards, until the
whole algebra equation is
circled by the final outer skin.

5. Transposing a Formula Using Onion Skins
Transpose : n + m = k to make “n” the subject
To rearrange the Formula, work from the biggest outer
skin, inwards through the smaller skins, applying
opposites, until we reach the required subject letter “n” at the
center.
n + m = k
n = k - m so “n” formula is : n = k - m
Eg. We need to rearrange n + m = k to convert it to an n = ? formula
Because “n” is the desired subject,
draw a skin around “n” first,
and then draw more skins
radiating outwards, until
the whole formula equation is
circled by the final outer skin.

6. Solving a 2 Step Equation Using Onion Skins
Solve the Equation : 2h + 3 = 11
To solve the Equation work from the biggest outer
skin, inwards through the smaller skins, applying
opposites, until we reach the letter variable.
2h + 3 = 11
Solution for h is: h = 11 - 3 2 h = 4
Draw the first skin around “h”,
and then draw more skins
radiating outwards, until the
whole algebra equation is
circled by the final outer skin.

7. Transposing a Formula Using Onion Skins
Transpose : v = u + at to make “a” the subject
Eg. We need to rearrange v = u + at to convert it to an a = ? formula
v = u + at
Because “a” is the desired subject,
draw a skin around “a” first,
and then draw more skins
radiating outwards, until
the whole formula equation is
circled by the final outer skin.
To rearrange the Formula, work from outer skin, inwards, applying
opposites, until we reach the required subject letter “a” at the center.
a = v - u t a = v - u
t
v - u
t
a =

8. Л h
Transposing a Squared Formula
Transpose to make “r” the subject
V = Л r2
h
Because “r” is the desired subject,
draw the skins radiating outwards
from “r”.
Note that the squaring of “r” is a
skin whose opposite is square root.
r = V Л h r = V
V = Лr2
h
Л h
V
r =

9. v2
Transposing a Formula with a Fraction
Rearrange to make “m” the subject
E = m v2 Make the 1/2 a “2”
in the bottom line of
the algebra fraction.
m = E x 2 v2
E = ½ mv2
2E
2
m =

10. 2E
m
Transposing an Exponent and a Fraction
Rearrange to make “v” the subject
E = m v 2
Make the 1/2 a “2”
in the bottom line of
the algebra fraction.
Note that the squaring of
“r” is a skin whose opposite
is square root.
m = E x 2 m
E = ½ mv2
2
m =

11. (100-D)
100S
Transposing Selling Price to Marked Price
Rearrange to an “M”= Formula
S = M (100 – D)
M = S x 100 (100-D)
S = M(100-D) / 100
100
M =

12. 3
hk - n
Transposing a Multi-Variable Formula
Rearrange to make an “c” the subject
c = k x h - n 3
(3c + n) / h = k
3c + n = k
h
c =

13. h 2
3
Transposing a Square Root Formula
Rearrange to make “k” the subject
h = 3 k
Note that the square root
is a skin whose opposite is
squaring.
k = h 3 Squared x L
h = 3 k/L
L
k = L

14. D
Transposing a Subject Denominator
Rearrange to make “v” the subject
D = m
When our Subject is in the bottom, Flip both sides first.
v = 1 x m
D = m/v
m
v
v =
1
1 = v
mD
D

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