Rearranging Equations

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Mathematical Skills II
Rearranging Formulas
Pro. Ignacio Anguera
Colegio Real de Panamá

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Re-write a formula in terms of
another letter.
THE UNDERLYING PRINCIPLE
A formula is a mathematical equation containing two or
more letters.
REARRANGING
FORMULAS
You will be familiar with the formula for the area of a circle
which states:
in which case we would say that A is the subject of the
formula
A = π r2
Alternatively, we could have written the formula as:
𝑟 =
2 𝐴
𝜋
in which case we would say that r is the subject of the
formula

3. 4/27
Re-write a formula in terms of
another letter.
CHANGING THE SUBJECT OF A FORMULA
The rules are the same as when we solved equations except
we do not end up with a solution but with another formula.
REARRANGING
FORMULAS
• add or subtract the same quantity to or from both sides
• multiply or divide both sides for the same quantity
• square and square root are inverse functions (same as
cube and cube root).
Example 1: Addition/subtraction a + b = c + d
In each case, make -a- the subject of the formula
Example 2: Multiplication/division b = a·c
Whatever you do to one side, you must do to the other
side too
If you move a term from one side of the equals sign to the
other, we change the operation to do the opposite.
OR

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PRACTICE! In each case, make the letter given at the end, the subject of
the formula
d = v t v P = I2 R R y = mx + n x
A = P + I P d = m t + b b 𝑎2
+ 𝒃2
= 𝑐2 b
C = 2 π r r A =
1
2
b a b E = mc2 m
A = π r2 r P = 2l + 2w w V = π r2 h r
V =
1
3
π r2 h h A =
𝑎+𝒃
2
b m =
𝒚 𝟐
+ 𝑦1
𝑥2
+ 𝑥1
y2