Rearranging Equations

Let’s say you get a question like this in the exam:

Make a the subject of b(a - ab) + 4(ab + a) = 2b

a) a = b(1 - b) ÷ 2b + 4
b) a = 2b ÷ (b(1 - b) + 4(b + 1))
c) a = (1 - b)(b + 1)
d) a = 2b(1 - b)(b + 4)

To answer this question, we need to get a on its own on one side of the equation.

To begin with, we can take a common factor of a out of the term b(a - ab) to get ab(1 - b).

We do this by dividing both terms by a (a ÷ a = 1, ab ÷ a = b), meaning that (a - ab) = a(1 - b).

Similarly, we can take a common factor of a out of the term 4(ab + a) to get 4a(b + 1). The left hand side of the equation now becomes ab(1 - b) + 4a(b + 1).

Next, we can take a common factor of a out of the entire left hand side of the equation. Both terms are multiplied by a, so if we divide out the a we get a(b(1 - b) + 4(b + 1)).

Our equation now reads a(b(1 - b)+ 4(b + 1)) = 2b.

Finally, since the left hand side of the equation is a term (b(1 - b) + 4(b + 1)) multiplied by a, we can divide both sides of the equation by this term to get a on its own. This gives us a result of a = 2b ÷ (b(1 - b) + 4(b + 1)), which is option (b). To recap:

1. Get a on its own to define the relationship between a and b
2. Simplify the expression as much as possible

Example Question/s

Watch video for explanation of the following question/s:

The formula for area is l x w (length x width).

Rearrange this formula (A = lw) to solve for l if A = 25 squared cm and width is 15 cm.

Your answer __________

If P = ½yz², rearrange to so that:

y is the subject. Your answer __________

z is the subject. Your answer __________

Key Rules to remember:

• Simplify the expression first to make it easier to rearrange.
• To rearrange, isolate out the subject of the formula by doing the inverse on both sides.

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