Teaching mathematics
Teaching mathematics

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3.4 Using multiplying factors to find an original amount given the result of a percentage change

Now consider the same problem using algebra.

The sale price of a coat is £81 and this is the result of a 10% discount. Let p be the original price of the coat.

10% discount leaves 90% or 0.9 of the price

You know that 0.9 p = 81

Divide both sides by 0.9 to get p

equation sequence p equals 81 divided by 0.9 equals 90

So, the original cost of the coat is £90.

This method can be used with much harder numbers and it is a simpler and more elegant way of reaching the solution. However, learners need to understand the method and why it works. This is known as procedural understanding. If learners do not have this procedural understanding then the method becomes a rule to be learned and there are too many such rules in mathematics if your approach is to learn rules rather than develop conceptual understanding.

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