Maths Olympiad

Simplification

The process of cancelling (reducing) e.g. ,

**e.g.1 remember that exponents are subtracted
Clearing one of the most common errors, an important “cancellation” rule:

only factors may be cancelled

Factors multiply, terms add and subtract

First count terms … > 1 term means that there is only 1 factor, the whole expression.

**e.g.2 1. 1 term, 3 factors 2. 2 terms, 1 factor 3. 2 terms, 1 factor, BUT … 1 term, 2 factors 4. 1 term, 2 factors 5. 2 terms, 1 factor i.e. cannot cancel cannot cancel cannot cancel

Factorisation is usually a necessary step for simplification of a fraction

**e.g.3 1. In simplest form, no cancelling 2.

3. 4. §Exercise 1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11

Multiplication

**e.g.4

Division by fractions is the same as multiplying by the inverse fraction.

**e.g.5
**e.g.6
**e.g.7
**e.g.8
**e.g.9

NOTE: Only the fractions FOLLOWING the sign invert.

§Exercise 2

2.1 2.2 2.3 2.4 2.5 2.6

§Exercise 3

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

Addition and subtraction

In this process 2 important principles are used:

1. The numerator (top) of the fraction indicates how many? and the denominator indicates what? e.g. : what? … quarters how many? … three i.e. in the same way that 3 dogs + 7 dogs 10 dogs, e.g. ; ; BUT, as with 7 dogs + 3 cats ???, cannot be added in this form, being unlike terms.

When working with fractions, we get around this by using the second principle:

2. The numerator and denominator can be multiplied by the same factor without the value of the fraction being changed. e.g. This is summarised by writing the equal denominators as a common denominator: …

Finding the common denominator