NZ Level 6 (NZC) Level 1 (NCEA)
Algebraic fractions
Lesson

## Simplifying algebraic fractions

Simplifying algebraic fractions is just the same as simplifying fractions that are made up of numbers only. We look for the highest common factor between the numerator and the denominator in the fraction.

#### Example

##### example 1

Simplify $\frac{9e}{54}$9e54

Think: $9$9 is the highest common factor between $9e$9e and $54$54.

Do: $\frac{9e}{54}=\frac{e}{6}$9e54=e6

## Substituting values into algebraic fractions

We've looked at how to substitute values into algebraic expressions. The process is just the same when we are substituting into algebraic fractions.

#### Example

##### example 2

Evaluate: If $a=5$a=5, what is the value of $\frac{8a}{10}$8a10?

Think: After substitution, we can write this question as $\frac{8\times5}{10}$8×510

Do:

 $\frac{8\times5}{10}$8×510​ $=$= $\frac{40}{10}$4010​ $=$= $4$4

Do you remember that when we are adding or subtracting fractions, we need to have common denominators? Well the same goes for algebraic fractions. We need to find a common factor between the fractions (remember you can always multiply the denominators together to find a common factor).

### The process

1. Find a common denominator

2. Multiply the numerators by the same number as the denominators to keep the fractions equivalent

4. Simplify the fraction if possible.

#### More examples

##### Question 1

Simplify: $\frac{8m}{32}$8m32.

##### Question 2

Simplify: $\frac{17y}{20}+\frac{14y}{20}$17y20+14y20.

##### Question 3

If $m=5$m=5, what is the value of $\frac{m}{2m}$m2m?

### Outcomes

#### NA6-5

Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns

#### NA6-6

Generalise the properties of operations with rational numbers, including the properties of exponents

#### 91027

Apply algebraic procedures in solving problems