Simplifying Algebraic Fractions (Cambridge (CIE) IGCSE International Maths): Revision Note

Exam code: 0607

Written by: Jamie Wood

Reviewed by: Dan Finlay

Updated on 7 June 2024

Simplifying Algebraic Fractions

What is an algebraic fraction?

A fraction with a numerator or denominator (or both) that contains an algebraic term is an algebraic fraction
For example
- $\frac{x}{4}$ or $\frac{48}{y^{2}}$ or $\frac{2 p^{3}}{4 p^{2} + 1}$

You need to be able to simplify basic algebraic fractions
- Like $\frac{x^{5}}{x^{2}}$ or $\frac{3}{6 p}$

How do I simplify algebraic fractions?

To simplify any powers (indices) it helps to write out the multiplications in full
- $\frac{n^{5}}{n^{2}} = \frac{n \times n \times n \times n \times n}{n \times n}$
Terms can then be "cancelled"
- $\frac{n^{5}}{n^{2}} = \frac{n \times n \times n \times n \times n}{n \times n} = n \times n \times n = n^{3}$
- $\frac{m^{2}}{m^{3}} = \frac{m \times m}{m \times m \times m} = \frac{m \times m}{m \times m \times m} = \frac{1}{m}$

Any numerical fractions can be simplified as usual
- $\frac{4}{12} = \frac{2}{6} = \frac{1}{3}$
You also need to be familiar with alternative ways of writing fractions
- $\frac{3 x}{4}$ is the same as $3 \times \frac{x}{4}$ or $\frac{3}{4} x$ or $0.75 x$
- $\frac{5}{6 y}$ is the same as $5 \times \frac{1}{6 y}$ or $\frac{5}{6} \times \frac{1}{y}$

Worked Example

Simplify the following expressions.

(a) $\frac{4 p^{3}}{12 p^{6}}$

Separate the numerical part from the algebraic part

$\frac{4}{12} \times \frac{p^{3}}{p^{6}}$

Simplify the numerical fraction

$\frac{1}{3} \times \frac{p^{3}}{p^{6}}$

Write out the algebraic terms in full

$\frac{1}{3} \times \frac{p \times p \times p}{p \times p \times p \times p \times p \times p}$

Cancel any terms that appear in both the numerator and denominator

$\frac{1}{3} \times \frac{p \times p \times p}{p \times p \times p \times p \times p \times p}$

$\frac{1}{3} \times \frac{1}{p \times p \times p}$

Simplify

$\frac{1}{3} \times \frac{1}{p^{3}}$

Combine into one term

$\frac{1}{3 p^{3}}$

(b) $\frac{32 q^{5}}{8 q^{2}}$

Separate the numerical part from the algebraic part

$\frac{32}{8} \times \frac{q^{5}}{q^{2}}$

Simplify the numerical fraction

$4 \times \frac{q^{5}}{q^{2}}$

Write out the algebraic terms in full

$4 \times \frac{q \times q \times q \times q \times q}{q \times q}$

Cancel any terms that appear in both the numerator and denominator

$4 \times \frac{q \times q \times q \times q \times q}{q \times q}$

$4 \times q \times q \times q$

Simplify

$4 q^{3}$

You've read 0 of your 5 free revision notes this week

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Test yourself

Did this page help you?

Previous:Collecting Like TermsNext:Algebraic Roots & Indices

Simplifying Algebraic Fractions (Cambridge (CIE) IGCSE International Maths): Revision Note

Simplifying Algebraic Fractions

What is an algebraic fraction?

How do I simplify algebraic fractions?

You've read 0 of your 5 free revision notes this week

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Number

Types of Numbers

Types of Numbers

Multiples, Factors & Primes

Squares, Cubes & Roots

Reciprocals

Reading & Ordering Numbers

Place Value

Negative & Directed Numbers

Ordering Numbers

Operations with Numbers & Decimals

Mathematical Symbols

Addition & Subtraction

Multiplication & Division

Order of Operations (BIDMAS/BODMAS)

Operations with Decimals

Sets

Set Notation & Venn Diagrams

Prime Factors, HCF & LCM

Prime Factor Decomposition

HCF & LCM

Powers, Roots & Standard Form

Powers & Roots

Laws of Indices

Converting to & from Standard Form

Operations with Standard Form

Introduction to Fractions

Introduction to Fractions

Fractions of Amounts

Equivalent & Simplified Fractions

Mixed Numbers & Improper Fractions

Operations with Fractions

Adding & Subtracting Fractions

Multiplying & Dividing Fractions

Percentages

Percentages of Amounts

Percentage Increases & Decreases

Percentage Change

Simple & Compound Interest

Simple Interest

Compound Interest

Converting Fractions, Decimals & Percentages

Converting Fractions, Decimals & Percentages

Ordering Fractions, Decimals & Percentages

Ratio & Proportion

Introduction to Ratios

Equivalent & Simplified Ratios

Sharing in a Ratio

Problem Solving with Ratios

Direct & Inverse Proportion

Money Calculations

Money Calculations

Time, Currency & Units

Time

Exchange Rates

Converting between Units

Squared & Cubic Units

Compound Measures & Speed

Speed

Compound Measures

Rounding & Estimation

Rounding to a Given Place Value

Rounding to Significant Figures

Estimation

Algebra & Sequences

Introduction to Algebra

Algebraic Notation

Algebraic Vocabulary

Substitution

Collecting Like Terms

Simplifying Algebraic Fractions

Simplifying Algebraic Fractions

Algebraic Roots & Indices