Algebraic Fractions

Tutorial Videos

Dividing Algebraic Expressions

Corbett Maths Dividing Algebraic Expressions

Online Platforms (with Videos & Exercises)

Activities & Resources

• Go Teach Maths
  • Simplifying Expressions: Dividing
• variationtheory.com
  • Simplifying algebraic fractions (basic)✦

Worksheets

• Dr Austin Maths
  • Simplifying Expressions by Dividing Fill in the Blanks (Word | PDF | Answers)
  • Multiplication and Division Fill in the Blanks (Word | PDF | Answers✦)
  • Simplifying Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Simplifying Practice Strips (Word | PDF | Answers)
  • Simplifying Odd One Out (Word | PDF✦ | Answers✦)
  • Simplifying Pixel Picture (Word | PDF | Answers)
• Corbettmaths
  • Dividing Terms Practice Questions & Solutions
  • Dividing Terms Worksheet & Solutions
• Access Maths
  • Simplifying Algebraic Fractions 1 Fluency & Reasoning Sheet
• Pret Homework (Jo Morgan)
  • Simplifying Algebraic Fractions✦ (Jo Morgan, docx)

Dr Frost Video

Key Skill – Divide algebraic terms.

K150: Divide Algebraic Terms.

Key Skill – Divide algebraic terms with powers.

K151: Divide Algebraic Terms With Powers.

Dr Frost Slides & Activities

• All in one summary sheet

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 192c: Divide an algebraic term by an algebraic term with coefficient of 1 (maximum power of 2).
• 192d: Divide algebraic terms with positive coefficients (maximum power of 2).
• 192e: Divide algebraic terms with negative coefficients (maximum power of 2).
• 194e: Divide algebraic terms with powers.
• 387a: Simplify a factorised algebraic fraction.
• 192: Exam Practice: Dividing single algebraic terms (no index laws)
• 194: Exam Practice: Algebraic index laws (basic)
• 387: Exam Practice: Simplifying single algebraic fractions by cancelling common factors

Tutorial Videos

Simplifying Algebraic Fractions

Corbett Maths Simplifying Algebraic Expressions

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Simplifying algebraic fractions: Videos & practice

Activities & Resources

• Pixi Maths
  • Simplifying Algebraic Fractions ppt (Slides 1-7)
• Andy Lutwyche
  • Simplifying Codebreaker
  • Simplifying Fully Codebreaker
• Miss Konstantine (MathsHKO)
  • Factors and Factorising (True or False)
• Math = Love (Sarah Carter)
  • Killing Cats Poster
  • Simplifying Rational Expressions Notes
• Interactive Maths
  • Simplifying Algebraic Fractions: Video
• Go Teach Maths
  • Simplifying Rational Expressions With Factorisation
  • Simplifying Rational Expressions Using The Difference of Two Squares
• Mr Thompson Maths
  • Ordering algebraic fractions✦
  • Simplifying Algebraic Fractions – Deliberate Practice✦
• Dr Austin Maths
  • Simplifying Algebraic Fractions Match-Up✦ (answers✦)
• #TypedUp
  • Simplification of Fractions by Factors II✦ (typed up by @mathsbox1)
• Ticktock Maths
  • Simplifying Algebraic Fractions lesson (slides)

Worksheets

• Corbettmaths
  • Algebraic Fractions Practice Questions (Q16-18) & Solutions
  • Simplifying Algebraic Fractions Worksheet & Solutions
  • Algebraic Fractions AQA Level 2 (Q1-6) Practice Questions & Solutions
• Maths 4 Everyone
  • Simplifying by Factorising Topic Review
  • Simplifying Algebraic Fractions GCSE Questions and Solutions
• Dr Austin Maths
  • Simplifying Match-Up (Word | PDF | Answers)
• Access Maths
  • Simplifying Algebraic Fractions 2 Fluency & Reasoning Sheet
• @taylorda01
  • Simplifying algebraic fractions by factorising questions✦ (answers✦)
• 1st Class Maths
  • Algebraic Fractions (simplifying)✦ (answers✦)
• MadAsMaths (T. Madas)
  • Algebraic Fractions Simplifying Rational Expressions Q1–5
• Starting Points Maths
  • Algebraic Fractions: Attending to Simplification
• Mr Morley Maths
  • Simplifying Algebraic Fractions: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme

Dr Frost Video

Key Skill – Simplify algebraic fractions where factorisation of one of the top/bottom is required.

K412: Simplify Algebraic Fractions Where Factorisation of One of the Numerator or Denominator is Required.

Key Skill – Simplify algebraic fractions where factorisation of both numerator/denominator required.

K413: Simplify Algebraic Fractions Where Factorisation of Both the Numerator and Denominator is Required.

Dr Frost Slides & Activities

• Dr Frost Slides (4)

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 387b: Simplify algebraic fractions where factorising out a common term in one of the numerator or denominator is required.
• 387c: Simplify algebraic fractions where factorising out a common term in both the numerator and denominator is required.
• 387d: Simplify algebraic fractions where factorisation of a simple quadratic on the numerator or denominator is required.
• 387e: Simplify algebraic fractions where factorisation of a simple quadratic on both the numerator and denominator is required.
• 387f: Simplify algebraic fractions where factorisation of a non-monic quadratic expression on the numerator or denominator is required.
• 387g: Simplify algebraic fractions where factorisation of a non-monic quadratic expression on both the numerator and denominator is required.
• 387h: Simplify algebraic fractions where one factorised term is a negative of another.
• 387: Exam Practice: Simplifying single algebraic fractions by cancelling common factors

Tutorial Videos

Multiplying Algebraic Fractions

Corbett Maths Multiplying Algebraic Fractions

Dividing Algebraic Fractions

Corbett Maths Dividing Algebraic Fractions

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Multiplying & dividing algebraic fractions: Videos & practice

Activities & Resources

• Pixi Maths
  • Simplifying Algebraic Fractions ppt (Slides 8-13)
• Math = Love (Sarah Carter)
  • Complex Fractions Organiser
  • Complex Fractions Notes
  • Multiplying & Dividing Notes
• Interactive Maths
  • Multiplying & Dividing Algebraic Fractions: Video
• Go Teach Maths
  • Multiplying & Dividing Algebraic Fractions
• BossMaths
  • A4f Simplifying, Multiplying & Dividing Algebraic Fractions (Parts 2 & 3 multiplying and dividing; videos)
• Ticktock Maths
  • Multiplying and Dividing Algebraic Fractions lesson (slides)

Worksheets

• Dr Austin Maths
  • Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Practice Strips (Word | PDF | Answers)
  • More Practice Strips (Word | PDF | Answers)
• Corbettmaths
  • Algebraic Fractions Practice Questions (Q9-15) & Solutions
  • Multiplying Algebraic Fractions Worksheet & Solutions
  • Dividing Algebraic Fractions Worksheet & Solutions
  • Algebraic Fractions AQA Level 2 (Q7-16) Practice Questions & Solutions
• Pixi Maths
  • Multiply Divide Algebraic Fractions RAG
• Access Maths
  • Multiplying & Dividing Algebraic Fractions: Multiplying (Fluency & Reasoning) | Dividing (Fluency & Reasoning)
• MadAsMaths (T. Madas)
  • Algebraic Fractions Multiplication & Division Q1–3
• Mr Morley Maths
  • Multiplying and Dividing Algebraic Fractions: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme

Dr Frost Video

Key Skill – Multiply algebraic fractions with single terms on the numerators and denominators.

K409: Multiply Algebraic Fractions With Single Terms on the Numerators and Denominators.

Key Skill – Divide algebraic fractions with single terms on the numerators and denominators.

K410: Divide Algebraic Fractions With Single Terms on the Numerators and Denominators.

Dr Frost Slides & Activities

• All in one summary sheet

Extra Questions

• Dr Frost Questions (no factorising required)

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 388a: Multiply algebraic fractions with single terms on the numerators and denominators.
• 388b: Divide algebraic fractions with single terms on the numerators and denominators.
• 388c: Multiply algebraic fractions with bracketed expressions on the numerators and denominators.
• 388d: Divide algebraic fractions with bracketed expressions on the numerators and denominators.
• 388e: Multiply algebraic fractions requiring prior simple factorisation.
• 388f: Divide algebraic fractions requiring prior simple factorisation.
• 388g: Multiply algebraic fractions requiring prior factorisation including monic quadratic expressions.
• 388h: Divide algebraic fractions requiring prior factorisation including monic quadratic expressions.
• 388i: Multiply algebraic fractions requiring prior factorisation, including non-monic quadratic expressions.
• 388j: Divide algebraic fractions requiring prior factorisation, including non-monic quadratic expressions.
• 388: Exam Practice: Multiplying and dividing algebraic fractions

Further Practice

• Practise Questions (may include angles in a triangle and on a straight line)

Tutorial Videos

Adding Algebraic Fractions

Corbett Maths Adding Algebraic Fractions (Up to 2:52)

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Adding & subtracting algebraic fractions: Videos & practice

Activities

• Andy Lutwyche
  • Codebreakers
  • Matching
• Go Teach Maths
  • Adding & Subtracting Algebraic Fractions
• BossMaths
  • A4g Adding & Subtracting Algebraic Fractions

Worksheets

• Corbettmaths
  • Algebraic Fractions Worksheet (Q1 & 3) & Solutions
• Maths 4 Everyone
  • Addition and Subtraction Topic Review (Top Row Only)
• Miss Konstantine (MathsHKO)
  • Algebraic Fractions✦
• Access Maths
  • Adding & Subtracting Algebraic Fractions Fluency & Reasoning Sheet

Dr Frost Video

Key Skill – Add and subtract algebraic fractions with integer denominator.

K408: Add and Subtract Algebraic Fractions With Integer Denominators.

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 389a: Add and subtract algebraic fractions with integer denominators and single terms on the numerators.
• 389b: Add algebraic fractions with integer denominators and linear expressions on the numerators.
• 389c: Subtract algebraic fractions with integer denominators and linear expressions on the numerators.
• 389: Exam Practice: Adding and subtracting algebraic fractions (no factorisation of denominators required)

Further Practice

• Practise Questions

Tutorial Videos

Adding Algebraic Fractions

Corbett Maths Adding Algebraic Fractions (From 2:52)

Online Platforms (with Videos & Exercises)

Activities

• Pixi Maths
  • Simplifying Algebraic Fractions ppt (Slides 14 Onwards)
• Andy Lutwyche
  • Clumsy Clive
  • Exploding
  • Codebreaker 4
  • Crack The Safe
  • Defuse The Bomb
  • Codebreaker
• Math = Love (Sarah Carter)
  • Common Denominators activity
  • Adding & Subtracting Foldable
  • Adding & Subtracting Notes
• Acute Learning Problem Pairs
  • Level 2 FM: Algebraic Fractions as PowerPoint or PDF
• Interactive Maths
  • Adding & Subtracting Algebraic Fractions: Video
• Ticktock Maths
  • Adding and Subtracting Algebraic Fractions lesson (slides)

Worksheets

• Dr Austin Maths
  • Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Practice Strips (Word | PDF | Answers)
  • Match-Up (Word | PDF✦ | Answers✦)
  • Mixed Operations Practice Strips (Word | PDF | Answers)
  • More Practice Strips (Word | PDF | Answers)
• Corbettmaths
  • Algebraic Fractions (Everything up to this point) Practice Questions & Solutions
  • Algebraic Fractions Worksheet (Q2 & 4) & Solutions
• Maths 4 Everyone
  • Addition and Subtraction Topic Review
• Pixi Maths
  • Add Subtract Algebraic Fractions RAG
• 1st Class Maths
  • Algebraic Fractions (operations)✦ (answers✦)
• MadAsMaths (T. Madas)
  • Algebraic Fractions Adding Algebraic Fractions Q1–10
• Mr Morley Maths
  • Adding and Subtracting Algebraic Fractions: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme

Dr Frost Video

Key Skill – Add algebraic fractions with algebraic linear denominators.

K605: Add Algebraic Fractions With Algebraic Linear Denominators.

Key Skill – Subtract algebraic fractions with algebraic linear denominators.

K606: Subtract Algebraic Fractions With Algebraic Linear Denominators.

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 389d: Add or subtract algebraic fractions with algebraic denominators made up of single terms.
• 389e: Add algebraic fractions with algebraic linear denominators.
• 389f: Subtract algebraic fractions with algebraic linear denominators.
• 389g: Add or subtract a mixture of fractional and non-fractional algebraic terms.
• 389h: Add and/or subtract three algebraic fractions all with different denominators. (not yet active)
• 389i: Add or subtract algebraic fractions with a factorised quadratic expression in one denominator.
• 389j: Combine multiplication or division of algebraic fractions with an addition or subtraction.
• 390a: Add or subtract algebraic fractions where non-quadratic factorising is required (changing one denominator).
• 390b: Add or subtract algebraic fractions where non-quadratic factorising is required (changing two denominators).
• 390c: Add or subtract algebraic fractions where quadratic factorising is required (changing one denominator).
• 390d: Add or subtract algebraic fractions where quadratic factorising is required (changing two denominators).
• 390e: Add or subtract three fractions requiring prior factorisation.
• 390f: Combine multiplication or division of algebraic fractions, requiring prior factorisation of the denominators, with an addition or subtraction.
• 389: Exam Practice: Adding and subtracting algebraic fractions (no factorisation of denominators required)
• 390: Exam Practice: Adding and subtracting algebraic fractions, requiring prior factorisation of the denominators

Further Practice

• Practise Questions

Tutorial Videos

Equations involving algebraic fractions – Corbettmaths

Corbett Maths Equations Involving Algebraic Fractions

Equations Cross Multiplying – Corbettmaths

Corbett Maths Equations Cross Multiplying

Online Platforms (with Videos & Exercises)

Activities

• Don Steward
  • Equations and Equivalent Fractions
• Transum
  • Equations with Fractions
• Interactive Maths
  • Solving Equations with Algebraic Fractions: Video
• Go Teach Maths
  • Solving Linear Rational Equations

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Practice Strips (Word | PDF | Answers)
  • Solving Equations with Fractions (Unknowns in the Denominator) Practice Grid (Word | PDF | Answers)
  • Fractional Coefficients Practice Grid (Word | PDF | Answers)
• Corbettmaths
  • Equations Involving Fractions Practice Questions & Solutions
  • Equations Involving Fractions Worksheet & Solutions
  • Cross Multiplication Practice Questions & Solutions
  • Cross Multiplication Worksheet & Solutions
  • Algebraic Fractions Worksheet (Q5 & some of 6) & Solutions
  • Algebraic Fractions AQA Level 2 (Q17-19) Practice Questions & Solutions
• Maths 4 Everyone
  • Unknown on Both Sides (Mixed) Extend
  • Algebraic Fractions Equations Topic Review
• Access Maths
  • Solving Algebraic Fractions Fluency & Reasoning Sheet
• MadAsMaths (T. Madas)
  • Equations Exam Questions I Q31 (difficulty 3 of 5)
  • Equations Basic Techniques Fractional Equations Q1–4
• Pret Homework (Rachel Mahoney)
  • Solving Equations with Fractions (Rachel Mahoney, pptx)

Dr Frost Video

Key Skill – Solve an equation with one fraction equals to a linear expression.

K371: Solve an Equation With One Fraction Equals to a Linear Expression.

Key Skill – Solve an equation with one fraction equal to another fraction.

K373: Solve an Equation With One Fraction Equal to Another Fraction.

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 258d: Solve equations of the form ax+b/c=d/e
• 258l: Solve equations of the form ax+b/c=dx+e/f
• 258p: Solve equations of the form ax+b/c+dx+e/f=gx+h
• 258q: Solve equations of the form ax+b/c=dx+e/f+gx+h
• 258: Exam Practice: Solving linear equations involving fractions

Further Practice

• Practise Questions

Tutorial Videos

Equations: Advanced Algebraic Fractions

Corbett Maths Equations: Advanced Algebraic Fractions

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Rational (algebraic fraction) equations: Videos & practice

Activities

• Andy Lutwyche
  • Defuse The Bomb – Solving Quadratics
• Math = Love (Sarah Carter)
  • Solving Rational Equations Foldable
• Don Steward
  • Equations Involving Algebraic Fractions
• Go Teach Maths
  • Solving Quadratic Rational Equations: Without Coefficients
  • Solving Quadratic Rational Equations: With Coefficients
• Ticktock Maths
  • Solving Equations with Algebraic Fractions lesson (slides)

Worksheets

• Corbettmaths
  • Solving Equations: Fractional (Advanced) Practice Questions & Solutions
  • Equations: Advanced Fractional Worksheet & Solutions
  • Algebraic Fractions Worksheet (Q6) & Solutions
  • Algebraic Fractions AQA Level 2 (Q20-23) Practice Questions & Solutions
• Maths 4 Everyone
  • Algebraic Fractions Equations Topic Review (Last Row)
  • Equations with Algebraic Fractions GCSE Questions and Solutions
• 1st Class Maths
  • Algebraic Fractions (equations)✦ (answers✦)
• MadAsMaths (T. Madas)
  • Algebraic Fractions Exam Questions Q3–4, 10–11, 13–14, 21–22 (difficulty 2–3 of 5)
  • Equations Exam Questions I Q1, 7, 11, 13, 15–16, 29–30, 53 (difficulty 2–4 of 5)
  • Identities Q25 (difficulty 4 of 5)
  • Equations Basic Techniques Fractional Equations Q5–11

Dr Frost Video

Key Skill – Solve an equation with fractions leading to a quadratic equation.

K614: Solve an Equation With Fractions Leading to a Quadratic Equation.

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 258e: Solve equations of the form a/bx=c
• 258f: Solve equations of the form a/x^k=b or fracasqrt[k]x=b
• 258g: Solve equations of the form a/bx+c=d
• 258h: Solve equations of the form a/bx+c=d
• 258m: Solve equations of the form ax/b=c/dx^k
• 258n: Solve equations of the form ax+b/cx=d
• 258o: Solve equations of the form ax+b/cx+d=e
• 462a: Solve an equation of the form ax + b/x + c = 0
• 462b: Solve an equation with a single algebraic fraction on one side of the equation, leading to a quadratic equation.
• 462c: Solve an equation of the form ax+b/cx+d = ex+f/gx+h
• 462d: Solve an equation of the form a/bx+c ± d/ex+f = g
• 462e: Solve an equation with fractions requiring prior factorisation of one of the fractions.
• 462f: Form and solve an equation with algebraic fractions on each side given algebraic terms in a geometric sequence. (not yet active)
• 462g: Form and solve a quadratic equation involving fractions from context. (not yet active)
• 258: Exam Practice: Solving linear equations involving fractions
• 462: Exam Practice: Solving equations involving fractions that lead to a quadratic equation

Further Practice

• Practise Questions

Acute Learning Problem Pairs

• Algebraic Fractions as PowerPoint or PDF

Worksheets

• Dr Austin Maths
  • Revision Practice Grid (Word | PDF✦ | Answers✦)
• Mathshelper (Jon Stone)
  • Algebraic Fractions✦
• MathedUp
  • Algebraic Fractions: Worksheet · Practice · Quiz · Exam · Question Gallery
  • Algebraic Fractions: Worksheet · Practice · Quiz · Question Gallery
• Maths Genie
  • Algebraic Fractions: Booklet · Worksheet · Solutions · Lesson · Topic page
• Physics & Maths Tutor
  • Expressions Involving Surds and Algebraic Fractions: Notes · Worksheet · Solutions
• MME
  • Algebraic Fractions (exam style): Questions | Answers  •  Algebraic Fractions (drill): Questions | Answers

Activities

• Math = Love (Sarah Carter)
  • Complex Fraction task
  • Rational Expressions Question Stack
• Intervention Tasks
  • Find the Mistake + Your Turn to Try (PDF)
• Don Steward
  • Algebraic Fractions from Numbers✦
• Transum
  • Algebraic Fractions
• Go Teach Maths
  • Mixed Arithmetic With Algebraic Fractions
• CP3 Maths (cparkinson3)
  • Collection of four lessons on algebraic fractions✦