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Equations with algebraic fractions worksheet (with solutions)

Equations with algebraic fractions worksheet (with solutions)

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

27 July 2026

pdf, 91.48 KB
pdf, 91.48 KB

A worksheet on equations involving algebraic fractions. Detailed solutions are provided.

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A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

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GCSE IGCSE Maths | Percentages, Functions & Algebraic Fractions Bundle

9 GCSE/IGCSE Math worksheets on the following topics: percentage increase and decrease, percentages, fractions and decimals, reverse percentage, functions, composite functions, domain of a function, inverse functions, simplifying algebraic fractions, equations with algebraic fractions. Detailed solutions are provided. Master percentages, functions, and algebraic fractions with this comprehensive 9-worksheet GCSE/IGCSE maths revision pack. Covering percentage multipliers, reverse percentages, composite functions, function domains, and algebraic fractions, every worksheet includes full, step-by-step worked solutions to save you hours of marking time. Perfect for KS4, GCSE, and IGCSE maths revision or lessons. ________________________________________ Are you looking for ready-to-print, high-quality revision packs to help your students master advanced percentage operations, algebraic functions, and algebraic fractions? This GCSE IGCSE Maths Practice Pack provides extensive, scaffolded practice across three critical pillars of secondary mathematics. Designed to build deep conceptual understanding and strong procedural fluency, this resource takes students from foundational fluency drills all the way to higher-tier, exam-style challenge questions. Perfect for Key Stage 4, GCSE/IGCSE Maths preparation, or international algebra curricula! ________________________________________ ⚡ **What’s Included in This 9-Worksheet Resource?** Each worksheet comes as a standalone clean printout, accompanied by an identical layout featuring full, step-by-step worked solutions for easy marking or student self-correction: 📈 **Module 1: Percentages & Multipliers (3 Worksheets)** • **Worksheet 1: Percentage Increase & Decrease Multipliers** – Focused on finding the exact decimal multipliers for percentage changes, including challenging fractional and decimal percentages (e.g., increase by 18.6%, decrease by 7.4%). • **Worksheet 2: FDP Conversions & Core Percentages** – Fluency drills for converting fluidly between fractions, decimals, and percentages, alongside direct multiplier practice to calculate standard increases and decreases. • **Worksheet 3: Reverse Percentages** – High-intent word problems requiring students to work backward to find original values before sales, salary increases, weight losses, or business profit margins were applied. 🔄 **Module 2: Advanced Functions & Notation (4 Worksheets)** • **Worksheet 4: Function Evaluation** – Introduction to evaluating individual functions using clean linear, quadratic, and cubic expressions. • **Worksheet 5: Composite Functions (Numeric Evaluation)** – Numeric evaluations of nested functions like fg(5) and gf(0) using linear, quadratic, radical, and cubic equations. • **Worksheet 6: Composite Functions (Algebraic Expressions)** – Challenges students to derive algebraic expressions for nested functions like fg(x) and hf(x), requiring full expansion and simplification of brackets. • **Worksheet 7: Domain of a Function** – Rigorous training in finding the restrictions and allowable domains for linear, quadratic, radical, rational, and combination functions using both inequalities and interval notation. ➗ **Module 3: Algebraic Fractions (2 Worksheets)** • **Worksheet 8: Simplifying Algebraic Fractions** – Focused on simplifying complex algebraic fractions by factorising numerators and denominators to cancel down common linear terms. • **Worksheet 9: Operations with Algebraic Fractions** – Structured exercises for adding, subtracting, multiplying, and dividing algebraic fractions with unlike denominators. ________________________________________ 🎯 **Why Teachers Love This Resource:** • No Prep Required: Just print, photocopy, and hand out to your classes immediately. • Scaffolded Progressions: Problems systematically build from fundamental drill skills to higher-tier extension concepts. • Versatile Class Use: Ideal for independent classroom study, homework tasks, emergency cover lessons, or structured exam revision packs. • Clear Work Space: Generous layouts leave students plenty of room to write out their formulas, multipliers, and workings neatly. ________________________________________ 📐 **Curriculum & Topics Covered:** • Key Stage 4 National Curriculum: Algebraic proficiency, numeric relationships, and scaling. • GCSE & IGCSE Maths (Foundation & Higher Tier): Work interchangeably with fractions, decimals, and percentages; solve reverse percentage problems using multipliers; simplify and manipulate algebraic fractions. • IGCSE Maths (Higher Tier Extension): Understand, evaluate, and find expressions for composite functions; determine the restricted domains of distinct functions. • Target Keywords: GCSE maths revision, IGCSE maths pack, reverse percentages, composite functions, domain of a function, algebraic fractions, expanding brackets, factorising expressions, maths worksheets bundle. ________________________________________

£9.90
Bundle

20 GCSE/IGCSE Algebra worksheets (with solutions)

Help your secondary students master the most challenging aspects of algebraic manipulation with this extensive, high-quality worksheet pack. Designed to build procedural fluency and conceptual confidence, this resource flows logically from foundational skills to advanced GCSE Higher tier topics.It is an ideal resource for **Key Stage 3 (Extension), Key Stage 4 (GCSE Foundation/Higher, IGCSE), and AS-Level bridging work.** **What’s Included?** This comprehensive PDF pack includes structured question sections covering three vital algebraic concepts: 📂 **1. Adding and Subtracting Algebraic Fractions (40 Questions)** * **Level 1**: Common numerical denominators and basic simplification. * **Level 2:** Different numerical denominators with linear expression numerators requiring expansion. * **Level 3**: Linear algebraic denominators requiring a common algebraic base (e.g. \(\frac{3}{x-2} - \frac{4}{x+3}\) ) (p. 2). * **Level 4 (Grade 7-9)**: Quadratic denominators requiring factoring first before finding the lowest common multiple. 📂 **2. Rearranging Formulae / Changing the Subject (18 Questions)** * **Level 1:** Formulae involving square roots, fractions, and multi-step inverse operations. * **Level 2 (Grade 8/9):** Complex manipulation where the subject appears multiple times, requiring expansion, grouping common terms, and factorising out the subject. 📂 **3. Equations with Algebraic Fractions (20 Questions)** * **Level 1:** Solving linear fractional equations by clearing the denominators. * **Level 2:** Solving advanced equations that simplify into quadratics, requiring either factorisation or the quadratic formula to solve. 📂 **4. Expanding & Factorising Quadratics** * Supplemental targeted practice on expanding double brackets and simplifying expressions. **Key Features** ✔️ **Full Worked Solutions Included:** Every question comes with a comprehensive, step-by-step written solution. Perfect for quick self-marking, peer assessment, or displaying on your interactive whiteboard. ✔️ **Highly Scaffolded:** Tasks naturally progress in difficulty, allowing students to build up to Grade 9/A* style questions seamlessly. ✔️ **Zero Preparation:** Simply download, select the pages you need, print, and teach! **Ideal For:** * **Main Lesson Practice**: Ideal for independent classwork following a teacher explanation. * **Homework & Revision:** Excellent for consolidation leading up to mock exams or final assessments. * **Cover Lessons:** Clear sequencing and comprehensive answer keys make this completely self-contained for supply or cover staff. * **Flipped Learning / Homework**: Perfect for independent study or remote learning tasks. **File Type**: PDF **Pages:** Complete bundle with question sheets and full answer keys.

£17.90
Bundle

Solving Equations Worksheets Pack | Linear, Systems, Quadratics & Fractions

6 worksheets on solving linear equations, quadratic equations, simultaneous equations and equations with algebraic fractions. Detailed solutions are provided. Master solving equations, simultaneous systems, quadratics and algebraic fractions with this complete KS3 and GCSE maths resource pack featuring worksheets and full answers. ________________________________________ Are your student groups struggling to solve complex multi-step equations? Do they get confused when transitioning from simple linear variables to simultaneous systems, algebraic fractions, or non-linear systems? Take the stress out of your lesson planning with this comprehensive algebra equations practice pack! This collection is meticulously designed to build numerical fluency, moving students smoothly from foundational balance calculations to rigorous secondary school algebra. ________________________________________ **What’s Included in This Resource Pack?** This all-in-one packet delivers distinct, targeted worksheets covering essential secondary algebra units. Each section features a clear, progressive problem set followed by a matching teacher answer key: **Unit 1: Foundational Linear Equations** Core fluency pages covering one-step, two-step, and multi-step equations, variables on both sides, distributing single or multiple brackets, and basic proportions. **Unit 2: Equations with Algebraic Fractions** Advanced practice requiring students to clear denominators by finding common multiples, and solve multi-step equations involving linear numerators. **Unit 3: Simultaneous Equations via Substitution** Structured practice solving classic systems of equations by isolating variables and performing algebraic substitutions. **Unit 4: Simultaneous Equations via Elimination** Targeted exercises focusing on adding, subtracting, or multiplying equations to eliminate variables systematically. **Unit 5: Linear-Quadratic Systems (One Linear, One Quadratic)** Advanced high school systems requiring substitution, expanding quadratic expressions, factorising trinomials, and finding dual coordinate solutions. **Full Teacher Answer Keys** Every single page includes fully worked-out solutions showing exact algebraic transformations, common denominator multipliers, substitution steps, and final fractional or integer answers. It is perfectly ready for quick marking, projectable self-assessment, or independent study checks! ________________________________________ **Ideal For Curriculum Delivery:** * KS3 Maths: Perfect for introducing balancing equations, expanding brackets, and applying simple algebraic rules in Years 7, 8, and 9. * KS4 / GCSE Maths (Foundation & Higher): Excellent as a comprehensive unit review covering simultaneous systems, algebraic fractions, and non-linear quadratic intersections. * Remedial Support / Revision: High-utility worksheets for intervention groups, homework packages, or independent learning centers. ________________________________________ ⭐ **Why Teachers Choose Our Resources:** * **Ready to Print:** No-prep layout saves valuable preparation time—simply print and copy. * **Scaffolded Progress:** The problem sets intentionally scale in difficulty to build student confidence. * **Spacious Design:** Clean layout gives learners plenty of room to write out their working directly on the sheet. If you find this maths resource helpful, please leave a review! Your feedback helps create better classroom tools. ________________________________________

£7.00
Bundle

Algebraic Fractions Worksheets Bundle | Simplify Add Multiply Divide Equations

A collection of 9 worksheets on algebraic fractions, including exercises on adding, subtracting, multiplying and dividing algebraic fractions, simplifying expressions with algebraic fractions and solving equations with algebraic fractions. Detailed solutions are provided. Master rational expressions with this comprehensive, no-prep Algebraic Fractions Worksheets Bundle | Simplify Add Multiply Divide Equations! Aligned to Key Stage 4, GCSE Higher Tier, and A-Level Maths objectives, this extensive, ready-to-print resource packet covers simplifying, adding, subtracting, multiplying, and dividing complex algebraic fractions. Complete with highly detailed, step-by-step worked solutions, it is the ultimate time-saving tool for main lessons, algebra homework, cover work, or exam revision. ________________________________________ Are your secondary students struggling to apply fractional rules to polynomial expressions? Simplify your algebra lesson planning with this high-utility Algebraic Fractions and Equations Resource Pack. This bundle contains carefully structured worksheets designed to build computational confidence and algebraic fluency across critical rational mathematics operations. Every single student problem page comes paired with a highly detailed, full-solution worked answer key that maps out the exact common denominators, quadratic factorisations, cross-cancelling steps, and reciprocal conversions required to reach the correct answer. It is perfect for student self-assessment, small group interventions, homework packets, cover lessons, or fast and easy teacher marking! **What's Inside this Worksheet Pack?** • **Simplifying Algebraic Fractions (4 Pages):** Practice cancelling basic monomial variables, factorising out highest common factors (HCF), and factorising complex quadratic trinomials (including the difference of two squares) to simplify fully. • **Adding & Subtracting Algebraic Fractions (2 Pages):** Scaffolded problems moving from identical denominators to unlike linear frameworks, single brackets, and quadratic denominators requiring lowest common multiple (LCM) adjustments. • **Multiplying & Dividing Algebraic Fractions (2 Pages):** Rigorous operations practicing numerator-denominator cancellations, applying the reciprocal method to divide rational expressions, and simplifying down large polynomial structures. • **Teacher Answer Keys:** Complete, visual step-by-step worked solutions matching every single student layout page exactly. **Why Teachers Love This Pack:** • **Zero Prep Required:** Just print out the PDF pages and you are ready to go! • **Scaffolded Progressions:** Problems move logically from simple single-variable cancelling to complex multi-step quadratic rearrangements. • **Clean Layouts:** Generous workspace for students to neatly line up their equations, fractions, and factorised brackets. • **Detailed Worked Keys:** Perfect for leaving with cover teachers or distributing digitally via a virtual learning environment (VLE) for independent study guide use. **Curriculum Alignment:** • UK National Curriculum (GCSE Maths Higher Tier): Algebra Objective A4 (Simplify and manipulate algebraic expressions, including algebraic fractions, by expanding products and factorising quadratics). • International Frameworks: Excellent for A-Level Maths (Year 12 foundational algebra bridging) and Higher Level IGCSE revision. ________________________________________

£11.90
Bundle

Algebra 1 Solving Equations with Algebraic Fractions Practice Worksheets

Three worksheets on solving linear and quadratic equations by cross multiplication and solving equations with algebraic fractions in which cross multiplication cannot be applied. Detailed solutions are included. Master algebraic fractions and solving equations by cross-multiplication! This comprehensive, no-prep worksheet pack offers scaffolded practice for linear and quadratic rational equations. Ideal for KS3, KS4, GCSE Higher/Foundation revision, and secondary math lessons, it includes full, step-by-step worked solutions to save you hours of marking time. ________________________________________ Save your evenings with these ready-to-print secondary maths worksheets! This comprehensive resource pack delivers highly organized, scaffolded practice to help your students confidently master solving equations with algebraic fractions and cross-multiplication. The worksheets step students logically through the curriculum, ensuring they grasp basic cross-multiplication before moving on to complex rational equations, binomial denominators, and equations that result in quadratics. **What is Included in this Pack?** * **Solving Equations by Cross-Multiplication (Basic):** Level 1 practice focused on single-variable linear equations and simple fractional proportions. * **Solving Equations by Cross-Multiplication (Advanced):** Level 2 practice featuring binomial terms, variables on both sides, and negative distributions. * **Equations with Algebraic Fractions (Linear):** Multi-step equations requiring students to find common denominators or cross-multiply linear terms. * **Equations with Algebraic Fractions (Quadratic):** High-level challenge problems where cross-multiplying results in a quadratic equation that must be solved by factoring or using the quadratic formula. * **Complete Worked Solutions:** Full, step-by-step answers for every single problem to make marking effortless or to allow students to self-assess! **Perfect For:** * KS3 Core Maths Lessons (Years 8 and 9) * GCSE Maths Foundation & Higher Tier Revision * Homework Assignments or Independent Classwork * Extension Work, Cover Lessons, and Maths Intervention Groups **Skills & Concepts Covered:** * Cross-multiplying basic linear fractions * Distributing across binomial numerators and denominators * Solving rational expressions by clearing fractions * Factoring quadratic equations arising from fractional equations ________________________________________

£3.50
Bundle

Algebraic Fractions Bundle | Simplifying Operations & Solving Equations

6 Worksheets on algebraic fractions. The exercises require to simplify algebraic fractions, add, subtract, multiply and divide algebraic fractions and solve equations with algebraic fractions. Detailed solutions are provided. Master algebraic fractions with this comprehensive, print-and-go worksheet pack! Perfect for advanced KS3, KS4, and GCSE maths lessons, this pack offers a clean, scaffolded progression through simplifying algebraic fractions, performing the four operations, and solving complex fractional equations. ________________________________________ Looking for a ready-to-use, highly effective way to help your students master algebraic fractions? This comprehensive worksheet pack provides targeted, scaffolded practice for working with complex algebraic fractions across distinct difficulty tiers. Whether your GCSE maths students are learning to simplify algebraic fractions for the first time or need a robust revision tool for clearing denominators to solve multi-step fractional equations, these resources offer the exact practice needed to build mathematical confidence and algebraic fluency. With clear formatting and fully worked solutions, this pack makes scaffolding, differentiation, and independent practice completely effortless! ________________________________________ **What’s Included in This Pack:** * **Simplifying Algebraic Fractions** – Focused practice on factoring out common terms, simplifying monomials and binomials, and reducing algebraic fractions to their simplest form. * **Adding and Subtracting Fractions** – Exercises requiring students to find a common denominator, expand numerators, collect like terms, and simplify. * **Multiplying and Dividing Fractions** – Targeted practice for fraction operations, including cross-cancelling, multiplying numerators and denominators, and dividing by multiplying by the reciprocal. * **Equations with Algebraic Fractions** – Advanced practice isolating variables by multiplying equations by their lowest common denominators to clear fractions, including linear and quadratic steps. * **Complete Step-by-Step Solutions** – Fully worked-out solutions for every single problem to save you hours of marking or to allow for quick student self-checking! ________________________________________ **Perfect For:** * Maths Rotations & Group Work * Independent Classwork or Daily Homework * Morning Starters, Warm-Ups, or Bell Ringers * Cover Lessons (completely self-contained!) * Assessment Preparation or Formative Check-ins ________________________________________ **Curriculum Links:** National Curriculum (UK): Key Stage 4 (GCSE) Algebra. Perfect for teaching students to simplify algebraic fractions, argue mathematically with rational expressions using the four operations, and solve equations that involve algebraic fractions. ________________________________________

£7.90
Bundle

Algebra Bundle 4 (5 worksheets with solutions)

A collection of five worksheets on the following algebra topics: adding and subtracting polynomials, arithmetic sequences, changing the subject of a formula, equations with algebraic fractions and solving quadratic equations. Detailed solutions are included.

£4.45
Bundle

Adding and subtracting algebraic fractions and solving equations with algebraic fractions worksheets (with solutions)

Three worksheets on algebraic fractions. Two on adding and subtracting algebraic fractions with introductory and harder exercises on this topic and a worksheet on equations involving algebraic fractions. Detailed solutions are provided.

£3.35
Bundle

Solving equations with algebraic fractions Bundle

Three worksheets on simplifying algebraic fractions and solving equations involving fractions. Detailed solutions are provided.

£3.65

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