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Operations with algebraic fractions worksheet (with solutions)

Operations with algebraic fractions worksheet (with solutions)

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

10 August 2026

pdf, 121.79 KB
pdf, 121.79 KB

A worksheet on simplifying expressions with algebraic fractions and the four operations between them. Detailed solutions are included.

Get this resource as part of a bundle and save up to 49%

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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Expanding Brackets, Factoring Quadratics & Algebraic Fractions Worksheets

A collection of 6 worksheets on algebraic manipulation based on the GCSE 9-1 specification. The following worksheet are included: * Multiplying out two brackets * Multiplying three brackets * Factorising quadratics * Simplifying algebraic fractions * Operations with algebraic fractions * Completing the square Detailed solutions are included. Master core algebra skills with this comprehensive, no-prep 6-worksheet bundle! Perfect for KS3 and GCSE 9-1 maths lessons, this print-and-go toolkit covers expanding double/triple brackets, factorising quadratics, completing the square, and algebraic fractions with full worked solutions included. ________________________________________ Are you looking for a rigorous, ready-to-print resource to help your students master algebraic manipulation? This complete 6-worksheet practice pack takes students from foundational polynomial expansion all the way up to complex rational operations. Highly suitable for Key Stage 3 extension and standard GCSE 9-1 Maths classes (both Foundation and Higher tiers), this bundle provides structured, scaffolded practice sheets that systematically build mathematical fluency and confidence. **What’s Included in This 6-Worksheet Bundle:** • **Worksheet 1: Multiplying Out Two Brackets** – Focused practice on expanding double brackets and simplifying advanced expressions containing multiple variables. • **Worksheet 2: Multiplying Three Brackets** – Higher-level expansion and simplification tasks to challenge student processing and accuracy. • **Worksheet 3: Factorising Quadratics** – Step-by-step practice covering common factors, trinomials (a=1 and a>1), and the difference of two squares. • **Worksheet 4: Simplifying Algebraic Fractions** – Targeted exercises requiring students to factorise numerators and denominators to reduce fractions to their simplest form. • **Worksheet 5: Operations with Algebraic Fractions** – Advanced problems covering multiplication, division, and fractions requiring a common denominator to add or subtract. • **Worksheet 6: Completing the Square** – Comprehensive practice for transforming quadratic expressions, including tricky examples with fractional steps and leading coefficients greater than 1. • **Full Worked Solutions** – Complete, step-by-step mathematical solutions for every single problem—ideal for quick marking, cover work, or student self-assessment! **Perfect For:** • Key Stage 3 Maths Extension (Years 8 and 9) • GCSE 9-1 Revision & Exam Prep (Foundation & Higher Tiers) • Independent Practice, Homework Tasks, or Cover Work • Maths Intervention Groups & Revision Packets **Curriculum Alignment:** Fully aligned with the UK National Curriculum for Mathematics and suitable for all major exam boards, including AQA, Edexcel, and OCR: • Algebra (A4): Simplify and manipulate algebraic expressions by maintaining the structure of an expression, including expanding products of two or more binomials and factorising quadratic expressions. • Algebra (A5): Understand and use standard mathematical formulae; complete the square on quadratic expressions. • Algebra (A7): Argue mathematically to show algebraic expressions are equivalent, and manipulate algebraic fractions.

£4.90
Bundle

GCSE Maths-Number and Algebra Revision Pack

A bundle of 20 worksheets (with detailed solutions) on Number and Algebra topics appropriate for GCSE students. Each worksheet contains questions for students of various abilities. The topics covered by these worksheets include: * Operations with positive and negative numbers * Recurring decimals * Surds * Sequences * Percentage of a quantity * Reverse percentage * Compound interest * Simple interest * Percentage change * Percentage Increase Decrease * Simplifying expressions by collecting like terms * Expanding single brackets * Expanding double brackets * Factorising simple expressions * Factorising quadratic expressions * Solving linear equations * Solving quadratic equations * Operations with algebraic fractions * Linear inequalities * Quadratic inequalities The pack is ideal for use in revision sessions or for individual study. The solutions provided are very clear and explanatory.

£18.90
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Algebra 1 Curriculum Bundle | Equations, Factoring, Systems, Polynomials & More

Streamline your math lessons with this complete Algebra 1 curriculum worksheets bundle. Covering equations, inequalities, factoring, simultaneous systems, functions, polynomials, and more, this comprehensive resource provides 20 ready-to-print lessons and full answer keys. Are your students struggling to keep up with the fast pace of Algebra 1? Do you find yourself spending hours hunting down high-quality practice problems for factoring, systems of equations, or polynomial operations? Take the stress out of your school year with this comprehensive Algebra 1 curriculum worksheets bundle! This massive, multi-unit collection features a carefully scaffolded learning track that moves students smoothly from foundational algebraic rules to advanced high school math concepts. **Full Breakdown of the 20 Worksheets Included:** This all-in-one resource delivers an expansive library of 20 distinct worksheets covering essential secondary algebra units. Each worksheet contains scaffolded exercises followed by a matching, step-by-step teacher answer key: **Worksheet 1:** Intro to Algebraic Notation & Simplifying Products **Worksheet 2:** Collecting Like Terms (Single Variable Addition & Subtraction) **Worksheet 3:** Simplifying Complex Multi-Variable Expressions **Worksheet 4:** Writing Expressions in Index Form (Laws of Exponents) **Worksheet 5:** Expanding Single Brackets (Distributive Property Basics) **Worksheet 6:** Expanding and Simplifying Expressions with Multi-Brackets **Worksheet 7:** Expanding Double Brackets & Polynomial Expansion **Worksheet 8:** Factoring Expressions (Finding the Greatest Common Factor) **Worksheet 9:** Factoring Complex Quadratic Expressions & Polynomials **Worksheet 10:** Introduction to Functions, Relations, & Function Notation **Worksheet 11:** Solving One-Step Linear Equations **Worksheet 12:** Solving Two-Step Linear Equations **Worksheet 13:** Solving Multi-Step Equations with Variables on Both Sides **Worksheet 14:** Solving Equations with Single Brackets **Worksheet 15:** Solving Complex Equations with Multiple Brackets **Worksheet 16:** Introduction to Fractional Equations (Basic Proportions) **Worksheet 17:** Solving Multi-Step Linear Equations Involving Fractions **Worksheet 18:** Solving and Graphing Linear Inequalities **Worksheet 19:** Simultaneous Equations (Systems of Equations by Substitution) **Worksheet 20:** Simultaneous Equations (Systems of Equations by Elimination) Note: Every single worksheet includes a complete, step-by-step teacher solution manual showing exact algebraic transformations and calculations. **Perfect For:** * Middle School Math (8th Grade): Advanced extension tracks and pre-algebra review. * High School Algebra 1: A full core instruction supplement or comprehensive daily homework routines. * Algebra 2 Remedial Review: High-utility fluency drills to fill in prerequisite gaps at the start of the year. * Sub Plans & Homework Packets: Clean layouts with clear instructions make these easy to use for independent study. **Educational Standards Covered** * CCSS 8.EE.C.7: Solve linear equations in one variable. * CCSS 8.EE.C.8: Analyze and solve pairs of simultaneous linear equations. * CCSS HSA-SSE.A.2: Use the structure of an expression to identify ways to rewrite it (Factoring). * CCSS HSA-APR.A.1: Add, subtract, and multiply polynomials. * CCSS HSA-REI.B.3: Solve linear equations and inequalities in one variable. **Why Teachers Love This Resource** * **Zero Prep Required:** Just print out the sections you need today, and your daily lesson plan or assessment tool is instantly ready! * **Scaffolded Progress:** The problem sets intentionally scale in difficulty to keep students from feeling overwhelmed. * **Spacious Formatting:** Clean design leaves plenty of breathing room for students to show their mathematical scratch work right on the sheet.

£18.99
Bundle

GCSE Maths-Algebra Revision Pack

A bundle of 10 worksheets (with detailed solutions) on Algebra topics appropriate for GCSE students. Each worksheet contains questions for students of various abilities. The topics covered by these worksheets include: * Simplifying expressions by collecting like terms * Expanding single brackets * Expanding double brackets * Factorising simple expressions * Factorising quadratic expressions * Solving linear equations * Solving quadratic equations * Operations with algebraic fractions * Linear inequalities * Quadratic inequalities The pack is ideal for use in revision sessions or for individual study. The solutions provided are very clear and explanatory.

£8.90

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