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