Solving Proportions Worksheet & Ratio Word Problems | 7th 8th Grade Math Review

A worksheet on solving proportions using cross multiplication and dividing amounts in a given ratio. The exercises require to solve given proportions (easy and harder), divide certain amounts in a given ratio and solve word problems where an amount is divided in a given ratio. Detailed solutions are included.

Master cross-multiplication and fractional equations with this comprehensive proportions worksheet pack. Perfect for Key Stage 3 and Key Stage 4 maths revision, homework, or exam prep covering algebraic equations and shared ratio word problems.

Take your students’ proportional reasoning to the next level with this ready-to-print Solving Proportions & Ratio Word Problems Pack! Moving past basic computational repetition, this resource provides an excellent scaffolding bridge between algebraic equations and real-world word problem modeling. This 10-page PDF download features 2 clean pages of student practice questions (10 comprehensive multi-part questions total) and 8 pages of beautifully worked, page-for-page teacher solutions showing every single algebraic step.

What’s Included in This 10-Page Pack?
• Section 1: Core Proportions Fluency (Q1): 8 questions guiding students through cross-multiplying simple fractional equations.
• Section 2: Advanced Algebraic Proportions (Q2): 8 high-rigour equations requiring cross-multiplication across binomial expressions (including variables in denominators and complex expanding terms like 3/x = 4/(x+3)).
• Section 3: Dividing Quantities into Ratios (Q3): 6 targeted fluency exercises where students calculate total parts to divide distinct amounts into specified ratio partitions.
• Section 4: Real-World Ratio Applications (Q4–Q7): Multi-step word problems involving shared cash allocations, retail furniture costing ratios, and classroom gender distributions.
• Section 5: Missing Parameter Variable Proofs (Q8–Q9): Advanced age relation modeling and workplace employment demographics featuring “fewer than” or older age difference balancing constraints.
• Section 6: Three-Way Ratio Sharing (Q10): A premium capstone challenge requiring a competition cash prize to be split proportionally across three distinct student results.
• Full Step-by-Step Solutions: Every problem features its full algebraic layout, distribution paths, constant isolations, and final variable totals to support quick marking or independent student self-assessment!

Perfect For:
• Key Stage 3 (KS3) and Key Stage 4 (KS4) Maths mastery
• Homework assignments, independent study booklets, or targeted revision sheets
• Maths bellringers, exit tickets, and quick formative assessments
• Emergency cover lesson plans (simply print and hand out!)

File Information:
• Format: High-quality, print-ready PDF document (10 pages including fully worked answers).