Recurring Decimals to Fractions Mixed Problems Worksheet with Step-by-Step Keys

A worksheet on changing recurring decimals into fractions. Including recurring decimals with repeating digits and recurring decimals with repeating and nonrepeating digits. Detailed solutions are provided.

Resource Overview
Mastering the transition from recurring decimals to fractions using algebraic proofs can be a challenging hurdle for Key Stage 3, Key Stage 4, and GCSE Maths students. This ready-to-print resource simplifies the process with a clean, highly structured layout designed to minimize tracking errors and build mathematical confidence.
Featuring 14 carefully leveled problems, this task guides students step-by-step from simple single-digit repeating patterns all the way up to complex mixed recurring decimals. A complete, fully worked algebraic answer key is included, making this perfect for independent practice, homework, revision lessons, cover work, or assessment.

Key Resource Features

• Leveled Progression: Problems transition naturally from basic pure repetitions (e.g., 0.1111…) to challenging, non-pure mixed recurring decimals (e.g., 0.2417417…).
• Side-by-Side Organized Grid Layout: Work boxes are aligned perfectly horizontally next to one another to help students keep their equations neatly cataloged.
• Eco-Friendly, High-Contrast Design: Zero color elements mean crisp, high-contrast printing on any standard school printer with no wasted color ink.
• Full Step-by-Step Solution Key: Every single problem features a completely written-out algebraic setup (x = …, 100x = …, etc.) showing the exact subtractions and simplest-form fraction simplifications so teachers can spot student misconceptions instantly.Persistent TES Store Link: Includes a subtle, clean footer redirecting back to your digital shopfront for seamless tracking and repeat teacher traffic.

Problem Difficulty Breakdown Included:

1. Pure Single-Digit Recurring Decimals (e.g., 0.1̇)
2. Pure Multi-Digit Recurring Decimals (e.g., 0.1̇9̇, 0.1̇35̇, 0.3̇82̇)
3. Mixed Recurring Decimals (Where the dot notation repetition begins after a non-repeating digit, e.g., 0.24̇17̇, 0.92̇7̇, 0.13̇45̇)

What’s Included in Your Download:

• Student Activity Booklet (Pages 1–2): Complete with a dedicated Name, Date, and Score header. Clear, explicit instructions direct students to show all required algebraic workflows.
• Teacher Solution Pages (Pages 3–5): A detached, highly legible 3-page key featuring shaded background solution boxes for quick reference during marking or displaying on an interactive whiteboard.