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

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

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

3 August 2026

pdf, 61.65 KB
pdf, 61.65 KB

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.

Get this resource as part of a bundle and save up to 44%

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

Bundle

Converting Recurring Decimals to Fractions Lesson & Worksheets | 8th Grade

Master converting recurring decimals to fractions with this complete lesson pack, scaffolded worksheets, and full step-by-step solution keys! Perfect for KS3 and GCSE Mathematics, this ready-to-teach bundle breaks down algebraic proofs into logical, easy-to-follow steps. It includes interactive presentation slides, structured workspace pages, and 14 targeted practice problems. Save hours of planning and help your students build absolute confidence with this essential number topic today! ________________________________________ Take the stress out of teaching how to change recurring decimals into fractions! This comprehensive, all-in-one instructional bundle takes students from the basics to formal algebraic mastery. Designed specifically for Key Stage 3 and GCSE Maths students (Foundation and Higher tiers), this resource provides the perfect balance of direct instruction and independent practice. Students will learn the exact multi-step algebraic method needed to formally prove and transform recurring decimals into simplified fractions. ________________________________________ **What Is Included in This Resource Pack?** 1. **Step-by-Step Presentation Slides** • Clear Definitions: Explains exactly what a recurring decimal is and how to spot the repeating pattern. • Dot Notation Guide: Visual walkthrough on reading single and multi-digit repeating patterns using dot notation. • 5-Step Master Formula: A reliable, structured algebraic process students can use to tackle any exam question. • 6 Scaffolded Teaching Examples: Gradually increases in difficulty from single repeating digits to complex mixed decimals. 2. **Comprehensive Student Worksheets** • 14 Unique Practice Problems: Divided cleanly into two targeted sections to build skill mastery. • Section 1 (Pure Repeating Digits): Problems where the pattern begins right after the decimal point (e.g., 0.8̇, 0.5̇4̇, 0.1̇3̇6̇). • Section 2 (Mixed Decimals): Advanced problems containing non-repeating digits before the repeating sequence begins (e.g., 0.15̇, 0.31̇6̇, 0.1246̇2̇). • Clean Formatting: Spacious workspace boxes for students to write out their full algebraic work neatly. 3. **Complete Solution Keys** • Includes a fully worked-out answer key showing every single algebraic step for all 14 worksheet problems—perfect for quick marking or student self-assessment! ________________________________________ **Curriculum & Exam Board Alignment** • Key Stages: Key Stage 3 (KS3) and Key Stage 4 (KS4 / GCSE) • Exam Boards: Fully covers the Number module for AQA, Edexcel, OCR, and Eduqas GCSE Mathematics. • Key Vocabulary: Rational Numbers, Terminating Decimals, Recurring Decimals, Dot Notation, Powers of 10, Algebraic Proof. ________________________________________ **Why Teachers Love This Bundle** • Zero Prep Required: Simply print the worksheets, project the slides, and you are ready to teach! • Scaffolded for Success: The gradual progression keeps struggling students from feeling overwhelmed while stretching higher-tier learners. • Versatile Use: Ideal for whole-class direct instruction, independent desk work, revision sessions, or target intervention groups. ________________________________________

£3.65
Bundle

Converting Recurring/Repeating Decimals to Fractions Worksheets Bundle | 8th

Three worksheets on Changing Recurring Decimals into Fractions. The first is on recurring decimals with repeating digits, the second is on recurring decimals with repeating and nonrepeating digits and the third covers both cases. Detailed solutions are provided. Good for GCSE/IGCSE students. Master fraction conversions with this comprehensive, no-prep Converting Recurring/Repeating Decimals to Fractions Worksheets Bundle! Aligned to Key Stage 3, Key Stage 4, and GCSE Maths objectives, this extensive, ready-to-print resource packet covers converting pure recurring decimals, mixed recurring decimals (with non-repeating digits), and simplifying answers. Complete with highly detailed, step-by-step algebraic worked solutions, it is the ultimate time-saving tool for main lessons, maths homework, or cover work. ________________________________________ Are your secondary mathematics students struggling to set up algebraic equations or handle place value shifts when converting recurring decimals to fractions? Simplify your maths lesson planning with this high-utility Recurring and Repeating Decimals Practice Pack. This bundle features three carefully scaffolded worksheet sets that guide students systematically from simple recurring single digits to complex patterns containing both non-repeating and repeating digits. Every single problem page comes paired with a highly detailed, full-solution worked answer key that maps out the exact algebraic setups, such as defining x, multiplying by powers of 10, subtracting equations, and simplifying down to the simplest form. It is perfect for student self-assessment, small group intervention, homework packets, cover lessons, or fast and easy teacher marking! **What's Inside this Worksheet Pack?** • **Worksheet Packet 1 (Repeating Digits Only):** Multi-page exercises practicing pure recurring decimals (including single-digit, two-digit, and multi-digit patterns like 0.8̇, 0.5̇4̇, and 0.352̇1̇) simplified to their lowest fractional forms. • **Worksheet Packet 2 (Mixed Recurring & Non-Repeating Digits):** Advanced practice working out complex configurations where some digits repeat and others do not (such as 0.15̇, 0.31̇6̇, or 0.1246̇2̇). • **Worksheet Packet 3 (Algebraic Workspace Review Pack):** A dedicated, exam-style practice set complete with designated problem boxes for students to clearly outline their complete step-by-step algebraic working out. • **Teacher Answer Keys:** Complete, detailed visual 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:** Skills move logically from basic single-digit repetitions to complex multi-step algebraic transformations. • **Clean Layouts:** Generous workspace for students to neatly keep track of their equations, subtraction rows, and fractions. • **Detailed Worked Keys:** Perfect for leaving with cover teachers or uploading to a virtual learning environment (VLE) for independent revision. **Curriculum Alignment:** • **UK National Curriculum (GCSE Maths Higher & Foundation):** Objective N6 (Use index laws for multiplication, division, and powers of a power, including negative and fractional indices, and change recurring decimals into fractions). • **International Frameworks:** Excellent for Year 8, Year 9, Year 10, and Year 11 mathematics classes, as well as Higher Level IGCSE revision or foundational A-Level maths bridging. ________________________________________

£3.00
Bundle

Recurring/Repeating Decimals Worksheets Bundle | 7th 8th Grade Math

4 worksheets on converting recurring decimals (with repeating digits only and with repeating and non repeating digits as well) to fractions. Detailed solutions are included. Master fraction conversions with this comprehensive, no-prep Recurring/Repeating Decimals Worksheets Bundle! Aligned to Key Stage 3 math objectives, this extensive, ready-to-print resource packet covers identifying, ordering, and converting repeating decimals into fractions. Complete with detailed, step-by-step worked solutions, it is the ultimate time-saving tool for main lessons, independent practice, homework, or cover work. ________________________________________ Are your secondary students struggling with fractional conversions and decimal notation? Simplify your maths lesson planning with this high-utility Recurring/Repeating Decimals Worksheet Bundle. This packet contains 4 carefully structured worksheets designed to build computational confidence with identifying, comparing, and converting repeating decimals into fractions. Every single problem page comes paired with a highly detailed, full-solution worked answer page that shows the exact algebraic or fractional conversion calculations needed to find the correct answer. It is perfect for student self-assessment, small group intervention, or fast and easy teacher marking! **What's Inside this Worksheet Pack?** • **Worksheet 1 (Notation & Identification):** Practice recognising recurring patterns and writing decimals using proper dot or bar notation. • **Worksheet 2 (Comparing & Ordering):** Activities focused on organising terminating and repeating decimals from least to greatest. • **Worksheet 3 (Simple Conversions):** Step-by-step practice converting single-digit recurring decimals into fractions. • **Worksheet 4 (Advanced Conversions):** Complex conversion practice for multi-digit recurring patterns and mixed numbers. • **Teacher Answer Keys:** Complete, detailed visual worked solutions matching every single student worksheet page. **Why Teachers Love This Pack:** • **Zero Prep Required:** Just print out the worksheets and you are ready to go! • **Scaffolded Learning:** Skills move logically from basic place value comparison to complex algebraic conversions. • **Clean Layouts:** Plenty of clear white space for students to write out their calculations and working out. • **Detailed Worked Keys:** Perfect for leaving with a cover teacher or sending home for parental homework support. **Curriculum Alignment:** • **UK National Curriculum:** Suitable for Year 7, Year 8, and Year 9 Mathematics (Fractions, Decimals, and Percentages / FDP fluency objectives). ________________________________________

£3.65
Bundle

Recurring decimals to fractions (4 worksheets)

Four worksheets about converting recurring decimals to fractions. Detailed solutions are provided. Good practice for GCSE/IGCSE students.

£3.50

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