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Positive & Negative Decimals Fractions Integers Operations Worksheet & Key

Positive & Negative Decimals Fractions Integers Operations Worksheet & Key

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

22 July 2026

pdf, 120.86 KB
pdf, 120.86 KB

A worksheet introducing the students to addition, subtraction, multiplication and division of positive and negative numbers (integers, fractions and decimals). The exercises require to perform calculations with two or more terms and one or more operations (using the order of operations when appropriate) and find missing terms in given calculations. Solutions are included.

Master four operations on directed numbers with this no-prep KS3 maths worksheet. Covers positive & negative integers, fractions, decimals & BIDMAS!

Looking for a rigorous, print-and-go resource to help your pupils master directed numbers, fractions, and decimals?
This comprehensive maths worksheet is designed to build procedural fluency and conceptual depth across positive and negative rational numbers. Moving sequentially from fundamental single-operation calculations to multi-step order of operations (BIDMAS) and missing number algebra frames, this pack provides an exceptional match for Key Stage 3 (KS3) and Key Stage 4 (KS4) Foundation Tier GCSE preparation, or early secondary homework and revision modules.

What is Included in This Download?
• Section 1: Direct Evaluation Basics – 18 targeted calculation problems establishing the rules of signs across all four operations. It moves intentionally from basic integers to signed fractions, decimals, and vertical fractional divisions.
• Section 2: Multi-Step Order of Operations (BIDMAS / BODMAS) – 20 rigorous simplification problems featuring nested brackets, multi-factor product strings (including 21-term and 44-term logic problems), and highly complex layered fractions requiring strong order of operations skills.
• Section 3: Missing Number Algebra Frames – 14 fill-in-the-blank box problems that build inverse arithmetic and algebraic thinking. Pupils must find the missing dividend, divisor, or factor across integers, fractions, and division statements.
• Full Worked Solutions – A complete teacher memorandum matching every page, showing every single fraction conversion, common denominator calculation, and cross-cancelling step for effortless marking, peer assessment, or student self-checking.

Why Teachers Love This Resource:
• Zero Prep Required: Simply download, print, and distribute directly to your classes—perfect for main lessons, homework tasks, or emergency cover work.
• Differentiated Rigour: Problems naturally scale from fundamental directed number mechanics to challenging multi-step BIDMAS extension questions.
• Versatile Use: Ideal for independent classwork, numeracy intervention groups, or standalone revision worksheets.

Curriculum & Exam Board Alignment:
• UK National Curriculum: Key Stage 3 (KS3) and Key Stage 4 (KS4) Mathematics – Order of operations, calculations with directed numbers, decimals, and fractions.
• Exam Boards: Highly relevant for Edexcel, AQA, and OCR GCSE Maths (Foundation Tier) modules.

Get this resource as part of a bundle and save up to 41%

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

Bundle

Rational Numbers Operations & Linear Equations Worksheet Bundle with Keys

Three worksheets on operations and linear equations with positive and negative numbers. A worksheet introducing the students to addition, subtraction, multiplication and division of positive and negative numbers (integers, fractions and decimals). The exercises require to perform calculations with two or more terms and one or more operations (using the order of operations when appropriate) and find missing terms in given calculations. And two worksheets on solving linear equations involving various cases such as: one-step and two-step linear , linear equations with brackets, linear equations with double brackets, linear equations with fractions and linear equations with the variable on both sides. Detailed solutions are included. Master four operations on directed numbers and linear equations with this no-prep KS3/KS4 maths bundle, covering integers, fractions, decimals, and BIDMAS. a Save time and money with this comprehensive, ready-to-print Directed Numbers and Linear Equations maths bundle! This high-quality printable pack brings together three complete resources designed to eliminate sign errors and build total procedural fluency. Moving sequentially from basic integers to complex algebraic fractions, it provides weeks of independent practice, homework tasks, or revision material. It is an exceptional match for Key Stage 3 (KS3) and Key Stage 4 (KS4) Higher or Foundation Tier GCSE preparation. **What is Included in This Bundle?** • **Directed Numbers Practice:** Master arithmetic rules for adding, subtracting, multiplying, and dividing. • **Rational Numbers Mastery:** Work with signed decimals, fractions, and vertical divisions. • **Advanced BIDMAS Practice:** Solve multi-step calculations with nested brackets and large product strings. • **Inverse Reasoning Tasks:** Complete fill-in-the-blank boxes using algebraic and inverse thinking. • **Linear Equation Foundations:** Solve one-step and two-step equations involving negative coefficients. • **Expanding Brackets:** Expand single and double parentheses with negative sign distributions. • **Algebraic Fractions:** Balance complex equations by finding common denominators and cross-multiplying. • **Fully Worked Solutions:** Access a complete teacher memorandum guide showing every balancing move. **Why Teachers Love This Bundle:** • **Zero Prep Required:** Download, print, and distribute directly to your classes immediately. • **Excellent Value:** Enjoy a built-in discount compared to buying resources individually. • **Scaffolded Rigour:** Questions naturally scale from core mechanics to challenging exam questions. • **Versatile Classroom Use:** Ideal for main lessons, structured revision, or emergency cover work. **Curriculum & Exam Board Alignment:** • UK National Curriculum: Key Stage 3 (KS3) and Key Stage 4 (KS4) Mathematics. • Exam Boards: Perfect for Edexcel, AQA, and OCR GCSE Maths modules. ________________________________________

£2.90
Bundle

All Operations with Integers & Rational Numbers Bundle PEMDAS Worksheets

Three worksheet introducing the students to addition, subtraction, multiplication and division of positive and negative numbers (integers, fractions and decimals) and the order of operations in calculations with such numbers. The exercises require to perform calculations with two or more terms and one or more operations (using the order of operations when appropriate) and find missing terms in given calculations. Solutions are included. Master four operations on directed numbers with this no-prep KS3 maths worksheet bundle. Covers positive & negative integers, fractions, decimals & BIDMAS! ________________________________________ Save time and money with this comprehensive, ready-to-print Directed Numbers and Fractions bundle! This comprehensive printable bundle brings together 3 rigorous, high-quality maths resources designed to build total procedural fluency with positive and negative numbers. Moving sequentially from basic integers to complex fractions, missing number algebra frames, inequalities, and multi-step order of operations (BIDMAS) review, this pack provides weeks of independent practice, homework tasks, or assessment material. It is an exceptional match for Key Stage 3 (KS3) and Key Stage 4 (KS4) Foundation Tier GCSE preparation, or early secondary numeracy intervention groups. **What resources are included in this bundle?** • **Resource 1: Basic Operations with Integers & Directed Numbers** o Focuses on foundational sign rules for adding, subtracting, multiplying, and dividing integers. o Includes missing addend algebra frames and multi-layered expression addition. • **Resource 2: Operations with Positive & Negative Decimals, Fractions** & Mixed Numbers o Targets the four operations across rational decimals, horizontal fractions, and mixed values. o Solidifies fractional inversion, common denominator calculations, and sign changes. • **Resource 3: Advanced Order of Operations (BIDMAS) Practice Sheet** o Features rigorous, layered fractional BIDMAS and order of operations challenge sets. o Includes nested brackets and complex multi-factor logic product strings. **Why Teachers Love This Bundle:** • **Excellent Value:** Purchasing this all-in-one pack gives you a built-in discount compared to buying each resource individually. • **Zero Prep Required:** Simply download, print out the PDFs, and hand them directly to your classes—perfect for main lessons, homework tasks, or emergency cover work. • **Progressive Rigour:** Within every file, questions naturally scale from fundamental directed number mechanics to challenging multi-step extension questions. • **Fully Worked Solutions:** Every single worksheet includes a thorough teacher memorandum showing all algebraic steps for effortless marking, peer assessment, or student self-checking. **Curriculum & Exam Board Alignment:** • **UK National Curriculum:** Key Stage 3 (KS3) and Key Stage 4 (KS4) Mathematics – Order of operations (BIDMAS), calculations with directed numbers, decimals, and fractions. • **Exam Boards:** Highly relevant for Edexcel, AQA, and OCR GCSE Maths (Foundation Tier) modules. ________________________________________

£2.90

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