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Dividing Positive & Negative Decimals Fractions Integers Practice Sheet + Key

Dividing Positive & Negative Decimals Fractions Integers Practice Sheet + Key

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

22 July 2026

pdf, 125.67 KB
pdf, 125.67 KB

A worksheet introducing the students to division of positive and negative numbers (integers, fractions and decimals). The exercises require to perform calculations with two or more terms, find missing terms in given calculations, and compare numerical expressions. Solutions are included.

Master dividing positive and negative numbers with this no-prep KS3 maths worksheet on signed integers, fractions, decimals, and BIDMAS. Full memo included!

Looking for a rigorous, print-and-go resource to help your pupils master dividing 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 integer division to multi-step fractional order of operations, 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 – 18 targeted calculation problems establishing the rules of signs. It moves intentionally from basic integers to positive/negative decimals, horizontal fractions, and complex mixed numbers.
• Section 2: Missing Number Algebra Frames – 18 fill-in-the-blank box problems that build algebraic and inverse thinking. Pupils must determine the missing dividend or divisor across integers, decimals, and equations.
• Section 3: Inequalities & Comparison – Four rigorous comparison tasks where pupils evaluate both sides of an expression and apply less than, greater than, or equal to symbols (<, >, =).
• Section 4: Order of Operations (BIDMAS / BODMAS) – 12 multi-step simplification problems. Problems start with basic grouped operations and scale up to highly complex, multi-layered fractional expressions featuring nested operations, multiplications, and signed denominators.
• Full Worked Solutions – A complete teacher memorandum showing every single algebraic step, cross-cancelling step, and sign change for easy 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 49%

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

Bundle

Positive & Negative Numbers Worksheet Bundle | Integers Fractions Decimals

Five worksheets on adding, subtracting, multiplying and dividing positive and negative numbers (integers, fractions, mixed numbers and decimals). One worksheet on each operation and one worksheet on all operations. Solutions are included. **Take your students beyond basic integer rules with this comprehensive, no-prep directed numbers worksheet bundle!** This resource is perfectly designed to help your secondary math classes build complete computational fluency, moving fluidly from whole number integers to challenging operations with negative fractions, decimals, indices, and multi-step calculation brackets. Whether you are teaching **KS3, KS4 (GCSE / iGCSE), Year 7-11, or foundational algebra review**, these structured practice sheets offer a complete range of problem types to ensure true mathematical mastery. **What is Included in This Bundle?** This package contains a massive collection of student practice pages along with **comprehensive, step-by-step worked answer keys** that show exactly how to find common denominators, cross-cancel, and apply correct operational signs. **Section 1: Adding and Subtracting Real Numbers** * Evaluating direct horizontal expressions with positive and negative integers). * Adding and subtracting signed decimals and mixed number fractions with unlike denominators. * Evaluating longer expressions containing multi-term string numbers. **Section 2: Multiplying and Dividing Signed Numbers** * Direct arithmetic with signed whole numbers, decimals, and negative fractional products. * Evaluating multi-factor strings to understand how even or odd numbers of negative signs impact the final value. * Solving fill-in-the-blank equations to target missing multipliers and unknown divisors. **Section 3: Order of Operations & Indices** * Applying correct calculation rules (BIDMAS/BOOM) to complex nested groupings and brackets. * Evaluating signed bases raised to integer powers and indices. * Solving highly complex, multi-step vertical calculation bar equations. **Section 4: Comparison & Inequality Tasks** * Evaluating values on both sides of an expression to compare using less than, greater than, or equal symbols. **Why Teachers Love This Resource:** * **Ready to Print & Go:** No prep required! Simply print the worksheets and you are completely ready for a cover lesson, classwork assignment, homework, or math revision session. * **Step-by-Step Solutions Included:** Save hours of marking time with a fully worked-out answer key that clearly maps out intermediate signs and fraction conversions (pp. 4, 15). Students can also use it to self-assess. * **Clean and Uncluttered Design:** Problems are laid out beautifully with plenty of white space so students can focus purely on the math without feeling overwhelmed by dense text. * **True Scaffolded Depth:** Tasks naturally progress from simple arithmetic tracking to high-level missing number equations, complex indices, and fraction operations. **Educational Standards Covered:** * **UK National Curriculum / GCSE:** Number and Calculations. Calculate exactly with fractions, decimals, and directed numbers; apply the four operations to integers, decimals, and proper/improper fractions; use conventional notation for the priority of operations, including brackets, powers, roots, and reciprocals. * **US Common Core Standards (for reference):** 7.NS.A.1, 7.NS.A.2, 7.NS.A.2.C, 7.NS.A.3, and 8.EE.A.1.

£4.30
Bundle

Positive & Negative Integers Decimals Fractions Operations Worksheet Bundle

Four worksheets 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, find missing terms in given calculations, and compare numerical expressions. 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 4 rigorous, high-quality math 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: Adding Positive & Negative Numbers Worksheet** o Focuses on integer sums, rational decimal columns, and signed horizontal fractions. o Includes missing addend algebra frames and multi-layered expression addition. • **Resource 2: Subtracting Positive & Negative Numbers Worksheet** o Targets the subtraction of signed integers, decimals, and mixed fractions. o Solidifies the concept of subtracting negatives (adding the additive inverse). • **Resource 3: Multiplying Positive & Negative Numbers Worksheet** o Establishes multiplication sign rules for cross-cancelling fractions and decimals. o Features inequality comparison tasks and multi-factor simplification problems. • **Resource 4: Dividing Positive & Negative Numbers Worksheet** o Covers integer division, horizontal fraction inversion, and division of mixed numbers. o Features rigorous, layered fractional BIDMAS/order of operations challenge sets. **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. ________________________________________

£3.55

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