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Adding Rational Numbers Worksheet - 7th Grade Integers, Decimals, & Fractions

Adding Rational Numbers Worksheet - 7th Grade Integers, Decimals, & Fractions

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

20 July 2026

pdf, 72.25 KB
pdf, 72.25 KB

A worksheet on adding positive and negative numbers. The numbers can have the same or different signs and they can be integers, fractions, mixed numbers or decimals. It contains 34 exercises. Detailed solutions are included.

Master the addition of directed numbers with this comprehensive 34-problem practice worksheet! Perfectly scaffolded for Key Stage 3 and Key Stage 4 math, this no-prep resource smoothly guides students from basic integer addition to adding positive and negative decimals, fractions, and mixed numbers. A complete, step-by-step teacher answer key is included for effortless marking!

Looking for a rigorous, no-prep way to build fluency in adding positive and negative numbers?
This Adding Directed & Rational Numbers Practice Worksheet provides a perfectly scaffolded progression to thoroughly test student understanding. It moves steadily from basic integer rules to complex expressions, challenging students with multi-digit decimals, proper fractions, and mixed numbers with unlike denominators.
Whether you need a focused classroom activity, targeted homework assignment, or a robust revision packet, this printable math resource has you covered!

What’s Included?
• 34 Carefully Scaffolded Addition Problems:
o Problems 1–10: Adding basic positive and negative integers (whole numbers).
o Problems 11–22: Transitioning into negative decimals, simple fractions, and basic mixed numbers.
o Problems 23–34: Advanced practice with larger multi-digit integers, complex decimals, and mixed numbers requiring common denominators.
• Step-by-Step Answer Key: The complete solutions page shows the exact mathematical shifts (such as common denominator conversions), making it incredibly easy for teacher marking, parental support, or student self-assessment!

Perfect For:
• Key Stage 3 (Year 7, 8 & 9): Core lessons on directed numbers and negative fractions.
• Key Stage 4 (Year 10 & 11): Ideal foundation math revision and non-calculator GCSE practice.
• Independent study, homework tasks, or emergency supply teacher covers.

Curriculum Alignment:
• UK National Curriculum (Key Stage 3 / 4): Fully covers statutory requirements for using positive and negative numbers, calculating with fractions and decimals, and mastering directed number arithmetic fluent operations.

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

Adding & Subtracting Rational Numbers Bundle | Integers Fractions Decimals

Three worksheets on adding positive and negative numbers. The numbers can have the same or different signs and they can be integers, fractions, mixed numbers or decimals. Detailed solutions to all worksheets are included. **Simplify your number sense topic planning with this comprehensive, no-prep Adding and Subtracting Negative Numbers Worksheets Bundle designed for KS3 and GCSE Higher/Foundation Tier Mathematics students!** This massive practice bundle features multiple distinct worksheet sets packed with carefully structured questions. It guides students through a rigorous review of positive and negative operations, combining integers, fractions, mixed numbers, and decimals all in one high-utility package. Perfect for secondary maths classrooms, this resource includes a fully worked solutions mark scheme to make marking completely effortless! Whether you need a complete topic workbook, daily homework assignments, starters, cover work, or a revision review for GCSE exam preparation, this worksheets bundle has everything you need. **What is Included in This Resource Bundle?** * **Multi-Page Student Practice Packet:** Carefully scaffolded exercises to help students build computational confidence and master directed number operations. * **Complete Worked Solutions / Mark Scheme:** A detailed, step-by-step key that shows exactly how common denominators are found, how numerators are altered, and how answers are simplified—perfect for student self-assessment or quick teacher marking! * **Comprehensive Topic Coverage:** Integer Operations: Working with positive and negative whole numbers, including adding inverse negatives and subtracting larger numbers. Fraction & Mixed Number Operations: Combining signed fractions and mixed numbers with both like and unlike denominators, challenging students to find common denominators. Decimal Operations: Adding and subtracting positive and negative decimals up to the hundredths place. **Ways to Use This Bundle in Your Classroom:** * **Full Topic Workbook:** Print the entire multi-page packet as a comprehensive workbook for your students to use throughout your directed numbers unit. * **Independent Practice / Homework:** Assign specific sections or pages after each daily lesson to reinforce calculation fluency. * **Maths Starters / Bell Ringers:** Cut the worksheets into smaller sections to use as daily sign-rule drills across a full week of lessons. * **No-Prep Cover Work:** The clear layout and comprehensive step-by-step mark scheme mean you can just print, copy, and leave it for a cover teacher at a moment's notice! * **GCSE Revision / Remediation:** Use it to diagnose and patch up foundational arithmetic gaps before moving into complex algebra topics. **Curriculum & Exam Board Alignment:** **UK National Curriculum (Key Stage 3 & 4):** * **KS3 Mathematics (Number):** Use positive and negative integers, decimals, and fractions; order positive and negative integers, decimals, and fractions. * **GCSE Mathematics (Foundation & Higher Tier):** Meets specifications for AQA, Edexcel, and OCR by reinforcing standard calculations with directed numbers, fractions, fractions with different denominators, mixed numbers, and decimals without a calculator.

£2.20

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