Easy Guide: Algebra Fractions & Completing Squares for Kids

Open

Kimberley

25/02/2023

Maths

National 5 maths (Block 1)

Subjects

Maths

Algebra

Algebraic expressions

Easy Guide: Algebra Fractions & Completing Squares for Kids

Name: Knowunity
Brand: Knowunity

This comprehensive study guide covers key mathematical concepts including expanding brackets in mathematics, completing the square quadratic example, and simplifying algebraic fractions. It provides detailed explanations and examples for students learning these topics.

• The guide covers expanding brackets, factorising, completing the square, indices, surds, scientific notation, and algebraic fractions.
• Each section includes multiple worked examples to illustrate the concepts.
• Important rules and formulas are highlighted throughout the guide.
• The material progresses from simpler to more complex applications of each topic.
• Practice problems are provided to reinforce understanding of the techniques.

...

25/02/2023

300

Block I
Exponding Brackets
1. (200-3)²
= (2x-3)(2x-3)
= 2x (2x-3)-3(2x-3)
= 4x² - 6x-60c +9
= 4x²-12x+9
2. (2x₁-1) (2x²-3x-4)
= 20 (2xx²-3xx

View

Quadratic Factorisation and Completing the Square

This section delves deeper into quadratic factorisation and introduces the method of completing the square.

Example: 3x² + 11x + 6 is factored as $3x+2$ $x+3$

The page provides multiple examples of factoring quadratic expressions, including those with a coefficient other than 1 for the x² term. It then transitions to completing the square, a technique used to rewrite quadratic expressions in a specific form.

Definition: Completing the square is a method used to convert a quadratic expression into the form $x+p$ ² + q.

Highlight: The completing the square quadratic example with solution shown is x² + 8x - 5, which is rewritten as $x+4$ ² - 21.

View

Indices, Expanding Brackets, and Surds

This page covers rules for indices, further examples of expanding brackets, and an introduction to surds.

Vocabulary: Indices $or exponents$ are the powers to which a number or variable is raised.

The page provides examples of simplifying expressions with indices and expanding brackets with more complex terms. It also introduces the concept of surds and their simplification.

Example: 3a³ × 4a / 8a² is simplified to 3/2a²

Highlight: The section on surds introduces important rules for simplifying and rationalising expressions involving square roots.

View

Surds and Scientific Notation

This page continues with more advanced surd operations and introduces scientific notation.

Definition: A surd is a root $usually a square root$ of a number that cannot be simplified to a whole or rational number.

The page provides examples of simplifying and rationalising surds, emphasizing the importance of fully simplifying expressions. It then transitions to scientific notation, demonstrating how to represent very large or small numbers.

Example: √27 + √48 - √12 is simplified to 5√3

Highlight: The scientific notation section includes practical examples, such as calculating the surface area of Jupiter relative to Earth.

View

Scientific Notation and Distance Calculations

This page focuses on applying scientific notation to real-world problems, particularly in astronomy and space travel.

Vocabulary: Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

The page provides examples of using scientific notation to perform calculations involving very large distances and speeds. It demonstrates how to use the distance-speed-time formula in conjunction with scientific notation.

Example: A rocket traveling at 1.32 × 10⁵ miles per second for 4 minutes covers a distance of 3.168 × 10⁸ miles.

Highlight: This section emphasizes the practical applications of scientific notation in fields like astronomy and space exploration.

View

Algebraic Fractions

The final page focuses on simplifying algebraic fractions, a crucial skill in advanced algebra.

Definition: An algebraic fraction is a fraction where the numerator, denominator, or both contain algebraic expressions.

The page provides examples of simplifying complex algebraic fractions, including those involving quadratic expressions. It demonstrates techniques for factoring and canceling common terms to simplify fractions.

Example: $b²-49$ / $b²-16$ is simplified to $b+7$ / $b+4$

Highlight: The simplifying algebraic fractions questions and answers provided here offer valuable practice for students preparing for advanced mathematics exams.

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

21 M

Pupils love Knowunity

#1

In education app charts in 17 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Subjects

Maths

Algebra

Algebraic expressions

Maths

•

300

•

25 Feb 2023

•

6 pages

Easy Guide: Algebra Fractions & Completing Squares for Kids

Kimberley

@kimberley_ncyf

• The guide covers... Show more

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Quadratic Factorisation and Completing the Square

This section delves deeper into quadratic factorisation and introduces the method of completing the square.

Example: 3x² + 11x + 6 is factored as $3x+2$ $x+3$

Definition: Completing the square is a method used to convert a quadratic expression into the form $x+p$ ² + q.

Highlight: The completing the square quadratic example with solution shown is x² + 8x - 5, which is rewritten as $x+4$ ² - 21.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Indices, Expanding Brackets, and Surds

This page covers rules for indices, further examples of expanding brackets, and an introduction to surds.

Vocabulary: Indices $or exponents$ are the powers to which a number or variable is raised.

The page provides examples of simplifying expressions with indices and expanding brackets with more complex terms. It also introduces the concept of surds and their simplification.

Example: 3a³ × 4a / 8a² is simplified to 3/2a²

Highlight: The section on surds introduces important rules for simplifying and rationalising expressions involving square roots.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Surds and Scientific Notation

This page continues with more advanced surd operations and introduces scientific notation.

Definition: A surd is a root $usually a square root$ of a number that cannot be simplified to a whole or rational number.

Example: √27 + √48 - √12 is simplified to 5√3

Highlight: The scientific notation section includes practical examples, such as calculating the surface area of Jupiter relative to Earth.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Scientific Notation and Distance Calculations

This page focuses on applying scientific notation to real-world problems, particularly in astronomy and space travel.

Vocabulary: Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

Example: A rocket traveling at 1.32 × 10⁵ miles per second for 4 minutes covers a distance of 3.168 × 10⁸ miles.

Highlight: This section emphasizes the practical applications of scientific notation in fields like astronomy and space exploration.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Algebraic Fractions

The final page focuses on simplifying algebraic fractions, a crucial skill in advanced algebra.

Definition: An algebraic fraction is a fraction where the numerator, denominator, or both contain algebraic expressions.

Example: $b²-49$ / $b²-16$ is simplified to $b+7$ / $b+4$

Highlight: The simplifying algebraic fractions questions and answers provided here offer valuable practice for students preparing for advanced mathematics exams.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Expanding Brackets and Factorising

This page covers techniques for expanding brackets and factorising expressions. It provides several examples to illustrate these important algebraic skills.

Example: $2x-3$ ² is expanded as 4x²-12x+9

The page demonstrates the step-by-step process of expanding squared terms and multiplying two binomials. It also covers factorising techniques, including the difference of two squares and quadratic expressions.

Highlight: Factorising quadratic expressions is a crucial skill in algebra, often used in solving equations and simplifying complex expressions.

Vocabulary: Difference of two squares - a special case in algebra where an expression can be factored into the product of two binomials.

We thought you’d never ask...

What is the Knowunity AI companion?

Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.

Where can I download the Knowunity app?

You can download the app from Google Play Store and Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Easy Guide: Algebra Fractions & Completing Squares for Kids

Quadratic Factorisation and Completing the Square

Indices, Expanding Brackets, and Surds

Surds and Scientific Notation

Scientific Notation and Distance Calculations

Algebraic Fractions

Similar content

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

21 M

#1

950 K+

Still not convinced? See what other students are saying...

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.

Easy Guide: Algebra Fractions & Completing Squares for Kids

Sign up to see the contentIt's free!

Quadratic Factorisation and Completing the Square

Sign up to see the contentIt's free!

Indices, Expanding Brackets, and Surds

Sign up to see the contentIt's free!

Surds and Scientific Notation

Sign up to see the contentIt's free!

Scientific Notation and Distance Calculations

Sign up to see the contentIt's free!

Algebraic Fractions

Sign up to see the contentIt's free!

Expanding Brackets and Factorising

We thought you’d never ask...

What is the Knowunity AI companion?

Where can I download the Knowunity app?

Is Knowunity really free of charge?

Similar content

maths

Topic 1- Algebra Basics

Completing the Square - GCSE Edexel Maths - Higher

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

4.8/5