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Fractions Made Easy: Simplifying, Comparing, and Calculating!

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Bill

5/23/2023

Arithmetic

Math 7 | Operations with Fractions Notes

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Adding & Subtracting Rational Numbers

Fractions Made Easy: Simplifying, Comparing, and Calculating!

A comprehensive guide to fundamental fraction operations covering simplification, comparison, and arithmetic operations.

  • Master the simplifying and comparing fractions technique through clear step-by-step instructions and practical examples
  • Learn adding and subtracting mixed numbers with detailed explanations of converting between mixed numbers and improper fractions
  • Understand the steps for multiplying and dividing fractions including cross-cancellation and working with reciprocals
  • Explore proper fractions, improper fractions, and mixed numbers with real-world applications
  • Practice with guided examples demonstrating each concept systematically
...

5/23/2023

179

➜ Simplifying & Comparing Fractions. Fraction represents a part of a whole piece. numerator denominator Ź 3/353 proper fraction Examples: Si

View

Adding and Subtracting Fractions

This section covers the essential techniques for adding and subtracting fractions, with special attention to working with mixed numbers and common denominators.

Definition: Sum refers to addition while difference refers to subtraction in fraction operations.

Example: When adding fractions with common denominators, add only the numerators: 5/8 + 3/8 = 8/8 = 1

Highlight: Converting mixed numbers to improper fractions is crucial before performing addition or subtraction operations.

Vocabulary: Mixed number conversion involves multiplying the whole number by the denominator and adding the numerator.

➜ Simplifying & Comparing Fractions. Fraction represents a part of a whole piece. numerator denominator Ź 3/353 proper fraction Examples: Si

View

Multiplying Fractions

The page details the systematic approach to multiplying fractions and mixed numbers effectively.

Definition: Cross canceling is the process of simplifying factors before multiplication.

Example: When multiplying fractions, multiply numerators together and denominators together: 1/3 × 3/1 = 3/3 = 1

Highlight: Always convert mixed numbers to improper fractions before multiplication.

Quote: "To multiply fractions or mixed numbers: 1. Rewrite mixed numbers and whole numbers as improper fractions. 2. Simplify factors if possible by cross canceling."

➜ Simplifying & Comparing Fractions. Fraction represents a part of a whole piece. numerator denominator Ź 3/353 proper fraction Examples: Si

View

Dividing Fractions

This final section explains the KCF Keep,Change,FlipKeep, Change, Flip method for dividing fractions effectively.

Definition: The KCF method stands for Keep the first fraction, Change division to multiplication, Flip the second fraction.

Example: When dividing fractions, multiply by the reciprocal of the divisor: 1/2 ÷ 3 = 1/2 × 1/3

Highlight: Converting mixed numbers to improper fractions is essential before applying the KCF method.

Vocabulary: Reciprocal - the fraction obtained by flipping the numerator and denominator.

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Subjects

Arithmetic

Rational Numbers

Adding & Subtracting Rational Numbers

 

Arithmetic

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179

•

May 23, 2023

•

4 pages

Fractions Made Easy: Simplifying, Comparing, and Calculating!

user profile picture

Bill

@bill_uidw

A comprehensive guide to fundamental fraction operations covering simplification, comparison, and arithmetic operations.

  • Master the simplifying and comparing fractions technique through clear step-by-step instructions and practical examples
  • Learn adding and subtracting mixed numberswith detailed explanations of converting between mixed... Show more

➜ Simplifying & Comparing Fractions. Fraction represents a part of a whole piece. numerator denominator Ź 3/353 proper fraction Examples: Si

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Adding and Subtracting Fractions

This section covers the essential techniques for adding and subtracting fractions, with special attention to working with mixed numbers and common denominators.

Definition: Sum refers to addition while difference refers to subtraction in fraction operations.

Example: When adding fractions with common denominators, add only the numerators: 5/8 + 3/8 = 8/8 = 1

Highlight: Converting mixed numbers to improper fractions is crucial before performing addition or subtraction operations.

Vocabulary: Mixed number conversion involves multiplying the whole number by the denominator and adding the numerator.

➜ Simplifying & Comparing Fractions. Fraction represents a part of a whole piece. numerator denominator Ź 3/353 proper fraction Examples: Si

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Multiplying Fractions

The page details the systematic approach to multiplying fractions and mixed numbers effectively.

Definition: Cross canceling is the process of simplifying factors before multiplication.

Example: When multiplying fractions, multiply numerators together and denominators together: 1/3 × 3/1 = 3/3 = 1

Highlight: Always convert mixed numbers to improper fractions before multiplication.

Quote: "To multiply fractions or mixed numbers: 1. Rewrite mixed numbers and whole numbers as improper fractions. 2. Simplify factors if possible by cross canceling."

➜ Simplifying & Comparing Fractions. Fraction represents a part of a whole piece. numerator denominator Ź 3/353 proper fraction Examples: Si

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Dividing Fractions

This final section explains the KCF Keep,Change,FlipKeep, Change, Flip method for dividing fractions effectively.

Definition: The KCF method stands for Keep the first fraction, Change division to multiplication, Flip the second fraction.

Example: When dividing fractions, multiply by the reciprocal of the divisor: 1/2 ÷ 3 = 1/2 × 1/3

Highlight: Converting mixed numbers to improper fractions is essential before applying the KCF method.

Vocabulary: Reciprocal - the fraction obtained by flipping the numerator and denominator.

➜ Simplifying & Comparing Fractions. Fraction represents a part of a whole piece. numerator denominator Ź 3/353 proper fraction Examples: Si

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Understanding Fraction Basics

This page introduces fundamental concepts of fractions and their simplification. The content focuses on proper fractions, improper fractions, and mixed numbers, along with methods for simplifying and comparing them.

Definition: A fraction represents a part of a whole piece, consisting of a numerator topnumbertop number and denominator bottomnumberbottom number.

Example: When simplifying fractions, reduce by finding common factors. For instance, 42/14 simplifies to 3/1.

Vocabulary: Proper fraction - numerator is less than denominator; Improper fraction - numerator is greater than denominator; Mixed number - whole number with a proper fraction.

Highlight: To find equivalent fractions, multiply or divide both the numerator and denominator by the same non-zero number.

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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.

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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

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Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

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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

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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.

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I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

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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

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

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

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

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

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user