Subjects

Subjects

More

Search

AI Knowunity

Subjects

/

Arithmetic

/

Negative Numbers

/

Multiply & Divide Negative Fractions

Fun with Fractions: Easy Tips on Multiplying, Dividing, and Simplifying

View

Fun with Fractions: Easy Tips on Multiplying, Dividing, and Simplifying
user profile picture

Chelsea

@zuncho

·

625 Followers

Follow

This lesson covers multiplying and dividing rational numbers fractions rules and simplifying fractions using order of operations. It explains how to multiply and divide fractions, including negative fractions, and emphasizes the importance of following the correct order of operations. The lesson also touches on the commutative and associative properties in fraction operations.

Key points include:

  • Rules for multiplying and dividing integers
  • Techniques for multiplying and dividing fractions
  • The importance of reducing fractions before or after multiplication
  • The use of reciprocals in fraction division
  • The order of operations for simplifying complex fraction expressions
  • Application of commutative and associative properties in fraction operations

5/15/2023

77

2.4A Multiplying & Dividing Rational Numbers - Fractions Recall the rules for multiplying and dividing integers: SAME signs = POSITIVE answe

View

Order of Operations and Fraction Simplification

This page focuses on the order of operations, which is crucial for simplifying fractions using order of operations. It provides a clear, step-by-step guide for evaluating expressions containing fractions and other operations.

The order of operations is presented as follows:

  1. Evaluate expressions inside grouping symbols: ( ) [ ] { } | | & fraction bars
  2. Evaluate powers: 2³
  3. Multiply and divide from left to right
  4. Add and subtract from left to right

Vocabulary: PEMDAS (Please Excuse My Dear Aunt Sally) is mentioned as a mnemonic device to remember the order of operations.

The page includes examples of simplifying complex fraction expressions:

Example: ¹/₃ ÷ (-4) · (-4) = ¹/₃ · ¹/₁ = ¹/₃

This example demonstrates the application of the order of operations and the commutative property in simplifying a fraction expression.

The lesson concludes with practice problems for students to apply their understanding of fraction operations and simplification:

Highlight: The practice problems include finding differences between fractions, emphasizing the importance of checking for reasonableness in answers.

These exercises reinforce the concepts of adding, subtracting, multiplying, and dividing fractions, as well as the application of the order of operations in more complex expressions.

2.4A Multiplying & Dividing Rational Numbers - Fractions Recall the rules for multiplying and dividing integers: SAME signs = POSITIVE answe

View

Multiplying and Dividing Rational Numbers - Fractions

This page introduces the fundamental rules for multiplying and dividing rational numbers, specifically focusing on fractions. It covers the sign rules for multiplication and division of integers, which are essential when working with negative fractions.

The page explains the process of multiplying fractions, which involves multiplying the numerators and denominators separately and then reducing the result if possible. For division, it introduces the concept of using the reciprocal of the divisor.

Definition: The reciprocal of a fraction is obtained by flipping the numerator and denominator. This is also referred to as the "re-FLIP-rocal" in the text.

Several examples are provided to illustrate these concepts:

Example: -²/₇ × ³/₅ = -⁶/₃₅

This example demonstrates multiplication of fractions with different signs, resulting in a negative fraction.

Example: ¹⁷/₄ ÷ ¹/₃ = ¹⁷/₄ × ³/₁ = ⁵¹/₄

This example shows division of fractions by multiplying by the reciprocal of the divisor.

The page also touches on important mathematical properties:

Highlight: The commutative property (changing order), associative property (changing grouping), multiplicative inverse (multiplying by reciprocal equals 1), and multiplicative identity (multiplying by 1 equals itself) are all mentioned as key concepts in fraction operations.

These properties are crucial for understanding more complex fraction operations and for simplifying expressions efficiently.

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

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

/

Arithmetic

/

Negative Numbers

/

Multiply & Divide Negative Fractions

Fun with Fractions: Easy Tips on Multiplying, Dividing, and Simplifying

user profile picture

Chelsea

@zuncho

·

625 Followers

Follow

This lesson covers multiplying and dividing rational numbers fractions rules and simplifying fractions using order of operations. It explains how to multiply and divide fractions, including negative fractions, and emphasizes the importance of following the correct order of operations. The lesson also touches on the commutative and associative properties in fraction operations.

Key points include:

  • Rules for multiplying and dividing integers
  • Techniques for multiplying and dividing fractions
  • The importance of reducing fractions before or after multiplication
  • The use of reciprocals in fraction division
  • The order of operations for simplifying complex fraction expressions
  • Application of commutative and associative properties in fraction operations

5/15/2023

77

 

7th/8th

 

Arithmetic

7

2.4A Multiplying & Dividing Rational Numbers - Fractions Recall the rules for multiplying and dividing integers: SAME signs = POSITIVE answe

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Order of Operations and Fraction Simplification

This page focuses on the order of operations, which is crucial for simplifying fractions using order of operations. It provides a clear, step-by-step guide for evaluating expressions containing fractions and other operations.

The order of operations is presented as follows:

  1. Evaluate expressions inside grouping symbols: ( ) [ ] { } | | & fraction bars
  2. Evaluate powers: 2³
  3. Multiply and divide from left to right
  4. Add and subtract from left to right

Vocabulary: PEMDAS (Please Excuse My Dear Aunt Sally) is mentioned as a mnemonic device to remember the order of operations.

The page includes examples of simplifying complex fraction expressions:

Example: ¹/₃ ÷ (-4) · (-4) = ¹/₃ · ¹/₁ = ¹/₃

This example demonstrates the application of the order of operations and the commutative property in simplifying a fraction expression.

The lesson concludes with practice problems for students to apply their understanding of fraction operations and simplification:

Highlight: The practice problems include finding differences between fractions, emphasizing the importance of checking for reasonableness in answers.

These exercises reinforce the concepts of adding, subtracting, multiplying, and dividing fractions, as well as the application of the order of operations in more complex expressions.

2.4A Multiplying & Dividing Rational Numbers - Fractions Recall the rules for multiplying and dividing integers: SAME signs = POSITIVE answe

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Multiplying and Dividing Rational Numbers - Fractions

This page introduces the fundamental rules for multiplying and dividing rational numbers, specifically focusing on fractions. It covers the sign rules for multiplication and division of integers, which are essential when working with negative fractions.

The page explains the process of multiplying fractions, which involves multiplying the numerators and denominators separately and then reducing the result if possible. For division, it introduces the concept of using the reciprocal of the divisor.

Definition: The reciprocal of a fraction is obtained by flipping the numerator and denominator. This is also referred to as the "re-FLIP-rocal" in the text.

Several examples are provided to illustrate these concepts:

Example: -²/₇ × ³/₅ = -⁶/₃₅

This example demonstrates multiplication of fractions with different signs, resulting in a negative fraction.

Example: ¹⁷/₄ ÷ ¹/₃ = ¹⁷/₄ × ³/₁ = ⁵¹/₄

This example shows division of fractions by multiplying by the reciprocal of the divisor.

The page also touches on important mathematical properties:

Highlight: The commutative property (changing order), associative property (changing grouping), multiplicative inverse (multiplying by reciprocal equals 1), and multiplicative identity (multiplying by 1 equals itself) are all mentioned as key concepts in fraction operations.

These properties are crucial for understanding more complex fraction operations and for simplifying expressions efficiently.

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

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying