Subjects

Math (SAT®)

Overview

Easy Math Tricks: Substitution, Population Change, and Factoring Fun!

Name: Knowunity
Brand: Knowunity

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Easy Math Tricks: Substitution, Population Change, and Factoring Fun!

@dodd

3 Followers

A comprehensive guide to mathematical expressions and conversions, focusing on simplification techniques, percentage calculations, and unit conversions. The material covers essential algebraic concepts and practical applications.

Introduces the law of substitution for simplifying math expressions
Demonstrates methods for calculating population decrease percentage over years
Explores understanding important factoring identities in algebra
Covers conversion factors and their applications
Presents problem-solving strategies with real-world examples

9/14/2023

310

lesson 3: Simpliying Expression S
1
The law of Substitution -
-- if two things are equal, you can
always Substitute one for the other
ex: If

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Page 2: Simplifying Operations and Factoring Identities

This page covers advanced operations and crucial algebraic identities.

Definition: Important factoring identities include:

a² + b² = (a+b)(a-b)
a² + 2ab + b² = (a+b)(a+b)
a² - 2ab + b² = (a-b)(a-b)

Example: When increasing a number by 25% and then decreasing by 50%, the process can be expressed as 0.50(1.25n) = 0.625n.

Highlight: Complex expressions can often be simplified using these standard factoring patterns.

View

Page 3: Pattern Recognition in Algebraic Expressions

This section focuses on identifying and utilizing patterns in mathematical expressions.

Highlight: Pattern recognition is crucial for efficient problem-solving in algebra.

Example: The pattern (x+2)² = x² + 4x + 4 can be used for clever substitutions.

Vocabulary: Substitution patterns help transform complex expressions into simpler forms.

View

Page 4: Conversion Fundamentals

This page introduces the concept of conversion factors and their practical applications.

Definition: A conversion factor is a fraction where the numerator and denominator are equal but expressed in different units.

Example: Converting 10 kilometers to miles using the conversion factor (1 mile/1.609 kilometers) = 6.215 miles.

Highlight: Units must cancel properly like common factors when using conversion factors.

View

Page 5: Types of Conversions

The final page distinguishes between different types of conversion factors and their applications.

Definition: Universal conversions are standard relationships (like 1 pound = 16 ounces), while problem-specific conversions depend on the context.

Example: In manufacturing calculations, converting between days, production rates, and costs requires problem-specific conversion factors.

Highlight: Understanding whether to use universal or problem-specific conversions is crucial for solving real-world problems accurately.

View

Page 1: Law of Substitution and Percentage Problems

The first page introduces fundamental concepts in mathematical simplification and percentage calculations.

Definition: The law of substitution states that if two things are equal, you can substitute one for the other in any expression.

Example: When solving equations like 3x-2y=7, if x=3 and y=1 satisfy the equation, these values can be used to evaluate related expressions.

Highlight: For percentage problems, to decrease a number by a%, multiply by (100-a)%.

Example: In calculating sea urchin population decrease, three consecutive 10% decreases result in multiplying by (0.90)³, yielding a 27.1% total decrease rather than an intuitive 30%.

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.

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

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Subjects

Math (SAT®)

Overview

Easy Math Tricks: Substitution, Population Change, and Factoring Fun!

@dodd

3 Followers

Introduces the law of substitution for simplifying math expressions
Demonstrates methods for calculating population decrease percentage over years
Explores understanding important factoring identities in algebra
Covers conversion factors and their applications
Presents problem-solving strategies with real-world examples

9/14/2023

310

12th

Math (SAT®)

Page 2: Simplifying Operations and Factoring Identities

This page covers advanced operations and crucial algebraic identities.

Definition: Important factoring identities include:

a² + b² = (a+b)(a-b)
a² + 2ab + b² = (a+b)(a+b)
a² - 2ab + b² = (a-b)(a-b)

Example: When increasing a number by 25% and then decreasing by 50%, the process can be expressed as 0.50(1.25n) = 0.625n.

Highlight: Complex expressions can often be simplified using these standard factoring patterns.

Page 3: Pattern Recognition in Algebraic Expressions

This section focuses on identifying and utilizing patterns in mathematical expressions.

Highlight: Pattern recognition is crucial for efficient problem-solving in algebra.

Example: The pattern (x+2)² = x² + 4x + 4 can be used for clever substitutions.

Vocabulary: Substitution patterns help transform complex expressions into simpler forms.

Page 4: Conversion Fundamentals

This page introduces the concept of conversion factors and their practical applications.

Definition: A conversion factor is a fraction where the numerator and denominator are equal but expressed in different units.

Example: Converting 10 kilometers to miles using the conversion factor (1 mile/1.609 kilometers) = 6.215 miles.

Highlight: Units must cancel properly like common factors when using conversion factors.

Page 5: Types of Conversions

The final page distinguishes between different types of conversion factors and their applications.

Definition: Universal conversions are standard relationships (like 1 pound = 16 ounces), while problem-specific conversions depend on the context.

Example: In manufacturing calculations, converting between days, production rates, and costs requires problem-specific conversion factors.

Highlight: Understanding whether to use universal or problem-specific conversions is crucial for solving real-world problems accurately.

Page 1: Law of Substitution and Percentage Problems

The first page introduces fundamental concepts in mathematical simplification and percentage calculations.

Definition: The law of substitution states that if two things are equal, you can substitute one for the other in any expression.

Example: When solving equations like 3x-2y=7, if x=3 and y=1 satisfy the equation, these values can be used to evaluate related expressions.

Highlight: For percentage problems, to decrease a number by a%, multiply by (100-a)%.

Example: In calculating sea urchin population decrease, three consecutive 10% decreases result in multiplying by (0.90)³, yielding a 27.1% total decrease rather than an intuitive 30%.

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.

Download in

Google Play

Download in

App Store

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