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Algebra 1

Basics

Overview and History of Algebra

1,214

•

Oct 22, 2023

•

4 pages

Fun with Numbers: Integer Rules and Order of Operations for Kids!

user profile picture

Kate

@kate628

Integer rules in algebra form the foundation for performing operations... Show more

UNIT 1: DAY I' INTEGER RULES integer a positive or negative whole numbers and zero. ¡ INTEGER RULES Subtraction addition Same signs: when ad

Order of Operations

This page covers the essential concept of order of operations, which provides the rules for simplifying expressions with multiple steps.

The order of operations is represented by the acronym PEMDAS:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division lefttorightleft to right
  4. Addition and Subtraction lefttorightleft to right

Definition: Order of operations refers to the rules that determine the sequence in which mathematical operations should be performed when simplifying expressions.

Vocabulary:

  • Base: The number being multiplied in an exponent expression
  • Exponent: The number indicating how many times to multiply the base
  • Square root: A value that, when multiplied by itself, gives the number under the root
  • Cube root: A value that, when multiplied by itself three times, gives the number under the root
  • Absolute value: The distance between a number and zero on a number line

Example: Simplify 23x4−53 x 4 - 5 + 6 x 10 + 4 using the order of operations

UNIT 1: DAY I' INTEGER RULES integer a positive or negative whole numbers and zero. ¡ INTEGER RULES Subtraction addition Same signs: when ad

Evaluating Algebraic Expressions

This page focuses on the process of evaluating algebraic expressions by substituting values for variables and following the order of operations.

Steps to evaluate an algebraic expression:

  1. Replace each variable with the given value useparenthesesuse parentheses
  2. Multiply when a variable is next to a number
  3. Use the order of operations to simplify the expression

Definition: An algebraic expression is a mathematical sentence containing variables, numbers, and operations.

Vocabulary:

  • Substitute: Replace a variable with a defined number
  • Term: A number, variable, or number multiplied by variabless
  • Constant: A fixed value without a variable being multiplied with it
  • Coefficient: A number used to multiply a variable
  • Like terms: Terms with the same variables and exponents

Example: Evaluate 3x² - 7 when x = 2

UNIT 1: DAY I' INTEGER RULES integer a positive or negative whole numbers and zero. ¡ INTEGER RULES Subtraction addition Same signs: when ad

Simplifying Algebraic Expressions and Applications

This final page covers techniques for simplifying algebraic expressions, including combining like terms and using the distributive property. It also introduces geometry applications and translating word problems into expressions.

Steps to simplify expressions:

  1. Distribute ifnecessaryif necessary
  2. Combine like terms

The distributive property states that multiplying a number by a group of numbers added together gives the same result as doing each multiplication separately.

Example: 42x+12x + 1 = 42x2x + 411 = 8x + 4

Geometry application: To find the perimeter of a shape, add up the lengths of all sides.

Translating word problems into expressions:

  • Addition: sum, total, all together, plus, increase, more than
  • Subtraction: minus, difference, fewer, take away, decrease, less than
  • Multiplication: product, times, per, each
  • Division: quotient, average, per, each

Highlight: When simplifying expressions, remember to only combine like terms and keep the variables and exponents unchanged.

Vocabulary: Translate in mathematics means expressing a word problem or situation in mathematical language.

UNIT 1: DAY I' INTEGER RULES integer a positive or negative whole numbers and zero. ¡ INTEGER RULES Subtraction addition Same signs: when ad

Integer Rules

This page introduces the fundamental rules of integers for addition, subtraction, multiplication, and division. Understanding these rules is crucial for working with positive and negative numbers in algebra.

Addition Rules for Integers:

  • For same signs, add the numbers and keep the sign
  • For different signs, subtract the numbers and keep the sign of the larger number

Subtraction Rule for Integers:

  • Use the "keep-change-change" method: keep the first number, change subtraction to addition, and change the sign of the second number

Multiplication and Division Rules for Integers:

  • Same signs result in a positive answer
  • Different signs result in a negative answer

Example: 12 - −5-5 = 12 + 5 = 17 usingthekeep−change−changemethodusing the keep-change-change method

Vocabulary: An integer is defined as a positive or negative whole number, including zero.

Highlight: The "keep-change-change" method for subtraction is a key technique for working with negative numbers.



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

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

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

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

Subjects

Algebra 1

Basics

Overview and History of Algebra

 

Algebra 1

•

1,214

•

Oct 22, 2023

•

4 pages

Fun with Numbers: Integer Rules and Order of Operations for Kids!

user profile picture

Kate

@kate628

Integer rules in algebra form the foundation for performing operations with positive and negative whole numbers. This guide covers key concepts including integer rules in algebra 1 with examples, order of operations, evaluating and simplifying algebraic expressions, and translating... Show more

UNIT 1: DAY I' INTEGER RULES integer a positive or negative whole numbers and zero. ¡ INTEGER RULES Subtraction addition Same signs: when ad

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

Order of Operations

This page covers the essential concept of order of operations, which provides the rules for simplifying expressions with multiple steps.

The order of operations is represented by the acronym PEMDAS:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division lefttorightleft to right
  4. Addition and Subtraction lefttorightleft to right

Definition: Order of operations refers to the rules that determine the sequence in which mathematical operations should be performed when simplifying expressions.

Vocabulary:

  • Base: The number being multiplied in an exponent expression
  • Exponent: The number indicating how many times to multiply the base
  • Square root: A value that, when multiplied by itself, gives the number under the root
  • Cube root: A value that, when multiplied by itself three times, gives the number under the root
  • Absolute value: The distance between a number and zero on a number line

Example: Simplify 23x4−53 x 4 - 5 + 6 x 10 + 4 using the order of operations

UNIT 1: DAY I' INTEGER RULES integer a positive or negative whole numbers and zero. ¡ INTEGER RULES Subtraction addition Same signs: when ad

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

Evaluating Algebraic Expressions

This page focuses on the process of evaluating algebraic expressions by substituting values for variables and following the order of operations.

Steps to evaluate an algebraic expression:

  1. Replace each variable with the given value useparenthesesuse parentheses
  2. Multiply when a variable is next to a number
  3. Use the order of operations to simplify the expression

Definition: An algebraic expression is a mathematical sentence containing variables, numbers, and operations.

Vocabulary:

  • Substitute: Replace a variable with a defined number
  • Term: A number, variable, or number multiplied by variabless
  • Constant: A fixed value without a variable being multiplied with it
  • Coefficient: A number used to multiply a variable
  • Like terms: Terms with the same variables and exponents

Example: Evaluate 3x² - 7 when x = 2

UNIT 1: DAY I' INTEGER RULES integer a positive or negative whole numbers and zero. ¡ INTEGER RULES Subtraction addition Same signs: when ad

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

Simplifying Algebraic Expressions and Applications

This final page covers techniques for simplifying algebraic expressions, including combining like terms and using the distributive property. It also introduces geometry applications and translating word problems into expressions.

Steps to simplify expressions:

  1. Distribute ifnecessaryif necessary
  2. Combine like terms

The distributive property states that multiplying a number by a group of numbers added together gives the same result as doing each multiplication separately.

Example: 42x+12x + 1 = 42x2x + 411 = 8x + 4

Geometry application: To find the perimeter of a shape, add up the lengths of all sides.

Translating word problems into expressions:

  • Addition: sum, total, all together, plus, increase, more than
  • Subtraction: minus, difference, fewer, take away, decrease, less than
  • Multiplication: product, times, per, each
  • Division: quotient, average, per, each

Highlight: When simplifying expressions, remember to only combine like terms and keep the variables and exponents unchanged.

Vocabulary: Translate in mathematics means expressing a word problem or situation in mathematical language.

UNIT 1: DAY I' INTEGER RULES integer a positive or negative whole numbers and zero. ¡ INTEGER RULES Subtraction addition Same signs: when ad

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

Integer Rules

This page introduces the fundamental rules of integers for addition, subtraction, multiplication, and division. Understanding these rules is crucial for working with positive and negative numbers in algebra.

Addition Rules for Integers:

  • For same signs, add the numbers and keep the sign
  • For different signs, subtract the numbers and keep the sign of the larger number

Subtraction Rule for Integers:

  • Use the "keep-change-change" method: keep the first number, change subtraction to addition, and change the sign of the second number

Multiplication and Division Rules for Integers:

  • Same signs result in a positive answer
  • Different signs result in a negative answer

Example: 12 - −5-5 = 12 + 5 = 17 usingthekeep−change−changemethodusing the keep-change-change method

Vocabulary: An integer is defined as a positive or negative whole number, including zero.

Highlight: The "keep-change-change" method for subtraction is a key technique for working with negative numbers.

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

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

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

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