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Algebra 1

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Basics

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Overview and History of Algebra

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

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

@kate628

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67 Followers

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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 word problems into mathematical expressions. Students will learn essential skills for working with integers, variables, and algebraic expressions through clear explanations and practice problems.

• Integer rules cover addition, subtraction, multiplication, and division of positive and negative numbers
• Order of operations (PEMDAS) provides the sequence for simplifying multi-step expressions
• Evaluating expressions involves substituting values for variables and following order of operations
• Simplifying expressions requires combining like terms and applying the distributive property
• Translating word problems into algebraic expressions uses key phrases to represent operations

10/22/2023

994

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

View

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 (left to right)
  4. Addition and Subtraction (left 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 2(3 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

View

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 (use 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 variable(s)
  • 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

View

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 (if 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: 4(2x + 1) = 4(2x) + 4(1) = 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

View

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) = 12 + 5 = 17 (using 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.

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Subjects

/

Algebra 1

/

Basics

/

Overview and History of Algebra

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

user profile picture

Kate

@kate628

·

67 Followers

Follow

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 word problems into mathematical expressions. Students will learn essential skills for working with integers, variables, and algebraic expressions through clear explanations and practice problems.

• Integer rules cover addition, subtraction, multiplication, and division of positive and negative numbers
• Order of operations (PEMDAS) provides the sequence for simplifying multi-step expressions
• Evaluating expressions involves substituting values for variables and following order of operations
• Simplifying expressions requires combining like terms and applying the distributive property
• Translating word problems into algebraic expressions uses key phrases to represent operations

10/22/2023

994

 

9th/10th

 

Algebra 1

69

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

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Access to all documents

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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 (left to right)
  4. Addition and Subtraction (left 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 2(3 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 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

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 (use 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 variable(s)
  • 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 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

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 (if 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: 4(2x + 1) = 4(2x) + 4(1) = 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 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

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) = 12 + 5 = 17 (using 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.

Similar Content

Algebra 1 - Perpendicular bisectors theorem

Perpendicular bisectors theorem notes

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Know Perpendicular bisectors theorem thumbnail

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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