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3.3.1 - Addition and Subtraction

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Understanding Like Terms

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Teacher
Teacher

Today, we're diving into the world of addition and subtraction in algebra. Who can tell me what like terms are?

Student 1
Student 1

Are like terms just terms that have the same number?

Teacher
Teacher

Not quite! Like terms are terms that have the same variable raised to the same power. For example, 2x and 5x are like terms because they both contain the variable x to the first power.

Student 2
Student 2

So, can we just add their coefficients?

Teacher
Teacher

Exactly! If we have 2x + 5x, we combine those coefficients to get 7x. Remember, we only combine like terms!

Teacher
Teacher

Now, let's all remember: 'Only combine terms that are alike!' Can everyone repeat that?

Students
Students

Only combine terms that are alike!

Teacher
Teacher

Great job! Let’s move on to an example.

Combining Terms through Subtraction

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Teacher
Teacher

Now, let’s explore subtraction of like terms. What happens when we subtract them? Who can give an example?

Student 3
Student 3

If we have 5x - 2x, we would just subtract the coefficients, right?

Teacher
Teacher

That's correct! So, what do we get for 5x - 2x?

Student 4
Student 4

That would be 3x!

Teacher
Teacher

Awesome! Just remember that you keep the variable part the same. If you have different variables, you cannot combine them.

Student 2
Student 2

What if one term is negative?

Teacher
Teacher

Excellent question! If we have something like 3x - 4y, we can't combine them because the variables are different. They remain as is.

Practical Application

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Teacher
Teacher

Let’s apply what we learned today. If I give you the expression 4x + 3y - 2x + y, could someone walk me through simplifying it?

Student 1
Student 1

Sure! First, I see that 4x and -2x are like terms.

Teacher
Teacher

Right! What do you get when you combine those?

Student 1
Student 1

That would be 2x.

Student 4
Student 4

And then I see 3y and y. Those are like terms, too!

Teacher
Teacher

Absolutely! What do we get from combining those?

Student 4
Student 4

That will be 4y!

Teacher
Teacher

Great work! So the final simplified expression is 2x + 4y. Remember, practice makes perfect!

Introduction & Overview

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Quick Overview

This section introduces the concepts of addition and subtraction of algebraic expressions, emphasizing the importance of combining like terms.

Standard

In this section, we explore the operations of addition and subtraction within algebraic expressions. The key focus is on the process of combining like terms by adding or subtracting their coefficients, which simplifies expressions and leads to efficient problem-solving.

Detailed

In algebra, understanding addition and subtraction is fundamental to manipulating algebraic expressions. This section delves into the process of combining like terms, which involves identifying terms that share the same variable parts. The coefficients of these terms are then added or subtracted to simplify expressions. Mastering these operations not only aids in performing more complex algebraic manipulations but also lays the groundwork for further topics such as multiplication and division of algebraic expressions.

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Combining Like Terms

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● Combine like terms by adding or subtracting their coefficients.

Detailed Explanation

Combining like terms is a fundamental step in simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power. To combine them, you simply add or subtract their coefficients, which are the numerical parts of these terms. For instance, if you have the terms 3x and 5x, they are like terms because they both contain the variable x. You would add their coefficients (3 + 5) to get 8x. On the other hand, if you had 3x and 4y, you cannot combine them because they are not like terms.

Examples & Analogies

Think of like terms as apples and oranges. If you have 3 apples and 5 apples, you can say you have 8 apples in total. But if you have 3 apples and 4 oranges, you can’t combine them – you still have 3 apples and 4 oranges.

Definitions & Key Concepts

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Key Concepts

  • Combining Like Terms: The process of summing or subtracting the coefficients of like terms.

  • Coefficients: The numerical part that multiplies the variable in an expression.

Examples & Real-Life Applications

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Examples

  • Combine the like terms: 3x + 5x = 8x.

  • Subtract the like terms: 6y - 2y = 4y.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • Combine terms that are alike, coefficients you will hike!

📖 Fascinating Stories

  • Once in the land of Algebra, the brave knight only combined like terms, ensuring his kingdom remained orderly and balanced.

🧠 Other Memory Gems

  • C.L.T. - Combine Like Terms: Always remember to combine those that are alike!

🎯 Super Acronyms

L.T. - Like Terms

  • Remember
  • only combine when it's L.T.!

Flash Cards

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Glossary of Terms

Review the Definitions for terms.

  • Term: Algebraic Expression

    Definition:

    A mathematical phrase that contains numbers, variables, and operations.

  • Term: Like Terms

    Definition:

    Terms that have the same variables raised to the same powers.

  • Term: Coefficient

    Definition:

    The numerical factor in front of a variable in an algebraic term.

  • Term: Unlike Terms

    Definition:

    Terms that have different variables or different powers.