# Copy - Equivalent Expressions

Tania Slother

Created on July 2, 2024

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## Transcript

equivalent expressions

Module 3

Lesson 6

Start

navigation

Learning session

Objectives

Introduction

Self-evaluation

Vocabulary

Summary

For more infomation

Liam inserted his card into the terminal, typed in his PIN number, then hit the cash back button. He wanted to get $20 out of his account. Automatically, the clerk replied, "How would you like it back?" meaning, how would you like it to be broken down? There were many combinations that $20 could be broken into. The clerk could have given him:

- one twenty-dollar bill
- two ten-dollar bills
- four five-dollar bills
- one ten-dollar bill, one five-dollar bill, and five one-dollar bills

equivalent expressions

Goals

Objectives:

- understand that an expression written in different ways can be equivalent

- identify when two expressions are eqiuvalent

The McMillen and Dunlap families went to the same carnival over the weekend. Each family purchased amusement tickets and popcorn combos. Let the variable t represent the price per ticket and p represent the price per popcorn combos. Here is the breakdown of their expenses:

Do these two expressions represent the sum correctly? Are these two expressions equivalent? Can you prove it using mathematical operations and properties?

Questions:

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Equivalent EXpressions-scenario

The table shows the total cost for each family, but what about an expression that is equivalent to the sum of both individual expressions? Can there be an expression for that? Look at these two expressions below:

18t + 14p = 2(9t + 7p)?

8t + 6p + 10t + 8p = 18t + 14p?

The McMillen family’s cost is represented with the expression 8t + 6p. The Dunlap family’s cost is represented with the expression 10t + 8p. Notice how both expressions contain two terms. You would think if a two-term expression was added to another two-term expression, there would be four terms total, right? But why does the sum of these two expressions result in a two-term expression, 18t + 14p? This could only happen if some of the terms were combined. Take, for example, 4 + 3 = 7. One number plus one number results in one number, not two separate numbers. This is an example of combining like terms! What are like terms, and how do they work with an algebraic expression? Let’s take a look. Be sure to review the parts of an express if you need a quick reminder.

exploration

check your work

Parts of an Expression

Sometimes, an expression can contain terms that have the same variable. These terms are called like terms. Like terms have identical variable parts but may have different coefficients. When terms have variable parts that are different, they are called unlike terms. Let’s look at a few examples of like and unlike terms:

exploration

unlike terms

like terms

click to enlarge

Practice

Please complete to check your understanding

Combining like terms means combining the coefficients of the like terms. The purpose of combining like terms is to help simplify an expression. Take a look at the examples below to understand what it means to combine like terms:

combine like terms

Combining like terms

practice:

Combine the like terms in the expression shown below. Be sure to show all your steps.

7t + 10 + 3

Combine the like terms in the expression shown below. Be sure to show all your steps.

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3x + 5x

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Complete these problems on your own before checking your answer.

click for answer

click for answer

mathematical properties

Show with another number

Show how they are equivalent

Show with substitution

Show with substitution

In an algebraic expression, you can use the mathematical properties to group and combine like terms. The properties also allow you to prove that two expressions are equivalent. Take a look at the examples below to learn how to identify if other expressions are equivalent using various properties. Be sure to review the mathematical properties if needed, as you will use them to identify equivalent expressions.

MATHEMATICal PROPERTIES

Show with another number

Show how they are equivalent

Show with substitution

Example 1:

Example 2:

Example 3:

Show that the expression 4x + 1 + 3x + 8 is equivalent to 7x + 9. Can you identify which properties are used to show that the two expressions are equivalent? Think about which property allows you to move from step to step.

Use the mathematical properties to prove that 8b + 0 − b is equivalent to 8b.

Use the mathematical properties to prove that 2(x + 5 + 7x) is equivalent to 15x + 10.

learning session / 02

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Question 1/5

True ✓

False

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correctanswer

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Question 2/5

learning session / 02

Write thewrong option hereLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod

Write thecorrect option hereLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod

Write thewrong option hereLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod

His audiam deserunt in, eum ubique voluptatibus te. In reque dicta usu. Ne rebum dissentiet eam, vim omnis deseruisse id. Ullum deleniti vituperata at quo.

correctanswer

Write thewrong option hereLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod

Write thecorrect option hereLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod

Write thewrong option hereLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua?

Question 3/5

learning session / 02

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correctanswer

Write the wrong option here

Write the correct option here

Write the wrong option here

Question 4/5

learning session / 02

Write the wrong option here

correctanswer

Write the wrong option here

Write the correct option here

Write the wrong option here

Question 5/5

learning session / 02

Write the wrong option here

Write the wrong option here

Write the wrong option here

correctanswer

congratulations!

You have answered everything correctly

What knowledgehave you acquired?

- Lorem ipsum dolor sit amet consectetur adipiscing, elit nunc taciti luctus consequat ultricies turpis,
- Lobortis nulla vehicula ultrices egestas. Eu metus quam luctus rutrum eleifend ornare egestas dictumst velit.
- Vulputate mauris lacinia commodo diam dignissim nisi tempor quis integer fermentum lobortis imperdiet.

Summary

learning session / 02

learning session / 03

20XX

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His audiam deserunt in, eum ubique voluptatibus te. In reque dicta usu. Ne rebum dissentiet eam, vim omnis deseruisse id. Ullum deleniti vituperata at quo, insolens complectitur te eos.

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His audiam deserunt in, eum ubique voluptatibus te. In reque dicta usu. Ne rebum dissentiet eam, vim omnis deseruisse id. Ullum deleniti vituperata at quo, insolens complectitur te eos.

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learning session / 03

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Nunc lobortis dui in feugiat fames mattis sodales

Nunc lobortis dui in feugiat fames mattis sodales

Nunc lobortis dui in feugiat fames mattis sodales

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learning session / 03

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+ info

Write a title here

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nulla ut nisl placerat, mattis odio in, ullamcorper dolor. In aliquet purus at odio ullamcorper egestas. Nunc nec semper enim. Cras vel metus nisl. Nullam ut turpis id lorem viverra dictum. Aenean elementum, lectus nec mattis euismod, enim diam cursus diam,id gravida erat turpis in risus. Nulla tellus metus, lobortis at iaculis quis, posuere at diam. Quisque lacinia commodo augue ut lobortis.

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learning session / 03

key ideas

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learning session / 03

example

reflect

case study resolution

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Write a title here

- Mail: aliquet purus dignissim auctor erat habitant
- Drive: feugiat vehicula ultrices taciti ad dis praesent
- Dropbox: nostra himenaeos at mi luctus pharetra

CHECK

vocabulary

Terms in an expression that have the same exact variable part; for example, 5x and 4x are like terms in the expression 5x + 4x.

Like terms

Unlike terms

combine like terms

Terms in an expression that do not have the same exact variable part; for example, 5x and y are unlike terms in the expression 5x + y.

A process of combining terms that have identical variable parts.

example

example

example

summary

Like and Unlike Terms

Like terms have identical variables but may have different coefficients. When terms have vari ables that are different they are called unlike terms.

Proof Expressions are Equivalent

Proof using mathematical properties and simplifying:8t + 6p + 10t + 8p = 8t + 10t + 6p + 8p Use the commutative property. = (8 + 10)t + (6 + 8)p Use the distributive property. = 18t + 14p Combine like terms.= 18t + 14pProof using substitution:18t + 14p 8t + 6p + 10t + 8p =18(1) + 14(1) 8(1) + 6(1) + 10(1) + 8(1) =18 + 14 8 + 6 + 10 + 8 =32 32

Combining Like Terms

Combining like terms means to combine the coefficients of the like terms. Remember, the coefficient of a variable includes the number and the sign in front of the number. The purpose of combining like terms is to simplify an expression. Simplifying makes it easier to evaluate the expression and to prove if it is equivalent to another expression.

Proving Expressions Are Equivalent

In an algebraic expression, you can use the mathematical properties to group and combine like terms. The properties also allow you to prove that the simplified expression is equivalent to the beginning expression.Example: Prove the expression 8t + 6p + 10t + 8p is equivalent to the expression 18t + 14p.

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Self-evaluation

Start

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1/5

correctanswer

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Write thewrong option hereLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod

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2/5

correctanswer

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3/5

correctanswer

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4/5

correctanswer

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Write the wrongoption hereLorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod

5/5

correctanswer

self-evaluation

congratulations

You have answered everything correctly

What knowledgehave you acquired?

- Lorem ipsum dolor sit amet consectetur adipiscing, elit nunc taciti luctus consequat ultricies turpis,
- Lobortis nulla vehicula ultrices egestas. Eu metus quam luctus rutrum eleifend ornare egestas dictumst velit.
- Vulputate mauris lacinia commodo diam dignissim nisi tempor quis integer fermentum lobortis imperdiet.

Summary

Book titleAuthor's Name (2013), Book title. Place of publication: Publisher.

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Título libroAuthor's Name (2013), Book title. Place of publication: Publisher.

Título libroAuthor's Name (2013), Book title. Place of publication: Publisher.

Título libroAuthor's Name (2013), Book title. Place of publication: Publisher.

For more information

Bibliography

Links to resources of interest

- Recommended reading 1

- Recommended reading 2

- Recommended reading 3

- Recommended reading 4

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Learning unit completed

Reflect on what you have learned inthis module.

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NO! 4x² and 2x are not like terms because the variable parts are not identical. One variable is squared, and the other is not.

4x and x are like terms in this algebraic expression. In addition, the constants 2 and 9 are like terms in this expression.

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YES! 6x and -5x are like terms because the variable parts are identical.

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NO! 2x and 2p are unlike terms because the variable parts are not identical.

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