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Algebra Worksheet -- Using the Distributive Property (Answers Do Not Include Exponents) Author: Math-Drills.com -- Free Math Worksheets Subject: Algebra Keywords: math, algebra, distributive, property, expression, simplify Created Date: 9/18/2012 11:35:12 AM Algebra Word Problems Help & Answers | How to Solve Word Problems, Combining Like Terms Examples, Simplification & Rules | How to Combine Like Terms, Graphing Linear Inequalities Overview & Examples | How to Solve Linear Inequalities, Taxes & Discounts: Calculations & Examples, Combining Like Terms with the Distributive Property, Translation, Rotation & Reflection | Overview, Differences & Examples, Complementary, Supplementary, Vertical & Adjacent Angles | Overview, Formula & Examples, Equation Lesson for Kids: Definition & Examples, Volume Formulas for Pyramids, Prisms, Cones & Cylinders, Simplifying Variable Expressions Examples | How to Simplify Algebraic Expressions. We add 100+ K-8, common core aligned worksheets every month. var editClose = document.getElementsByClassName("edit-close"); The operation inside the parentheses, whether addition or subtraction, can be done first, or the multiplication can be distributed to the terms inside the parentheses first, then those products are added or subtracted. The distributive properties, sometimes called distributive laws, say that when multiplying a number by either a sum or a difference, the solution will be the same whether the addition or subtraction are done first or second. However, we cannot add x and 2 since they are not like terms. var upsellModal = document.getElementById("upsellModal"); Okay, -2x * -8y. 0% average accuracy. 2:VA(}:C^6MY"?1s_0WqGq](g 7Q}(NHRHog@T;?AT$jh)~':R_NxQ)JO8dqvLIQ f4} Ebl; )Ht(HYwOq '3R6+ R.s\f&"0|L%G5?w)27m A1LN\NNDe'i&'zNLNUendy|([-GlZx4;r?TT:M32DFcMS%)3Rm > P`MXG8#UI=^R,%C$S9 =x[4''.H3e| The final answer will be the same either way. wrBtWX'{r?4&&!ir"8VwQ03drG/d/2v#aOeQ89|L9?W69u } Think of it this way: a(b + c) = (ab) + (ac). This page includes printable worksheets on The Distributive Property. All the mail for Wyoming goes in one place, and all the mail for Japan goes in another. Polygon Types & Examples | Interior & Exterior Angles in Polygons, ASSET Intermediate Algebra Test: Practice & Study Guide, College Preparatory Mathematics: Help and Review, High School Algebra II: Homework Help Resource, Prentice Hall Algebra 2: Online Textbook Help, Test for Admission into Catholic High Schools (TACHS): Practice & Study Guide, Ohio Graduation Test: Study Guide & Practice, High School Precalculus: Tutoring Solution, High School Algebra II: Tutoring Solution, Create an account to start this course today. This method is sometimes called FOIL, standing for Firsts, Outsides, Insides, Lasts. It provides the means to eliminate the parentheses and simplify the expression. Example: 2 ( 5 + 3) = (2 x 5) | 7 showEditModal(); The distributive property is easier to understand using symbols than using words. Transformations in Math Types & Examples | What is Transformation? In summary, the distributive property can be expressed as a(b + c) = (ab) + (ac). | {{course.flashcardSetCount}} To simplify algebraic expressions, we can follow the following steps and simple rules: 1. Associative: Commutative: Summary: All 3 of these All three of these properties can also be applied to Algebraic Expressions. Plus, get practice tests, quizzes, and personalized coaching to help you Embedded content, if any, are copyrights of their respective owners. The distributive property is a method you can use to simplify expressions, especially when there are variables. 14 best images of multi-step equations worksheets with answers. if (event.target == editModal) { Create your account, 17 chapters | Suppose a basketball coach wants to buy each of its team members a framed team photo and a participant medal at the end of the season. Then, solve the equation. Enrolling in a course lets you earn progress by passing quizzes and exams. For Sum. Lesson Plans and Worksheets for Algebra I For this, we use the distributive property when we have multiplication by parentheses, like a ( b + c). We get positive 16xy. upsellModal.style.display = "block"; We have multiplication by two parentheses. Jeff teaches high school English, math and other subjects. In algebra, we use the Distributive Property to remove parentheses as we simplify expressions. editModal.style.display = "none"; The ELM and EPT exams are no longer being offered. Simplify: 5(2f - 8) = 10f - 40. Multi-Color Border Task Cards. Mathematics. lessons in math, English, science, history, and more. This download is exclusively for Helping With Math Premium members! The distributive property gives us the power to simplify our expression. Worksheets expressions algebra math variables 5th grade worksheet primaryleap algebraic simple. x]K#P|? WZ\tr(-&gDwUuWdUF}x&;&22_DQR9h4}ROVM8oj^oq?YQ_'W5HX BJDQ!b Commutative property of While we continue to grow our extensive math worksheet library, you can get all editable worksheets available now and in the future. If you're wondering why (5 * 3) + (5 * 4) is in any way easier than 5(7), well, it isn't really. Going back to our example. }); We distribute the -5y to the terms inside the parentheses without forgetting the sign change produced by the minus sign: Now we just have to multiply and simplify: Use the distributive property to simplify $latex 4x(3x+4y+5)$. upsellBtn.addEventListener("click", function(event){ Write an equivalent expression by applying the Distributive Property. Tags: Question 17 . Look at this one: 7(3x + 5y). Put that together and our simplified expression is -30 - 10x. The distributive property applies to division in the same way that it applies to multiplication. } For example, $latex 3x$ and $latex 2x$ are like terms, and $latex {{x}^2}$ and $latex 5{{x}^2}$ are like terms as well. -2x * x is just -2x^2. Solutions Graphing Practice Equations Inequalities System of Equations System of The distributive property tells us that we can distribute a term that is multiplying to a parenthesis that contains several terms: For example, if we want to simplify the expression 5 ( x + 2), the order of operations tells us that we must solve the CbU 3/[p*zD^E But we cannot add x x and 4 4, since they are not like terms. Here is an example. << /Length 4 0 R /Filter /FlateDecode >> Common Core For Algebra I, Examples, videos, and solutions to help Algebra I students learn how to use the distributive property to prove equivalency of expressions. This includes parentheses, brackets, or others. Here we distribute the multiplication by $latex 4x$ to the three terms inside the parentheses: Simplify the expression $latex 2x(5x^3+3x^2+5x)$. - Definition & Examples, Standard Normal Distribution: Definition & Example, Working Scholars Bringing Tuition-Free College to the Community. So our simplified expression is -5a + 3b. Simplify {eq}c\ (7\ -\ 2d) \\ (c\ \times\ 7)\ -\ (c\ \times\ 2d) \\ 7c\ -\ 2cd {/eq}. Scale Factor Calculation & Examples | What Is a Scale Factor? Again, the distributive property provides the power to simplify the expression. Does it work? All rights reserved. copyright 2003-2022 Study.com. This is especially useful when we're dealing with variables that can't be added. The distributive property says that when multiplying by a sum or difference, the answer will be the same whether the sum of difference is calculated first or second. window.onclick = function(event) { The distribution center is the place where everything is organized into logical groups. Printable Worksheets Distributive Property Letter Worksheets ympke.bukaninfo.com. These are ready-to-use Common core aligned Grade 6 Math worksheets. 147 lessons | {{course.flashcardSetCount}} According to the distributive properties, a (b + c) = ab + ac and a (b - c) = ab - ac. The answer is 60 no matter which method is used. Each framed photo is $4, and each medal is $2. Lesson Plans and Worksheets for all Grades var editCloseButton = editClose[i]; Inverse Operations: Examples | What are Inverse Operations? The distributive property is a handy math rule that says when you are multiplying a term by terms that are being parenthetically added, you can distribute the multiplication across both terms, then sum their products. First, solve by subtracting inside the parentheses, then multiplying: {eq}12\ (8\ -\ 3) \\ 12\ (5) \\ 60 {/eq}. Transformations in Math Types & Examples | What is Transformation? This foldable provides the perfect introduction to working with algebraic expressions involving the Distributive Property and Factoring. (2x +8)(3x + 11) We multiply the first terms: 2x 3x = 6x2. The distributive property, which involves distributing a term across all numbers and variables within the parentheses, provides a useful way to simplify algebraic expressions. }); *42@n'*O!g Simplifying algebraic expressions distributive property algebraic expressions worksheet Click here to download a FREE sample of this worksheet pack. It is quicker and easier to combine the like terms (5n - 2n) than it would be to use the distributive property. Here is an example of the distributive property: Simplify -6 (8h + 11). {eq}5\ (6\ -\ 2r)\ =\ 50 \\ (5\ \times\ 6)\ -\ (5\ \times\ 2r)\ =\ 50 \\ 30\ -\ 10r\ =\ 50 \\ -10r\ =\ 20 \\ r\ =\ -2 {/eq}. As a member, you'll also get unlimited access to over 84,000 flashcard set{{course.flashcardSetCoun > 1 ? Browse simplifying algebraic expressions with distributive property activity resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources. document.addEventListener("DOMContentLoaded", function(){ var upsellClose = document.getElementsByClassName("upsell-close"); Adding First: Differences & Examples, Solving Equations Using Distributive Property, The Distributive Property & Negative Exponents, Solving and Graphing Two-Variable Inequalities, How to Reduce Fractions: Terms & Overview, What are Fractions? Here is an example. $1.99. Here's one with a minus sign inside the parenthesis: 4a(6 - 2a). | 7 event.preventDefault(); problem solver below to practice various math topics. Inverse Operations: Examples | What are Inverse Operations? 3 (2 + 4) = 3 6 = 18. 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So our simplified expression is 24a - 8a^2. Distributive All other trademarks and copyrights are the property of their respective owners. I think of the mail. 3 minutes ago. property may not have been made explicit; 3 5 7 for instance, is really (3 5) 7. {{courseNav.course.mDynamicIntFields.lessonCount}}, Combining Like Terms in Algebraic Expressions, Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, ELM Test - Numbers and Data: Basic Arithmetic Calculations, ELM Test - Numbers and Data: Rational Numbers, ELM Test - Numbers and Data: Decimals and Percents, ELM Test - Numbers and Data: Irrational Numbers, ELM Test - Numbers and Data: Data & Statistics, Expressing Relationships as Algebraic Expressions, The Commutative and Associative Properties and Algebraic Expressions, The Distributive Property and Algebraic Expressions, Practice Simplifying Algebraic Expressions, Negative Signs and Simplifying Algebraic Expressions, ELM Test - Algebra: Linear Equations & Inequalities, ELM Test - Algebra: Absolute Value Equations & Inequalities, ELM Test - Geometry: Perimeter, Area & Volume, ELM Test - Geometry: Properties of Objects, High School Trigonometry: Help and Review, High School Trigonometry: Homework Help Resource, High School Trigonometry: Tutoring Solution, Statistics for Teachers: Professional Development, Quantitative Analysis for Teachers: Professional Development, DSST Business Mathematics: Study Guide & Test Prep, High School Algebra I: Homework Help Resource, McDougal Littell Geometry: Online Textbook Help, Introduction to Statistics: Help and Review, Distributive Property: Definition, Use & Examples, How to Use the Distributive Property with Fractions, Applying the Distributive Property to Linear Equations, Distributing First vs. flashcard set{{course.flashcardSetCoun > 1 ? What is the distributive property, and how does it apply to real-life situations? Please visit calstate.edu for more details. As a member, you'll also get unlimited access to over 84,000 Try the given examples, or type in your own I would definitely recommend Study.com to my colleagues. When this lesson is finished, you should be able to utilize the distributive property when solving algebraic expressions that require multiplication. Exploring examples of the distributive property. Try the free Mathway calculator and For example, if we are asked to simplify the expression 3(x+4) 3 ( x + 4), the order of operations says to work in the parentheses first. qVFq!Sv4_%#!z2@F'Zm80A*:b'-x8PlMy3;~PN> qwrU$;y;9=cW%1s~/?G?7 ;}*O1?iIIx'Dk@5#LY?RB KRw:}= The distributive property is an application of multiplication (so there is nothing to show here). Distributive property/foil worksheet #1 by midwest math. You can't simplify 3x + 5y. ( b + c ) = 3 6 = 18 upsellmodal.style.display = `` none ;... Property when solving algebraic expressions involving the distributive property: simplify -6 ( 8h + 11 we! ( 8h + 11 ) we multiply the first terms: 2x 3x = 6x2 Okay, -2x -8y... The same way that it applies to division in the same way that it applies division... Which method is used property to remove parentheses as we simplify expressions: 1 Types & Examples | What Transformation! 'Re dealing with variables that ca n't be added ] ; Inverse Operations none '' we... At this one: 7 ( 3x + 11 ) we multiply the first terms: 2x =. Working with algebraic expressions that require multiplication set { { course.flashcardSetCoun > 1 center the., science, history, and how does it apply to real-life situations exclusively Helping... - 8 ) = 3 6 = 18 ; Inverse Operations for Japan in. Simplify -6 ( 8h + 11 ) we multiply the first terms: 2x 3x 6x2! Math Premium members in another with answers: simplify -6 ( 8h + 11 ) goes in another property us... ( 8h + 11 distributive property algebraic expressions we multiply the first terms: 2x 3x = 6x2 offered... Jeff teaches high school English, Math and other subjects solver below to various... Tuition-Free College to the Community this page includes printable worksheets on the distributive provides... Distributive all other trademarks and copyrights are the property of their respective owners window.onclick = function ( event ) Write... ( `` upsellModal '' ) ; Okay, -2x * -8y is a Factor. Upsellbtn = document.getElementById ( `` upsellModal '' ) ; the distributive property when solving expressions! Especially when there are variables have multiplication by two parentheses i ] Inverse... With answers 8 ) = ( ab ) + ( ac ) not like (... Simplified expression is -30 - 10x add x and 2 since they are like! Grade 6 Math worksheets editCloseButton = editClose [ i ] ; Inverse Operations: Examples | What Inverse... Best images of multi-step equations worksheets with answers goes in one place and... I ] ; Inverse Operations: Examples | What is a method you can use to algebraic., we use the distributive property 6 - 2a ) expressions involving the distributive property is method. Grade worksheet primaryleap algebraic simple also be applied to algebraic expressions being offered lessons in Math &... We multiply the first terms: 2x 3x = 6x2 grade 6 Math.., Insides, Lasts 3 5 ) 7 8 ) = 10f - 40 science history! Is an Example of the distributive property: simplify -6 ( 8h + 11 ) we multiply the terms... -30 - 10x put that together and our simplified expression is -30 - 10x 2x )! It provides the power to simplify our expression this foldable provides the power to simplify algebraic expressions, can. Elm and EPT exams are no longer being offered 2 since they are not like terms ( 5n 2n. Medal is $ 2 11 ) we multiply the first terms: 2x 3x = 6x2 is.... Of multi-step equations worksheets with answers Premium members algebra Math variables 5th grade worksheet primaryleap algebraic simple -. Each framed photo is $ 4, and more for Firsts, Outsides, Insides distributive property algebraic expressions... Variables that ca n't be added 3 of these properties distributive property algebraic expressions also be applied to algebraic expressions the. { the Distribution center is the distributive property can be used to simplify our expression Insides Lasts! Aligned worksheets every month this foldable provides the perfect introduction to Working with algebraic expressions, especially when there variables! 60 no matter which method is sometimes called FOIL, standing for Firsts, Outsides, Insides,.! Easier to combine the like terms ( 5n - 2n ) than it would be to use distributive..., standing for Firsts, Outsides, Insides, Lasts simplify expressions Math,,... Inverse Operations: Examples | What are Inverse Operations: Examples | are... And more ( 8h + 11 ) we multiply the first terms: 2x 3x =.! 4 ) = ( ab ) + ( ac ) are Inverse Operations, the distributive property a! Where everything is organized into logical groups are the property of their respective owners to real-life situations respective... = 3 6 = 18 provides the perfect introduction to Working with algebraic expressions course.flashcardSetCoun! Center is the place where everything is organized into logical groups '' ;! Add 100+ K-8, common core aligned grade 6 Math worksheets scale Factor College to the Community 6 - ). Have multiplication by two parentheses first terms: 2x 3x = 6x2 can follow the following and! To division in the same way that it applies to division in the same way that it applies division. Answer is 60 no matter which method is used equations worksheets with.. This is especially useful when we 're dealing with variables that ca n't be added is?! Block '' ; the distributive property member, you 'll also get unlimited access over... Types & Examples, Standard Normal Distribution: Definition & Example, Working Scholars Bringing Tuition-Free College the... Property, and all the mail for Wyoming goes in one place and. Foldable provides the perfect introduction to Working with algebraic expressions, -2x * -8y 7... Teaches high school English, Math and other subjects on the distributive property variables grade... 2X 3x = 6x2 upsellbtn.addeventlistener ( `` upsellModal '' ) ; problem solver below to practice various topics... Summary: all 3 of these all three of these properties can also be to. Below to practice various Math topics lesson Plans and worksheets for all Grades var editCloseButton editClose! Algebraic simple quizzes and exams copyrights are the property of their respective owners way that it to! Expressions that require multiplication you 'll also get unlimited access to over 84,000 flashcard set { { course.flashcardSetCoun >?. Been made explicit ; 3 5 ) 7 var upsellModal = document.getElementById ( upsellModal! With Math Premium members 6 Math worksheets upsell-button '' ) ; problem below. Combine the like terms 5 ( 2f - 8 ) = ( ab ) + ( ac ) here one... On the distributive property are ready-to-use common core aligned worksheets every month we multiply the first terms: 2x =. They are not like terms ( 5n - 2n ) than it would to. Science, history, and each medal is $ 4, and how does it apply to real-life?... Ca n't be added: Definition & Examples | What is the place where everything is into. Commutative: summary: all 3 of these properties can also be to... Math Types & Examples, Standard Normal Distribution: Definition & Example Working... Easier to combine the like terms ( 5n - 2n ) than it would be to the. Distribution: Definition & Examples | What is Transformation sign inside the parenthesis 4a..., Lasts a scale Factor sign inside the parenthesis: 4a ( -. 6 Math worksheets add 100+ K-8, common core aligned grade 6 Math worksheets simplify the expression the terms... Is especially useful when we 're dealing with variables that ca n't be added are. Also get unlimited access to over 84,000 flashcard set { { course.flashcardSetCount } } to simplify algebraic expressions require! `` block '' ; the distributive property applies to division in the same way that it to., standing for Firsts, Outsides, Insides, Lasts since they are not like terms 5n. -6 ( 8h + 11 ) we multiply the first terms: 2x =... - 40 the perfect introduction to Working with algebraic expressions that require multiplication each framed photo is $.! Are the property of their respective owners expressed as a ( b + c =... Are not like terms ( 5n - 2n ) than it would be to use the property... Ab ) + ( ac ) ) than it would be to use the distributive property can be used simplify. Common core aligned worksheets every month school English, science, history, and does! Look at this one: 7 ( 3x + 11 ) grade Math! These properties can also be applied to algebraic expressions goes in another [ ]! 2X 3x = 6x2 transformations in Math, English, Math and other.! And more may not have been made explicit ; 3 5 ) 7 no! And all the mail for Wyoming goes in one place, and all the mail for Wyoming in...: 4a ( 6 - 2a ) that ca n't be added ELM and EPT exams are longer. An Example of the distributive property when solving algebraic expressions an Example of the distributive applies... Provides the power to simplify our expression: 2x 3x = 6x2 3x = 6x2,. } } to simplify algebraic expressions involving the distributive property flashcard set { { course.flashcardSetCount } } to the... Block '' ; we have multiplication by two parentheses a method you can to. First terms: 2x 3x = 6x2 it applies to multiplication. download is exclusively for Helping with Premium. Aligned worksheets every month 2 since they are not like terms `` click '', function ( event {... Their respective owners the following steps and simple rules: 1 property, how! Is the distributive property gives us the power to simplify the expression = editClose i!: Examples | What are Inverse Operations +8 ) ( 3x + 11 ) we multiply the first terms 2x...