{"id":5676,"date":"2022-02-06T12:18:37","date_gmt":"2022-02-06T12:18:37","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=5676"},"modified":"2022-02-06T12:18:37","modified_gmt":"2022-02-06T12:18:37","slug":"subtracting-algebraic-expressions-word-problems","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/subtracting-algebraic-expressions-word-problems\/","title":{"rendered":"Subtracting Algebraic Expressions Word Problems"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Subtracting Algebraic Expressions Word Problems<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]In mathematics, just like we subtract many numbers as we can and find the difference, we subtract two or many algebraic expressions too. However, for the subtraction of algebraic expressions, we combine all the like terms and then subtract them.<\/p>\n<p>Like terms are the terms that have the same power for the same variables. In like terms, one can only change the numerical coefficient. Terms that have different variables or the same variables raised to different powers are known as, unlike terms.<\/p>\n<p>Word problems that include subtraction of algebraic expressions can be solved with ease if we know how to subtract them. We need to write out an algebraic expression that we can evaluate to find our answer. To write our algebraic expression, we carefully read the problem to figure out what our important numbers are and what kind of operation we are dealing with.<\/p>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]<strong>There are two methods to do the subtraction of algebraic expressions:<\/strong><br \/>\nHorizontal method of Subtraction of Algebraic Expressions<br \/>\nColumn method for Subtraction of Algebraic Expressions<\/p>\n<p><strong>Horizontal method of Subtraction of Algebraic Expressions<\/strong><br \/>\n1. Write all the expressions in a horizontal line by putting them into brackets and put a subtraction sign in between.<br \/>\n2. Change the subtraction to addition by using the additive inverse.<br \/>\n2. Group all the like terms together from all the expressions and rewrite the expression so formed.<br \/>\n3. Add numerical coefficients of all the like terms followed by the common variable.<br \/>\n4. Rewrite the simplified expression, and make sure all the terms in the final answer should be unlike terms.<\/p>\n<p><strong>Column method for Subtraction of Algebraic Expressions<\/strong><br \/>\n1. Change the subtraction to addition by using the additive inverse.<br \/>\n2. Write all the expressions one below the other . Make sure to like terms in one column. If there a term whose like term is not there in the second expression, then either write below it or leave that column blank.<br \/>\n3. Add the numerical coefficient of each column (like terms) and write below it in the same column followed by the common variable. [\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">The number of pepperoni pizza ordered in one evening is represented by 3x + 1. The number of cheese pizza ordered is represented by 6x – 2. How many more cheese pizzas were ordered than pepperoni, if = 4? <\/span><\/strong>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]1. Write the expression showing cheese pizzas minus pepperoni pizzas.<br \/>\n(6x \u2013 2) \u2013 (3x + 1)<\/p>\n<p>2. Group by like terms and use additive inverses to solve.<br \/>\n6x \u2013 2 + (-3x \u2013 1)\u00a0 \u00a0 <strong>The additive inverse of 3x + 1 is (-3x \u2013 1)<\/strong><br \/>\n= (6x – 3x) + (-2 – 1)<br \/>\n= 3x – 3<\/p>\n<p>When x = 4,<br \/>\n3x – 3<br \/>\n3(4) \u2013 3<br \/>\n12 \u2013 3 = 9<\/p>\n<p><span style=\"color: red;\">9 more cheese pizzas were ordered than pepperoni.<\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Subtracting Algebraic Expressions Word Problems[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Carol is (2x – 1) years old. Her brother Gary is (x + 1) years younger than Carol. Their aunt Helen is 6 times as old as Gary. Write and simplify an expression that represents Helen\u2019s age. Find the number that represents Helen\u2019s age if x = 7. <\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/subtract-linear-expressions\"><img loading=\"lazy\" class=\"alignnone wp-image-5678 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/54.png\" alt=\"\" width=\"338\" height=\"63\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/54.png 338w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/54-300x56.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/subtract-linear-expressions”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Write a linear expression in the simplest form to represent the side of the triangle if the perimeter is represented by (13x – 1) centimeters. <\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/subtract-linear-expressions\"><img loading=\"lazy\" class=\"alignnone wp-image-5682 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/1600778246552.png\" alt=\"\" width=\"181\" height=\"118\" \/><\/a><br \/>\n<strong><span style=\"color: #16a085;\">Find the side of the triangle if x = 3. <\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/subtract-linear-expressions\"><img loading=\"lazy\" class=\"alignnone wp-image-5684 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/55-1.png\" alt=\"\" width=\"339\" height=\"62\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/55-1.png 339w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/55-1-300x55.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/subtract-linear-expressions”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">Ruth’s number of stickers is represented by <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;{\\color{Teal}&space;\\frac{1}{2}}\" alt=\"\\fn_phv {\\color{Teal} \\frac{1}{2}}\" align=\"absmiddle\" \/>(8x + 2). She gave (x + 1) to her friend Mark. Write and simplify the expression that represents the remaining number of Ruth’s stickers. Find the remaining number of Ruth’s stickers if x = 6.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/subtract-linear-expressions\"><img loading=\"lazy\" class=\"alignnone wp-image-5686 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/56.png\" alt=\"\" width=\"336\" height=\"64\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/56.png 336w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/56-300x57.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/subtract-linear-expressions”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Linear Expression<\/strong> \u2013 an algebraic expression in which the variable is raised to the first power, and variables are not multiplied or divided.<\/p>\n<p><strong>Term<\/strong> \u2013 either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or \u2212 signs.<\/p>\n<p><strong>Like terms<\/strong> – Terms that have the same power for the same variables. In like terms, one can only change the numerical coefficient.<\/p>\n<p><strong>Unlike terms<\/strong> – Terms that have different variables or the same variables raised to different powers.<\/p>\n<p><strong>Distributive Property<\/strong> \u2013 to multiply a sum or difference by a number, multiply each term inside the parenthesis by the number outside the parenthesis.<\/p>\n<p><strong>Constant<\/strong> \u2013 a term without a variable.<\/p>\n<p><strong>Variable<\/strong> – In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation or expression.<\/p>\n<p><strong>Coefficient<\/strong> – is an integer that is multiplied with the variable of a single term or the terms of a polynomial.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/evaluate-variable-expressions-addition-and-subtraction\"><span style=\"color: #ed5600;\">Evaluate Variable Expressions-addition and subtraction<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/evaluate-expressions-multiplication-and-division\"><span style=\"color: #ed5600;\">Evaluate Expressions (Multiplication and Division)<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/solve-algebraic-equations-addition-and-subtraction\"><span style=\"color: #ed5600;\">Solve Algebraic Equations – Addition and Subtraction<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/solve-algebraic-equations-multiplication-and-division\"><span style=\"color: #ed5600;\">Solve Algebraic Equations – Multiplication and Division<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/evaluate-algebraic-expressions\"><span style=\"color: #ed5600;\">Evaluate Algebraic Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/write-algebraic-expressions\"><span style=\"color: #ed5600;\">Write Algebraic Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/the-distributive-property\"><span style=\"color: #ed5600;\">The Distributive Property<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/simplifying-complex-algebraic-expressions\"><span style=\"color: #ed5600;\">Simplifying Complex Algebraic Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/add-linear-expressions\"><span style=\"color: #ed5600;\">Add Linear Expressions<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1637585757988{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/factor-linear-expressions\"><span style=\"color: #333399;\">Factor Linear Expressions<\/span><\/a><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-one-step-equations-by-addition-and-subtraction\">Solve One-Step Equations by Addition and Subtraction<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-one-step-equations-by-multiplying-and-dividing\">Solve One-Step Equations by Multiplying and Dividing<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-equations-with-rational-coefficients\">Solve Equations with Rational Coefficients<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-two-step-equations\">Solve Two-Step Equations<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-complex-equations\">Solve Complex Equations<\/a><\/span>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” 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img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Subtracting Algebraic Expressions Word Problems [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]In mathematics, just like we subtract many numbers as we can and find the difference, we subtract two or many algebraic expressions too. However, for the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Subtracting Algebraic Expressions Word Problems | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/subtracting-algebraic-expressions-word-problems\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Subtracting Algebraic Expressions Word Problems\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Subtracting Algebraic Expressions Word Problems [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]In mathematics, just like we subtract many numbers as we can and find the difference, we subtract two or many algebraic expressions too. 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