{"id":445,"date":"2022-04-13T05:13:01","date_gmt":"2022-04-13T05:13:01","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=445"},"modified":"2025-08-19T18:20:47","modified_gmt":"2025-08-19T18:20:47","slug":"w-4-write-and-solve-equations-that-represent-diagrams","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/w-4-write-and-solve-equations-that-represent-diagrams\/","title":{"rendered":"W.4 Write and solve equations that represent diagrams"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Write and solve equations that represent diagrams<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGwHSe4LdM\/0XrWpmbSwtdJYagpwtAHHA\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwHSe4LdM&#x2F;0XrWpmbSwtdJYagpwtAHHA&#x2F;watch?utm_content=DAGwHSe4LdM&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Class 8: Topic: Solving Equations that represent diagrams<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>What Does It Mean?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Sometimes math problems show <strong>pictures, diagrams, or models<\/strong> instead of words.<br>Your job is to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Understand<\/strong> what the diagram is showing.<\/li>\n\n\n\n<li><strong>Write an equation<\/strong> that matches the diagram.<\/li>\n\n\n\n<li><strong>Solve<\/strong> the equation to find the unknown value.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Why Is This Important?<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Helps you connect <strong>visual information<\/strong> to <strong>mathematical expressions<\/strong>.<\/li>\n\n\n\n<li>Improves <strong>problem-solving skills<\/strong> for real-life situations (like maps, shapes, or patterns).<\/li>\n\n\n\n<li>Makes equations <strong>less abstract<\/strong> and easier to understand.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Steps to Write and Solve Equations from Diagrams<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Step 1: Study the diagram carefully<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Identify <strong>what is known<\/strong> (numbers, labels, lengths).<\/li>\n\n\n\n<li>Identify <strong>what is unknown<\/strong> (often marked with a letter like x).<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Step 2: Translate the picture into math<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Addition if parts are put together.<\/li>\n\n\n\n<li>Multiplication if equal groups are shown.<\/li>\n\n\n\n<li>Subtraction if something is taken away.<\/li>\n\n\n\n<li>Division if something is split into equal parts.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Step 3: Write the equation<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use <strong>symbols<\/strong> (+, \u2013, \u00d7, \u00f7) and variables to match the diagram.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Step 4: Solve the equation<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use inverse operations (undo the math) to find the unknown.<\/li>\n\n\n\n<li>Keep both sides of the equation <strong>balanced<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Examples<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Example 1: Equal groups<\/strong><\/h4>\n\n\n\n<p>Diagram: 3 bags each with x apples = 18 apples in total.<br>Equation: 3x=18<\/p>\n\n\n\n<p>Solution: x=18\u00f73=6<\/p>\n\n\n\n<p><strong>Answer:<\/strong> Each bag has <strong>6 apples<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Example 2: Shape perimeter<\/strong><\/h4>\n\n\n\n<p>Diagram: Rectangle with length = x cm and width = 4 cm, perimeter is 18 cm.<br>Formula: P=2L+2W<\/p>\n\n\n\n<p>Substitute: 18=2x+2(4)<\/p>\n\n\n\n<p>18=2x+8<\/p>\n\n\n\n<p> 2x=10<\/p>\n\n\n\n<p> x=5<\/p>\n\n\n\n<p><strong>Answer:<\/strong> The length is <strong>5 cm<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>Example 3: Balance scale diagram<\/strong><\/h4>\n\n\n\n<p>Diagram: Left side has <strong>1 box and 3 marbles<\/strong>, right side has <strong>7 marbles<\/strong>.<br>Equation: x+3=7<\/p>\n\n\n\n<p> x=4<\/p>\n\n\n\n<p><strong>Answer:<\/strong> The box weighs <strong>4 marbles<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Key Tips<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always <strong>define the variable<\/strong> (e.g., \u201cLet x be the number of\u2026\u201d).<\/li>\n\n\n\n<li>Check your answer in the diagram to make sure it works.<\/li>\n\n\n\n<li>Diagrams often hide <strong>simple patterns<\/strong> \u2014 look for equal groups or matching parts.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Practice Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A triangle has a base of 8 cm and height x cm. Its area is 32 cm\u00b2. Find x.<\/li>\n\n\n\n<li>Two identical books and 5 pens cost \u20b995. One book costs \u20b935. Find the price of one pen.<\/li>\n\n\n\n<li>A balance scale shows 2 boxes and 3 coins on the left, and 9 coins on the right. Find the weight of 1 box in coins.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#3c0319\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-07fac218f3805828f1994113013eece2\" style=\"color:#b00012\"><strong>Write an equation that says that the length of the green line is equal to the length of the black line. Combine like terms.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-7-2.png\" alt=\"\" class=\"wp-image-13156\" style=\"width:467px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-7-2.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-7-2-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p>equation : _______<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-e419d71d11529e15fa20174333b43ec4\">We want to replace both sides of the equation below with numbers and variable expressions:<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-368d22381975a047b5b4e49780fdb357\">length of green line=length of black line<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-d0a3d1db5acbcf0fcdede8e94fd5a6f7\">The length of the green line is 30.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-9976b27c35dc2acee625327e8df26db6\">The black line is the sum of its segments, so:<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-34b8fdd40bedb9b787669aa4f7512c07\">length of black line=3<em>g<\/em>&nbsp;+ 2<em>g<\/em>&nbsp;+&nbsp;<em>g<\/em><\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-50cc02c84dd2a4cbdaab88c2f2f7917a\">                               =6g<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c23ebc1a57d78488ed9cae5cae2be632\">Putting these together gives:<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-2df458abf131a08d3a4275ca57571646\">30=6g<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#043503\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-07fac218f3805828f1994113013eece2\" style=\"color:#b00012\"><strong>Write an equation that says that the length of the green line is equal to the length of the black line. Combine like terms.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-8-2.png\" alt=\"\" class=\"wp-image-13157\" style=\"width:449px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-8-2.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-8-2-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p>equation :  ______<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-e419d71d11529e15fa20174333b43ec4\">We want to replace both sides of the equation below with numbers and variable expressions:<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-368d22381975a047b5b4e49780fdb357\">length of green line=length of black line<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-5957b3c3f3e8d067496cfc843df41921\">The length of the green line is 12.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-9976b27c35dc2acee625327e8df26db6\">The black line is the sum of its segments, so:<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-ea908f3e140135f1940917be41f23d56\">length of black line=v+3<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c23ebc1a57d78488ed9cae5cae2be632\">Putting these together gives:<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-fa84b4f68b27610cc2944a9143f1065c\">12=v+3<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#0c0542\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-07fac218f3805828f1994113013eece2\" style=\"color:#b00012\"><strong>Write an equation that says that the length of the green line is equal to the length of the black line. Combine like terms.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-6-1.png\" alt=\"\" class=\"wp-image-13155\" style=\"width:472px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-6-1.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-6-1-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p>equation :  _____<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-e419d71d11529e15fa20174333b43ec4\">We want to replace both sides of the equation below with numbers and variable expressions:<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-368d22381975a047b5b4e49780fdb357\">length of green line=length of black line<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-ba8f2a8c5a2157573ce602bab13108c0\">The length of the green line is 41.<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-9976b27c35dc2acee625327e8df26db6\">The black line is the sum of its segments, so:<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c04acaf01ea9335a179ded6d262cf124\">length of black line=2f+5<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-c23ebc1a57d78488ed9cae5cae2be632\">Putting these together gives:<\/p>\n\n\n\n<p class=\"has-background-color has-text-color has-link-color wp-elements-5548c640c144fa8bc6a449de63821982\">41=2f+5<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/95840\/847\/955\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-138.png\" alt=\"\" class=\"wp-image-8907\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-138.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-138-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-138-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/36263\/698\/969\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142.png\" alt=\"\" class=\"wp-image-8908\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-142-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Write and solve equations that represent diagrams Class 8: Topic: Solving Equations that represent diagrams by Delta publications What Does It Mean? Sometimes math problems show pictures, diagrams, or models instead of words.Your job is to: Why Is This Important? Steps to Write and Solve Equations from Diagrams Step 1: Study the diagram carefully Step<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/w-4-write-and-solve-equations-that-represent-diagrams\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.4 Write and solve equations that represent diagrams&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-445","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/445","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=445"}],"version-history":[{"count":18,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/445\/revisions"}],"predecessor-version":[{"id":21250,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/445\/revisions\/21250"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=445"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}