{"id":447,"date":"2022-04-13T05:13:16","date_gmt":"2022-04-13T05:13:16","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=447"},"modified":"2025-08-19T18:22:49","modified_gmt":"2025-08-19T18:22:49","slug":"w-5-properties-of-equality","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/w-5-properties-of-equality\/","title":{"rendered":"W.5 Properties of equality"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Properties of equality<\/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\/DAGwHpzQnpw\/TyfbCzPxCzyL59BWw_tNSw\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwHpzQnpw&#x2F;TyfbCzPxCzyL59BWw_tNSw&#x2F;watch?utm_content=DAGwHpzQnpw&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Class 8: Topic: Properties of Equality<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4d4696560822e7cb72ec4be90d4370b1\" style=\"color:#74008b\">Key Notes:<\/p>\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 Are the Properties of Equality?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The <strong>properties of equality<\/strong> are rules that help us keep an equation <strong>balanced<\/strong> while solving it.<br>They tell us what operations we can perform on both sides of an equation without changing its truth.<\/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>Why Are They Important?<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>They help us <strong>solve equations step-by-step<\/strong>.<\/li>\n\n\n\n<li>They prevent mistakes when moving numbers or variables around.<\/li>\n\n\n\n<li>They keep the <strong>balance<\/strong> of the equation (like a scale).<\/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>Main Properties of Equality<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading has-normal-font-size\"><strong>1. Reflexive Property<\/strong><\/h4>\n\n\n\n<p>a=a<\/p>\n\n\n\n<p>Anything is equal to itself.<br><strong>Example:<\/strong> 7=7<\/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>2. Symmetric Property<\/strong><\/h4>\n\n\n\n<p>If a=b, then b=a.<br><strong>Example:<\/strong> If x=5, then 5=x.<\/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>3. Transitive Property<\/strong><\/h4>\n\n\n\n<p>If a=b and b=c, then a=c.<br><strong>Example:<\/strong> If x=4 and 4=y, then x=y.<\/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>4. Addition Property of Equality<\/strong><\/h4>\n\n\n\n<p>If a=b, then a + c = b + c.<br>(You can add the same number to both sides without changing the equation.)<br><strong>Example:<\/strong> x=3 \u2192 x+5=3+5<\/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>5. Subtraction Property of Equality<\/strong><\/h4>\n\n\n\n<p>If a=b, then a\u2212c=b\u2212c.<br>(You can subtract the same number from both sides.)<br><strong>Example:<\/strong> x=10 \u2192 x\u22122=10\u22122<\/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>6. Multiplication Property of Equality<\/strong><\/h4>\n\n\n\n<p>If a=b, then a\u00d7c=b\u00d7c.<br>(You can <strong>multiply both sides<\/strong> by the same number.)<br><strong>Example:<\/strong> x\/4=3\u2192 Multiply both sides by 4 \u2192 x=12.<\/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>7. Division Property of Equality<\/strong><\/h4>\n\n\n\n<p>If a=b, then a\/c=b\/c\u200b, where c\u22600.<br>(You can <strong>divide both sides<\/strong> by the same non-zero number.)<br><strong>Example:<\/strong> 5x=20 \u2192 Divide by 5 \u2192 x=4.<\/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>8. Substitution Property<\/strong><\/h4>\n\n\n\n<p>If a=b, then you can replace aaa with bbb in any expression.<br><strong>Example:<\/strong> If y=8 and 2y+1, replace y with 8 \u2192 2(8)+1=17.<\/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>How to Use Them in Solving Equations<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Example: Solve x\u22125=12<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use <strong>Addition Property<\/strong>: Add 5 to both sides \u2192 x\u22125+5=12+5<\/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>Quick Table<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><strong>Property<\/strong><\/th><th><strong>Rule<\/strong><\/th><th><strong>Example<\/strong><\/th><\/tr><\/thead><tbody><tr><td>Reflexive<\/td><td>a=a<\/td><td>7=7<\/td><\/tr><tr><td>Symmetric<\/td><td>a=b\u21d2b=a<\/td><td>x=5\u21d25=x<\/td><\/tr><tr><td>Transitive<\/td><td>a=b,b=c\u21d2a=c<\/td><td>3+1=4,4=y\u21d23+1=y<\/td><\/tr><tr><td>Addition<\/td><td>a=b\u21d2a+c=b+c<\/td><td>4=4\u21d24+2=4+2<\/td><\/tr><tr><td>Subtraction<\/td><td>a=b\u21d2a\u2212c=b\u2212c<\/td><td>8=8\u21d28\u22123=8\u22123<\/td><\/tr><tr><td>Multiplication<\/td><td>a=b\u21d2ac=bc<\/td><td>2=2\u21d22\u00d73=2\u00d73<\/td><\/tr><tr><td>Division<\/td><td>a=b\u21d2a\/c=b\/c<\/td><td>10=10\u21d210\u00f75=10\u00f75<\/td><\/tr><tr><td>Substitution<\/td><td>Replace equals with equals<\/td><td>y=6,x=y+2\u21d2x=8<\/td><\/tr><\/tbody><\/table><\/figure>\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>If a=b, what is true about a+7 and b+7?<\/li>\n\n\n\n<li>If x\u22124=10, which property do you use to solve for x?<\/li>\n\n\n\n<li>If 3y=15, which property lets you divide both sides by 3?<\/li>\n\n\n\n<li>If m=2 and 2m=p2, what is p?<\/li>\n\n\n\n<li>If x=12, what is 5x5x5x using substitution?<\/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:#a9e7f3\"><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-d1fe6da848ca1e40433d2ef4c27f9195\" style=\"color:#b00012\"><strong>Which property of equality is shown below?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"400\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-9-1.png\" alt=\"\" class=\"wp-image-13160\" style=\"width:521px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-9-1.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-9-1-300x179.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Find what changed.<\/p>\n\n\n\n<p>if:             t=u-28<\/p>\n\n\n\n<p>then:       t+v=c-28+v<\/p>\n\n\n\n<p>The second equation has&nbsp;<em>v<\/em>&nbsp;added to both sides. This shows the Addition Property of Equality.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#c9fccf\"><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-d1fe6da848ca1e40433d2ef4c27f9195\" style=\"color:#b00012\"><strong>Which property of equality is shown below?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"400\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-11-1.png\" alt=\"\" class=\"wp-image-13165\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-11-1.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-11-1-300x179.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Find what changed.<\/p>\n\n\n\n<p>if:                                  g=-49f<\/p>\n\n\n\n<p>then:                       h+g=h+-49f<\/p>\n\n\n\n<p>The second equation has&nbsp;<em>h<\/em>&nbsp;added to both sides. This shows the Addition Property of Equality.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#aac9fa\"><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-d1fe6da848ca1e40433d2ef4c27f9195\" style=\"color:#b00012\"><strong>Which property of equality is shown below?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"400\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-10-2.png\" alt=\"\" class=\"wp-image-13162\" style=\"width:508px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-10-2.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/11\/Untitled-design-10-2-300x179.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Find what changed.<\/p>\n\n\n\n<p>if:                 -38=rq<\/p>\n\n\n\n<p>then:         -38-s=rq-s<\/p>\n\n\n\n<p>The second equation has&nbsp;<em>s<\/em>&nbsp;subtracted from both sides. This shows the Subtraction Property of Equality.<\/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\/95841\/245\/471\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-137.png\" alt=\"\" class=\"wp-image-8904\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-137.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-137-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-137-150x150.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\/95841\/669\/732\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141.png\" alt=\"\" class=\"wp-image-8905\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Properties of equality Class 8: Topic: Properties of Equality by Delta publications Key Notes: What Are the Properties of Equality? The properties of equality are rules that help us keep an equation balanced while solving it.They tell us what operations we can perform on both sides of an equation without changing its truth. Why Are<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/w-5-properties-of-equality\/\">Continue reading <span class=\"screen-reader-text\">&#8220;W.5 Properties of equality&#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-447","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\/447","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=447"}],"version-history":[{"count":22,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/447\/revisions"}],"predecessor-version":[{"id":21251,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/447\/revisions\/21251"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}