{"id":234,"date":"2022-04-13T04:34:04","date_gmt":"2022-04-13T04:34:04","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=234"},"modified":"2025-12-19T06:04:21","modified_gmt":"2025-12-19T06:04:21","slug":"k-7-multi-step-problems-with-percents","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/k-7-multi-step-problems-with-percents\/","title":{"rendered":"K.7 Multi-step problems with percents"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Multi-step problems with percents<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-071aec683c99d954104ee0068dfb63f9\" style=\"color:#74008b\">Key notes:<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2705 Understand What Is Given<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Read the problem <strong>carefully<\/strong>.<\/li>\n\n\n\n<li>Identify:\n<ul class=\"wp-block-list\">\n<li>The <strong>original value<\/strong><\/li>\n\n\n\n<li>The <strong>percentage<\/strong><\/li>\n\n\n\n<li>What is being <strong>asked<\/strong> (increase, decrease, discount, tax, profit, loss, etc.)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd04 Convert Percent to Decimal or Fraction<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Percent means <strong>\u201cout of 100\u201d<\/strong><\/li>\n\n\n\n<li>Convert before calculating:\n<ul class=\"wp-block-list\">\n<li>25% = 0.25<\/li>\n\n\n\n<li>12.5% = 0.125<\/li>\n\n\n\n<li>150% = 1.5<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2795\u2796 Perform Steps in the Correct Order<\/h3>\n\n\n\n<p>Multi-step percent problems usually involve <strong>more than one operation<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First: <strong>Find the percent of a number<\/strong><\/li>\n\n\n\n<li>Next: <strong>Add or subtract<\/strong> (for increase or decrease)<\/li>\n\n\n\n<li>Sometimes: <strong>Repeat with a new percent<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udccc Always solve <strong>step by step<\/strong>, not all at once.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udcb8 Percent Increase Problems<\/h3>\n\n\n\n<p>Steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find the <strong>increase amount<\/strong><br>\u2192 Increase = Original \u00d7 Percent<\/li>\n\n\n\n<li>Add to the original value<\/li>\n<\/ol>\n\n\n\n<p>\ud83d\udcd8 Example idea:<br>Price increases by 10% \u2192 Add the increase to the original price.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83c\udff7\ufe0f Percent Decrease \/ Discount Problems<\/h3>\n\n\n\n<p>Steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find the <strong>discount amount<\/strong><br>\u2192 Discount = Original \u00d7 Percent<\/li>\n\n\n\n<li>Subtract from the original value<\/li>\n<\/ol>\n\n\n\n<p>\ud83d\udcd8 Used in:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Discounts<\/li>\n\n\n\n<li>Sales<\/li>\n\n\n\n<li>Price reductions<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83e\uddfe Problems with Tax or GST<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First calculate the <strong>tax amount<\/strong><\/li>\n\n\n\n<li>Then <strong>add<\/strong> it to the original price<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udccc Tax is always calculated on the <strong>original price<\/strong>, not the total.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd01 Successive Percent Changes<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When more than one percent change is applied:\n<ul class=\"wp-block-list\">\n<li>Apply the <strong>first percent<\/strong><\/li>\n\n\n\n<li>Use the <strong>new value<\/strong> for the next percent<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Do <strong>not<\/strong> add the percentages directly.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u270f\ufe0f Use Equations When Helpful<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let the unknown be <strong>x<\/strong><\/li>\n\n\n\n<li>Write equations like:\n<ul class=\"wp-block-list\">\n<li>Final value = Original \u00b1 (Percent \u00d7 Original)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>This helps in <strong>word problems<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd0d Check Your Answer<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Does the answer make sense?\n<ul class=\"wp-block-list\">\n<li>Increase \u2192 final value should be <strong>greater<\/strong><\/li>\n\n\n\n<li>Decrease \u2192 final value should be <strong>less<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Recheck calculations to avoid small mistakes.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83e\udde0 Common Mistakes to Avoid<\/h3>\n\n\n\n<p>\u274c Adding percentages directly<br>\u274c Forgetting to convert percent to decimal<br>\u274c Skipping steps<br>\u274c Using the wrong base value<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2b50 Tip for Students<\/h3>\n\n\n\n<p>\ud83d\udc49 Write each step clearly<br>\ud83d\udc49 Label values (\u20b9, %, units)<br>\ud83d\udc49 Practice with real-life examples like shopping and bills<\/p>\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-large-font-size\" style=\"background-color:#d1c2c2\"><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-713d8dd53ca2cd17a526f0779fc6f1cc\" style=\"color:#b00012\"><strong>A store bought a tent at a cost of&nbsp;\u20b94,060 and marked it up 50%. Eliana, who works as a salesperson at the store, makes a 20% commission on all of her sales. Yesterday morning, Eliana sold the tent. How much commission did she make from this sale?\u20b9&#8212;&#8212;&#8212;.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First find the price. Write 50% as the decimal 0.50 before using it in the equation.<\/p>\n\n\n\n<p>price=cost+mark-up<\/p>\n\n\n\n<p>         =4060+0.50*4060<\/p>\n\n\n\n<p>        =4060+2030<\/p>\n\n\n\n<p>        =6090<\/p>\n\n\n\n<p>The price was&nbsp;\u20b96,090.<\/p>\n\n\n\n<p>Now find the commission. Write 20% as the decimal 0.20 before using it in the equation.<\/p>\n\n\n\n<p>commission=commission percentage\u00d7&nbsp;sales<\/p>\n\n\n\n<p>                   =0.20\u00d76090<\/p>\n\n\n\n<p>                   =1218<\/p>\n\n\n\n<p>The commission was&nbsp;\u20b91,218.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c5dcbd\"><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-5e55062a86bc54d749b6b0b6289a5659\" style=\"color:#b00012\"><strong>A store purchased a bike light and marked it up 80% from the original cost of&nbsp;\u20b9100. Then, wanting to make room for summer inventory, the store placed the light on sale for 5% off. What was the price after the discount?\u20b9&#8212;&#8212;&#8211;.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First find the original price. Write 80% as the decimal 0.80 before using it in the equation.<\/p>\n\n\n\n<p>price=cost+mark-up<\/p>\n\n\n\n<p>         =100+0.80\u00d7100<\/p>\n\n\n\n<p>        =100+80<\/p>\n\n\n\n<p>        =180<\/p>\n\n\n\n<p>The original price was&nbsp;\u20b9180.<\/p>\n\n\n\n<p>Now find the discount price. Write 5% as the decimal 0.05 before using it in the equation.<\/p>\n\n\n\n<p>discount price=original price-discount<\/p>\n\n\n\n<p>                       =180-0.50\u00d7180<\/p>\n\n\n\n<p>                       =180-9<\/p>\n\n\n\n<p>                       =171<\/p>\n\n\n\n<p>The discount price was&nbsp;\u20b9171.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e7dfdf\"><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-a3dfc257b8ef8cbc0d5beeefb55dc4e2\" style=\"color:#b00012\"><strong>A store priced a mobile phone at&nbsp;\u20b95,750 and later marked it down 60 percent. Today, a salesperson named Bobby sold the mobile phone, earning a 15% commission on the sale price. How much commission did Bobby make?\u20b9&#8212;.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First find the discount price. Write 60% as the decimal 0.60 before using it in the equation.<\/p>\n\n\n\n<p>discount price=original cost-discount<\/p>\n\n\n\n<p>                       =5750-0.60\u00d75750<\/p>\n\n\n\n<p>                       =5750-3450<\/p>\n\n\n\n<p>                       =2300<\/p>\n\n\n\n<p>The discount price was&nbsp;\u20b92,300.<\/p>\n\n\n\n<p>Now find the commission. Write 15% as the decimal 0.15 before using it in the equation.<\/p>\n\n\n\n<p>commission=commission percentage\u00d7&nbsp;sales<\/p>\n\n\n\n<p>                  =0.15\u00d72300<\/p>\n\n\n\n<p>                   =345<\/p>\n\n\n\n<p>The commission was&nbsp;\u20b9345.<\/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\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-22.png\" alt=\"\" class=\"wp-image-8487\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-22.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-22-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-22-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/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\/33999\/692\/782\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-22.png\" alt=\"\" class=\"wp-image-8488\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-22.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-22-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-22-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multi-step problems with percents Key notes: \u2705 Understand What Is Given \ud83d\udd04 Convert Percent to Decimal or Fraction \u2795\u2796 Perform Steps in the Correct Order Multi-step percent problems usually involve more than one operation: \ud83d\udccc Always solve step by step, not all at once. \ud83d\udcb8 Percent Increase Problems Steps: \ud83d\udcd8 Example idea:Price increases by 10%<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/k-7-multi-step-problems-with-percents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;K.7 Multi-step problems with percents&#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-234","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\/234","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=234"}],"version-history":[{"count":16,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/234\/revisions"}],"predecessor-version":[{"id":22465,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/234\/revisions\/22465"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}