{"id":35,"date":"2022-04-13T09:48:35","date_gmt":"2022-04-13T09:48:35","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=35"},"modified":"2025-03-05T06:47:03","modified_gmt":"2025-03-05T06:47:03","slug":"b-5-multiply-and-divide-rational-numbers","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/b-5-multiply-and-divide-rational-numbers\/","title":{"rendered":"B.5 Multiply and divide rational numbers"},"content":{"rendered":"\n<p class=\"has-text-align-center has-text-color has-link-color has-huge-font-size wp-elements-f66c03ef332868d0c9ae95d9a6903472\" style=\"color:#00056d;text-transform:uppercase\"><strong>Multiply and divide rational numbers<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4dde4300b7763c9a2a860fe18546dfe2\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h4 class=\"wp-block-heading has-large-font-size\"><strong>Multiplying Rational Numbers<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Definition:<\/strong>\n<ul class=\"wp-block-list\">\n<li>To multiply two rational numbers, multiply the numerators together and the denominators together.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Formula<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-28.png\" alt=\"\" class=\"wp-image-14637\" style=\"width:205px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Steps:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Multiply the numerators: a\u00d7c<\/li>\n\n\n\n<li class=\"has-large-font-size\">Multiply the denominators: b\u00d7d<\/li>\n\n\n\n<li>Simplify the resulting fraction, if possible.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Example:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-29.png\" alt=\"\" class=\"wp-image-14639\" style=\"width:598px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Multiplying by a Whole Number:<\/strong>\n<ul class=\"wp-block-list\">\n<li>When multiplying a rational number by a whole number, treat the whole number as a fraction with denominator 1.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-30.png\" alt=\"\" class=\"wp-image-14640\" style=\"width:441px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\"><strong>Dividing Rational Numbers<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Definition:<\/strong>\n<ul class=\"wp-block-list\">\n<li>To divide two rational numbers, multiply the first rational number by the reciprocal of the second rational number.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Formula:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-31.png\" alt=\"\" class=\"wp-image-14641\" style=\"width:278px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Steps:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Find the reciprocal of the divisor (flip the numerator and the denominator of the second fraction).<\/li>\n\n\n\n<li>Multiply the first fraction by this reciprocal.<\/li>\n\n\n\n<li>Simplify the resulting fraction, if possible.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Example:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-32.png\" alt=\"\" class=\"wp-image-14642\" style=\"width:498px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Dividing by a Whole Number:<\/strong>\n<ul class=\"wp-block-list\">\n<li>When dividing a rational number by a whole number, treat the whole number as a fraction with denominator 1 and then find its reciprocal.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-33.png\" alt=\"\" class=\"wp-image-14643\" style=\"width:549px;height:auto\"\/><\/figure><\/div>\n\n\n<h4 class=\"wp-block-heading\"><strong>Simplifying Rational Numbers<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After multiplying or dividing rational numbers, always simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number.<strong>Example:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-34.png\" alt=\"\" class=\"wp-image-14644\" style=\"width:415px;height:auto\"\/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\"><strong>Practice Problems<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Multiplying Rational Numbers:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-27.png\" alt=\"\" class=\"wp-image-14635\" style=\"width:178px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Dividing Rational Numbers:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-26.png\" alt=\"\" class=\"wp-image-14634\" style=\"width:175px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mixed Practice:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-25.png\" alt=\"\" class=\"wp-image-14633\" style=\"width:182px;height:auto\"\/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\">Tips for Success<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Reciprocals:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Remember to find the reciprocal when dividing by a fraction.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Simplifying:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Always simplify your answer to its lowest terms.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Multiplication and Division Rules:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Use the multiplication rule for both operations: multiply the numerators together and the denominators together for multiplication, and multiply by the reciprocal for division.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Check Your Work:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Double-check your multiplication and division to avoid small mistakes.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" 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:#f3a4a4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-8bc1439498b180b8740b8550a71cde86\" style=\"color:#b00012\">\ud83d\udd2e Divide.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-ea90dde9b334867da9d06185246f6989\" style=\"color:#b00012\">1\/10 \u00f7&nbsp;1\/2 =<\/p>\n<\/div><\/div>\n\n\n\n<p>Turn this from a division problem into a multiplication problem by multiplying by the reciprocal.<\/p>\n\n\n\n<p>1\/10 \u00f7&nbsp;1\/2 = 1\/10 x 2\/1<\/p>\n\n\n\n<p>Cancel common factors, then multiply.<\/p>\n\n\n\n<p>1\/10 x 2\/1 = 1\/5 x 1\/1<\/p>\n\n\n\n<p>= 1 x 1 \/ 5 x 1<\/p>\n\n\n\n<p>= 1\/5<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c4a5f7\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-8bc1439498b180b8740b8550a71cde86\" style=\"color:#b00012\">\ud83d\udd2e Divide.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-b73686c2504ab673c14e985c15f272f1\" style=\"color:#b00012\">1\/4 \u00f7&nbsp;1\/2 =<\/p>\n<\/div><\/div>\n\n\n\n<p>Turn this from a division problem into a multiplication problem by multiplying by the reciprocal.<\/p>\n\n\n\n<p>1\/4 \u00f7&nbsp;1\/2 = 1\/4 x 2\/1<\/p>\n\n\n\n<p>Cancel common factors, then multiply.<\/p>\n\n\n\n<p>1\/4 x 2\/1 = 1\/2 x 1\/1<\/p>\n\n\n\n<p>= 1 x 1 \/ 2 x 1<\/p>\n\n\n\n<p> = 1\/2<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9cc4f1\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8df9968d810ea606fbaadebaf5e891d4\" style=\"color:#b00012\">\ud83d\udd2e Divide.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-fe1751079f515d797d5a4bfc0fb62f66\" style=\"color:#b00012\">1\/8 \u00f7&nbsp;1\/6 =<\/p>\n<\/div><\/div>\n\n\n\n<p>Turn this from a division problem into a multiplication problem by multiplying by the reciprocal.<\/p>\n\n\n\n<p>1\/8 \u00f7&nbsp;1\/6 = 1\/8 x 6\/1<\/p>\n\n\n\n<p>Cancel common factors, then multiply.<\/p>\n\n\n\n<p>1\/8 x 6\/1 = 1\/4 x 3\/1<\/p>\n\n\n\n<p>= 1 x 3 \/ 4 x 1<\/p>\n\n\n\n<p>= 3\/4<\/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\/76556\/941\/873\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-13.png\" alt=\"\" class=\"wp-image-6517\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-13.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-13-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-13-150x150.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\/76168\/496\/357\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-13.png\" alt=\"\" class=\"wp-image-6518\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-13.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-13-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-13-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply and divide rational numbers key notes: Multiplying Rational Numbers Dividing Rational Numbers Simplifying Rational Numbers Practice Problems Tips for Success Learn with an example \ud83d\udd2e Divide. 1\/10 \u00f7&nbsp;1\/2 = Turn this from a division problem into a multiplication problem by multiplying by the reciprocal. 1\/10 \u00f7&nbsp;1\/2 = 1\/10 x 2\/1 Cancel common factors, then<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/b-5-multiply-and-divide-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;B.5 Multiply and divide rational numbers&#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-35","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/35","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=35"}],"version-history":[{"count":23,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/35\/revisions"}],"predecessor-version":[{"id":17573,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/35\/revisions\/17573"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}