{"id":468,"date":"2018-07-20T13:45:04","date_gmt":"2018-07-20T18:45:04","guid":{"rendered":"https:\/\/www.primefactorisation.com\/blog\/?p=468"},"modified":"2024-11-02T15:02:07","modified_gmt":"2024-11-02T20:02:07","slug":"adding-and-subtracting-rationals","status":"publish","type":"post","link":"https:\/\/www.primefactorisation.com\/blog\/2018\/07\/20\/adding-and-subtracting-rationals\/","title":{"rendered":"Adding and Subtracting Rationals"},"content":{"rendered":"<p>These are the notes I wrote for adding and subtracting rational expressions last year in Algebra 2.<\/p>\n<blockquote><p><a href=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/20140608_230139_Android.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-469 size-full\" src=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/20140608_230139_Android.jpg\" alt=\"\" width=\"750\" height=\"1000\" srcset=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/20140608_230139_Android.jpg 750w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/20140608_230139_Android-225x300.jpg 225w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/20140608_230139_Android-700x933.jpg 700w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><\/p><\/blockquote>\n<p>On the first page, I wanted to make the connection between rational expressions and fractions explicit, so I started with a reminder of how to add and subtract fractions. The two examples were chosen deliberately; the first only required changing the denominator on one fraction, while the other required changing both denominators. Students need to deal with both types of problems with rational expressions.<\/p>\n<p>The next part introduced two simple problems, with only one denominator being changed between them. They are both problems that require simplifying, as I wanted to emphasize the need to do this from the start. (Students had already seen how to simplify rational expressions and stating excluded values.)<\/p>\n<p><a href=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/IMG_20180720_124554075.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-470\" src=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/IMG_20180720_124554075.jpg\" alt=\"\" width=\"1333\" height=\"1000\" srcset=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/IMG_20180720_124554075.jpg 1333w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/IMG_20180720_124554075-300x225.jpg 300w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/IMG_20180720_124554075-768x576.jpg 768w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/IMG_20180720_124554075-700x525.jpg 700w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/a><br \/>\nThe next page was about finding the lowest common multiple. I had students use a strategy which emphasizes the definition of the LCM, having them multiply by factors so that the two expressions are the same.<\/p>\n<p>And finally, a couple of examples putting all of this together.<\/p>\n<p><a href=\"https:\/\/www.dropbox.com\/sh\/34gpfbnwud64is0\/AABmhZO-Nc8IIKg-587QyWZda?dl=0\">Downloads are available here.<\/a><\/p>\n<p><a href=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-08.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-472\" src=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-08.png\" alt=\"\" width=\"1076\" height=\"832\" srcset=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-08.png 1076w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-08-300x232.png 300w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-08-768x594.png 768w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-08-700x541.png 700w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/a> <a href=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-53.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-473\" src=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-53.png\" alt=\"\" width=\"1076\" height=\"832\" srcset=\"https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-53.png 1076w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-53-300x232.png 300w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-53-768x594.png 768w, https:\/\/www.primefactorisation.com\/blog\/wp-content\/uploads\/2018\/07\/2018-07-20_13-40-53-700x541.png 700w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>These are the notes I wrote for adding and subtracting rational expressions last year in Algebra 2. On the first page, I wanted to make the connection between rational expressions and fractions explicit, so I started with a reminder of how to add and subtract fractions. The two examples were chosen deliberately; the first only &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.primefactorisation.com\/blog\/2018\/07\/20\/adding-and-subtracting-rationals\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Adding and Subtracting Rationals&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[8,7,2,20,18],"class_list":["post-468","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-algebra-2","tag-inbs","tag-math","tag-polynomials","tag-rational-functions"],"_links":{"self":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts\/468","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/comments?post=468"}],"version-history":[{"count":3,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts\/468\/revisions"}],"predecessor-version":[{"id":475,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts\/468\/revisions\/475"}],"wp:attachment":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/media?parent=468"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/categories?post=468"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/tags?post=468"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}