{"id":807,"date":"2015-07-07t09:00:55","date_gmt":"2015-07-07t16:00:55","guid":{"rendered":"\/\/www.catharsisit.com\/act\/?p=807"},"modified":"2015-07-07t09:00:55","modified_gmt":"2015-07-07t16:00:55","slug":"tuesdact-video-red-book-math-test-4-48-integers","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/act\/tuesdact-video-red-book-math-test-4-48-integers\/","title":{"rendered":"tuesdact video: red book math test 4 #48 &#8211; integers"},"content":{"rendered":"<p><center><iframe width=\"600\" height=\"450\" src=\"\/\/www.youtube.com\/embed\/wynag69bdny\" frameborder=\"0\" allowfullscreen><\/iframe><\/center><br \/>\n&nbsp;<\/p>\n<p>in this episode of tuesdact, we are taking a look at the principles of multiplying and adding even and odd numbers using an example from <em><a href=\"\/\/www.catharsisit.com\/hs\/act\/best-act-prep-books\/\">the real act prep guide<\/a><\/em> that lots of students struggle with. <\/p>\n<p><em>real act prep guide<\/em> test 4 question 48 on page 599, we are coming for you!<\/p>\n<p>check out the video or read below for the explanation and a little lesson on even and odd integers.<br \/>\n&nbsp;<\/p>\n<p>if <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is a positive integer, which of the following expressions must be an odd integer? <\/p>\n<p>f. <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_16d5157e722f71749866445bf3f925f8.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"3^n\" title=\"3^n\"\/><br \/>\ng. <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_c5f668f442b57eaaa278e4b357879f1b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n^3\" title=\"n^3\"\/><br \/>\nh. <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_9142b3ad50e10e24f2d9c090a17d0bea.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"3n\" title=\"3n\"\/><br \/>\nj. <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_984_d09b6737ba262668b77b9522add260fe.png\" style=\"vertical-align:-16px; display: inline-block ;\" alt=\"n\/3\" title=\"n\/3\"\/><br \/>\nk. <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_9672a55860c81007c08083b37fb38235.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"3 + n\" title=\"3 + n\"\/> <\/p>\n<p>alright, let\u2019s pause and go over principles of adding, subtracting, and multiplying odd and even numbers. here\u2019s how it shakes out. <\/p>\n<p>even + even = even<br \/>\neven + odd = odd<br \/>\nodd + odd = even<br \/>\neven x even = even<br \/>\neven x odd = even<br \/>\nodd x odd = odd<\/p>\n<p>you don\u2019t need to memorize the rules; if you forget, just go through the examples with easy numbers like 2 and 3 and see what happens. it will be the same for all even and odd numbers.<\/p>\n<p>so, for example:  <\/p>\n<p>even + even = even  2 + 2 = 4<br \/>\neven + odd = odd     2 + 3 = 5<br \/>\nodd + odd = even     3 + 3 = 6<br \/>\neven x even = even  2 x 2 = 4<br \/>\neven x odd = even   2 x 3 = 6<br \/>\nodd x odd = odd      3 x 3 = 9<\/p>\n<p>question 48 is also a great example of how you can find important clues in the answer choices on the act. notice that all of our answer choices have the number 3 in them, so all of our answer choices are doing something with an odd number.<\/p>\n<p>now let\u2019s test with values for <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/>. don\u2019t forget that we don\u2019t know whether <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is even or odd, so we need to test for both cases. <\/p>\n<p><strong>answer choice f:<\/strong><\/p>\n<p>3 is raised to a power of <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/>.  if <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is even (2), this gives us 3 x 3 (odd x odd = odd). if <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is odd (3), this gives us 3 x 3 x 3 (odd x odd x odd), which is also always odd. <\/p>\n<p>since an odd number multiplied by an odd number is always an odd number, and because in this case we are just multiply 3 (an odd number) by itself a number of times, it will always be odd. so f is our answer, but let\u2019s check the rest. <\/p>\n<p><strong>answer choice g:<\/strong><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is raised to a power of 3. so if <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is odd, then we have 3 x 3 x 3  (odd x odd x odd) and we know that odd x odd = odd.  but if <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is even then we have 2 x 2 x 2, and even x even = even.  so <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_c5f668f442b57eaaa278e4b357879f1b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n^3\" title=\"n^3\"\/> is not necessarily odd.<\/p>\n<p><strong>answer choice h:<\/strong><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_9142b3ad50e10e24f2d9c090a17d0bea.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"3n\" title=\"3n\"\/>.  so if <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is even (2), we have 3 x 2 (odd x even = even); if <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is odd, we have 3 x 3 (odd x odd = odd). so <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_9142b3ad50e10e24f2d9c090a17d0bea.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"3n\" title=\"3n\"\/> is not necessarily odd. <\/p>\n<p><strong>answer choice j:<\/strong><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_984_d09b6737ba262668b77b9522add260fe.png\" style=\"vertical-align:-16px; display: inline-block ;\" alt=\"n\/3\" title=\"n\/3\"\/>. this is an interesting one, because if we pick a value for <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> that does not divide evenly by 3, then it is actually <u>neither even nor odd<\/u>. by rule, the terms even or odd apply only to integers not to fractions.   <\/p>\n<p><strong>answer choice k:<\/strong><\/p>\n<p><img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_9672a55860c81007c08083b37fb38235.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"3 + n\" title=\"3 + n\"\/>.  so if <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is even (2), then we have 3 + 2 (odd + even = odd); if <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993.5_a45192846640be85b0edaca33c2a3d3b.png\" style=\"vertical-align:-6.5px; display: inline-block ;\" alt=\"n\" title=\"n\"\/> is odd, then we have 3 + 3 (odd + odd = even). so <img decoding=\"async\" src=\"\/\/www.catharsisit.com\/hs\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_9672a55860c81007c08083b37fb38235.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"3 + n\" title=\"3 + n\"\/> is not necessarily odd. <\/p>\n<p>so our answer is f.<br \/>\n&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; in this episode of tuesdact, we are taking a look at the principles of multiplying and adding even and odd numbers using an example from the real act prep guide that lots of students struggle with. real act prep guide test 4 question 48 on page 599, we are coming for you! check out [&hellip;]<\/p>\n","protected":false},"author":88,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[90],"tags":[13,156,15],"ppma_author":[24868],"acf":[],"yoast_head":"<!-- this site is optimized with the yoast seo premium plugin v21.7 (yoast seo v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>tuesdact video: red book math test 4 #48 - integers - magoosh blog | high school<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"\/\/www.catharsisit.com\/hs\/act\/tuesdact-video-red-book-math-test-4-48-integers\/\" \/>\n<meta property=\"og:locale\" content=\"en_us\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"tuesdact video: red book math test 4 #48 - integers\" \/>\n<meta property=\"og:description\" content=\"&nbsp; in 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an ma degree from the catholic university, and ba degrees in secondary education and english literature from the university of maryland, college park. she was the recipient of the 2013 excellence in teaching award and the <a href=\"https:\/\/grad.uci.edu\/funding\/fellowships-awards\/internal\/chancellors-club-fellows.php\">chancellor\u2019s club fellowship<\/a> from the university of california, irvine. she\u2019s worked as a high school teacher and university professor, as an independent college and graduate school admissions counselor, and as an expert tutor for standardized tests, helping hundreds of students gain acceptance into premier national and international institutions. she now develops accessible and effective edtech products for magoosh. her free online content and<a href=\"https:\/\/www.youtube.com\/watch?v=-junkojw4y4\"> youtube videos<\/a> providing test prep and college admissions advice have received over 6 million views in over 125 countries. kristin is an advocate 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