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Dersin sonunda öğretmen, öğrencilere çeşitli kitaplardan ödevler vermektedir."]},"endTime":1975,"title":"Rasyonel Sayılar Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Rasyonel Sayılar Konusuna Giriş","list":{"type":"unordered","items":["Rasyonel sayılar en önemli matematik konularından biridir.","Rasyonel sayılar, tam sayılar ve doğal sayılar gibi sayı kümelerinin bir parçasıdır.","Bu derste rasyonel sayıların tanımı, sayı doğrusunda gösterimi ve ondalık gösterimi öğreneceğiz."]},"beginTime":2,"endTime":101,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=2&ask_summarization=1"},{"index":1,"title":"Rasyonel Sayıların Tanımı","list":{"type":"unordered","items":["Rasyonel sayılar, a/b şeklinde yazılan ifadelerdir (örneğin 3/1, 5/7, 18/13).","Rasyonel sayılar Q sembolüyle gösterilir.","Rasyonel sayılarda payda (b) hiçbir zaman sıfır 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böldüğümüzde sonuç tanımsızdır ve matematikçiler payda sıfır olamaz diye bir kural getirmiştir.","Rasyonel sayıların paydası negatif tam sayı olabilir, örneğin 5/(-4) bir rasyonel sayıdır."]},"beginTime":327,"endTime":552,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=327&ask_summarization=1"},{"index":4,"title":"Rasyonel Sayıların Özellikleri","list":{"type":"unordered","items":["Her tam sayı bir rasyonel sayıdır çünkü altında görünmez bir 1 vardır.","Her rasyonel sayı bir doğal sayı değildir, örneğin 8/7 bir doğal sayı değildir.","Paydası sıfır olan ifadeler rasyonel değildir."]},"beginTime":552,"endTime":682,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=552&ask_summarization=1"},{"index":5,"title":"Eksi İşareti ve Sayı Doğrusu","list":{"type":"unordered","items":["Eksi işareti kesirlerde her yere hareket edebilir, sadece bir tane eksi olabilir.","Sayı doğrusunda basit kesirler 0'dan 1'e veya -1'den 0'a arasındadır.","Basit kesir, payı paydasından küçük olan kesirdir, pay paydadan büyükse tam sayılı veya birleşik kesirdir."]},"beginTime":682,"endTime":936,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=682&ask_summarization=1"},{"index":6,"title":"Rasyonel Sayıların Sayı Doğrusunda Gösterimi","list":{"type":"unordered","items":["Eksi bir çeyrek, eksi bir ile eksi bir arasında dört parçaya bölünerek bulunur.","Beş buçuk, beş'i ikiye bölerek iki tam bir bölü iki olarak hesaplanır ve iki ile üç arasındadır.","Eksi iki tam bir bölü beş, eksi iki ile eksi üç arasında beş parçaya bölünerek bulunur."]},"beginTime":938,"endTime":1070,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=938&ask_summarization=1"},{"index":7,"title":"Sayı Doğrusu Sorusu","list":{"type":"unordered","items":["Dört ile beş arası sekiz eş parçaya bölünmüş bir sayı doğrusunda, 33/8, 17/4, 37/8 ve 21/4 sayıları incelenir.","33/8, 17/4, 37/8 sayıları dört ile beş arasındadır, ancak 21/4 (5 tam bir çeyrek) beş ile altı arasındadır.","Doğru cevap 21/4'tür ve bu soruyu Elif Sema Kızılkaya doğru cevaplamıştır."]},"beginTime":1070,"endTime":1194,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=1070&ask_summarization=1"},{"index":8,"title":"Rasyonel Sayıların Ondalık Gösterimi","list":{"type":"unordered","items":["Rasyonel sayıları paydayı on'un kuvvetleri yaparak (10, 100, 1000) ondalık olarak gösterebiliriz.","1/5, 2 ile genişletilerek 2/10 olur ve ondalık gösterimi 0,2'dir.","7/20, 5 ile genişletilerek 35/100 olur ve ondalık gösterimi 0,35'tir."]},"beginTime":1194,"endTime":1325,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=1194&ask_summarization=1"},{"index":9,"title":"Tam Sayı ve Ondalık Gösterim","list":{"type":"unordered","items":["2 tam 4/25, 4 ile genişletilerek 16/100 olur ve ondalık gösterimi 2,16'dır.","-375/8, 125 ile genişletilerek -375/1000 olur ve ondalık gösterimi -0,375'tir.","Ondalık gösterimde virgülün sağında, paydadaki sıfır sayısı kadar basamak olur."]},"beginTime":1325,"endTime":1455,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=1325&ask_summarization=1"},{"index":10,"title":"Ondalık Gösterim Sorusu","list":{"type":"unordered","items":["Fatma Hanım'ın manavdan aldığı meyvelerin kütleleri kilogram cinsinden verilmiş: 5/2 kg, 7/2 kg, 12/5 kg, 11/8 kg.","Soruda, tabloda verilen meyvelerin kütlelerinden birinin kilogram cinsinden ondalık gösterimi olamayacak olanı bulunması isteniyor.","5/2 kg = 2,5 kg, 7/2 kg = 3,5 kg, 12/5 kg = 2,4 kg, 11/8 kg = 1,25 kg olarak hesaplanıyor ve cevap 1,25 kg olarak bulunuyor."]},"beginTime":1458,"endTime":1630,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=1458&ask_summarization=1"},{"index":11,"title":"Rasyonel Sayılarla İlgili Beceri Temelli Soru","list":{"type":"unordered","items":["Bir rasyonel sayı olmak üzere, aşağı doğru ok a yuvarlak içerisinde a'dan küçük en büyük tam sayı, yukarı doğru ok yuvarlak a içerisinde a'dan büyük en küçük tam sayı anlamına geliyor.","(-11/3) sayı doğrusunda -4 ile -3 arasında bulunuyor ve bu sayıdan küçük en büyük tam sayı -4'tür.","11/5 sayı doğrusunda 2 ile 3 arasında bulunuyor ve bu sayıdan büyük en küçük tam sayı 3'tür.","(-4/3) sayı doğrusunda -1 ile -2 arasında bulunuyor ve bu sayıdan büyük en küçük tam sayı -1'dir."]},"beginTime":1630,"endTime":1903,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=1630&ask_summarization=1"},{"index":12,"title":"Ödevler","list":{"type":"unordered","items":["Öğrencilere rasyonel sayılar konusundan sayfa 24 ve 25'i yapmaları isteniyor.","Taktikli sayısal kitaptan test 5 ve test 5'i yapmaları gerekiyor.","Taktikle dinamodan test 13 ve test 14'ü, Zoru Bankası sayısaldan test 9 ve test 10'u yapmaları isteniyor."]},"beginTime":1903,"endTime":1961,"href":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=1903&ask_summarization=1"}],"linkTemplate":"/video/preview/1415700821601130589?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Rasyonel Sayılar | 7. 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Öncelikle rasyonel sayıların iki tam sayının birbirine bölümüyle oluştuğu, paydanın sıfırdan farklı olması gerektiği ve her tam sayının bir rasyonel sayı olduğu açıklanmaktadır. Daha sonra rasyonel sayıların sayı doğrusu üzerinde nasıl gösterileceği, tam sayılı kesirlerin nasıl yazılacağı ve sayı doğrusu üzerinde nasıl bulunacağı örneklerle anlatılmaktadır. Video, rasyonel sayıların farklı gösterimlerinin eşit olduğu bilgisiyle sonlanmaktadır."]},"endTime":501,"title":"Rasyonel Sayılar Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Rasyonel Sayılar Tanımı","list":{"type":"unordered","items":["Rasyonel sayı, iki tam sayının birbirine bölümüyle oluşur.","Rasyonel sayıda pay (üstteki sayı) ve payda (alttaki sayı) tam sayı olur, aralarında kesir çizgisi bulunur.","Payda mutlaka sıfırdan farklı olmalıdır çünkü bir sayı sıfıra bölünemez."]},"beginTime":15,"endTime":94,"href":"/video/preview/15203921353223531360?parent-reqid=1770030369789442-1890908421036636792-balancer-l7leveler-kubr-yp-klg-6-BAL&text=7tyOne&t=15&ask_summarization=1"},{"index":1,"title":"Rasyonel Sayıların Özellikleri","list":{"type":"unordered","items":["Her tam sayı bir rasyonel sayıdır ve paydası 1 olan bir kesir olarak ifade edilebilir.","Rasyonel sayılar Q harfi ile gösterilir.","Tam sayılı kesirler de rasyonel sayıdır ve paydası birden büyük olan 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