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While I was explaining the last question in the video, the video...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2369522/fddfdfab7f8619008e7df8b02f383e8c/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/aygDDAIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"18","reqid":"1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=videoid:356677748255401539","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin öğrencilere temel matematik kavramlarını ve problemleri anlattığı eğitim içeriğidir. Öğretmen, tahtada notlar alarak ve örnekler üzerinden konuyu açıklamaktadır.","Video, sayı çeşitleri ve sayı kümeleri (rakamlar, doğal sayılar, tam sayılar, rasyonel sayılar, irrasyonel sayılar ve reel sayılar) ile başlayıp, iki ve üç bilinmeyenli ifadelerde en büyük ve en küçük değer problemlerine geçiş yapmaktadır. Daha sonra tam sayılarla ilgili çeşitli problem türleri, toplamları ve çarpımları verilen sayıların en büyük ve en küçük değerlerini bulma teknikleri ve son olarak çarpanlar, ortak katlar ve denklemler konuları ele alınmaktadır.","Öğretmen, her problem için çözüm stratejilerini ve mantık açıklamakta, özellikle \"birbirinden farklı\" ifadesinin önemini ve soruların sonuna kadar dikkatli okunması gerektiğini vurgulamaktadır. Video boyunca \"Joe\" adında bir öğrenciden de yardım alınarak konular pekiştirilmektedir."]},"endTime":2772,"title":"Matematik Dersi: Sayı Kümeleri ve Problemler","beginTime":0}],"fullResult":[{"index":0,"title":"Sayı Çeşitleri","list":{"type":"unordered","items":["Rakamlar, sayıları yazmaya yarayan sembollerdir ve sıfırdan başlayıp dokuzda biten on tane sembolden oluşur.","Doğal sayılar sıfırdan başlayıp sonsuza kadar gider ve büyük N harfi ile gösterilir.","Sayma sayıları (pozitif doğal sayılar) birden başlayıp sonsuza kadar gider ve pozitif doğal sayılar kümesi olarak adlandırılır."]},"beginTime":0,"endTime":96,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=0&ask_summarization=1"},{"index":1,"title":"Tam Sayılar","list":{"type":"unordered","items":["Tam sayılar kümesi, pozitif ve negatif sayıları içeren bir kümedir ve Z harfi ile gösterilir.","Sayı doğrusu üzerinde sıfır orta nokta olarak alınır, sağ taraf pozitif tam sayılar, sol taraf negatif tam sayılar olarak gösterilir.","Sıfır işaretsizdir ve ne pozitif ne negatif sayıdır."]},"beginTime":96,"endTime":239,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=96&ask_summarization=1"},{"index":2,"title":"Rasyonel Sayılar","list":{"type":"unordered","items":["Rasyonel sayılar, a/b şeklinde yazılabilen ve a ile b'nin tam sayı olup b'nin sıfırdan farklı olduğu sayılardır.","Rasyonel sayılar Q harfi ile gösterilir.","Sıfıra bölme tanımsızdır, ancak bir sayıya sıfır bölme sıfırdır."]},"beginTime":239,"endTime":392,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=239&ask_summarization=1"},{"index":3,"title":"İrrasyonel Sayılar ve Reel Sayılar","list":{"type":"unordered","items":["İrrasyonel sayılar, a/b şeklinde yazılamayan ve virgülden sonrası kesin belli olmayan sayılardır.","Karekökün dışına çıkamayan sayılar (örneğin √2, √3) irrasyonel sayılardır.","Reel sayılar, sayfada görülen tüm sayı çeşitlerini kapsayan kümedir."]},"beginTime":392,"endTime":452,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=392&ask_summarization=1"},{"index":4,"title":"Sayı Kümeleri ve Özellikleri","list":{"type":"unordered","items":["Rakamlar doğal sayılar kümesinin bir parçasıdır ve her rakam doğal sayıdır.","Doğal sayılar tam sayılar kümesinin bir parçasıdır ve tam sayılar kümesi rasyonel sayılar kümesinin bir parçasıdır.","Reel sayılar, rasyonel sayılar ve irrasyonel sayılar kümesini kapsayan bir kümedir."]},"beginTime":462,"endTime":533,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=462&ask_summarization=1"},{"index":5,"title":"Rakamlarla İlgili Örnek Sorular","list":{"type":"unordered","items":["\"a ve b rakamdır, 2a+3b toplamının en büyük değeri kaçtır?\" sorusunda, a ve b'nin birbirinden farklı olup olmadığına bağlı olarak farklı sonuçlar elde edilir.","Rakamlar 0'dan 9'a kadar olduğundan, en büyük değer için her iki bilinmeyene de 9 yazılabilir (45).","Birbirinden farklı rakamlar isteniyorsa, en büyük değer için 1 ve 9 kullanılır (43)."]},"beginTime":533,"endTime":723,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=533&ask_summarization=1"},{"index":6,"title":"En Küçük Değer Problemleri","list":{"type":"unordered","items":["\"2a+3b toplamının en küçük değeri kaçtır?\" sorusunda, en küçük değer için her iki bilinmeyene de 0 şeklinde yazılır (0) veya birbirinden farklı rakamlar isteniyorsa, 0, 1 ve 9 kullanılır (2).","\"2a-3b farkının en büyük değeri kaçtır?\" sorusunda, en büyük değer için büyük sayıdan küçük sayı çıkarılır (18).","Birbirinden farklı rakamlar isteniyorsa bile, en büyük değer için 1 ve 9 kullanılır (18)."]},"beginTime":723,"endTime":974,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=723&ask_summarization=1"},{"index":7,"title":"En Küçük Değer Problemleri (Devam)","list":{"type":"unordered","items":["\"2a-3b farkının en küçük değeri kaçtır?\" sorusunda, en küçük değer için küçük sayıdan büyük sayı çıkarılır (−27).","Birbirinden farklı rakamlar isteniyorsa bile, en küçük değer için 0, 7 ve 9 kullanılır (−27)."]},"beginTime":974,"endTime":1049,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=974&ask_summarization=1"},{"index":8,"title":"Rakamlarla İfadelerin En Büyük ve En Küçük Değerleri","list":{"type":"unordered","items":["a, b ve c birbirinden farklı rakamlar olmak üzere 3a + 2b - c ifadesinin en büyük değeri için pozitif katsayılara büyük sayılar, negatif katsayılara küçük sayılar verilir.","3a + 2b - c ifadesinin en küçük değeri için pozitif katsayılara küçük sayılar, negatif katsayılara büyük sayılar verilir.","Birbirinden farklı rakamlar kullanıldığında, en büyük değer için pozitif katsayılara en büyük sayılar, negatif katsayılara en küçük sayılar verilir."]},"beginTime":1051,"endTime":1311,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=1051&ask_summarization=1"},{"index":9,"title":"İki Basamaklı Sayıların Toplamı","list":{"type":"unordered","items":["İki basamaklı üç doğal sayının toplamı en çok 297 olabilir (99 + 99 + 99).","İki basamaklı üç doğal sayının toplamı en az 33 olabilir (10 + 11 + 12).","Soruları dikkatli okumak ve altını çizmek önemlidir, aksi takdirde hata yapılabilir."]},"beginTime":1311,"endTime":1484,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=1311&ask_summarization=1"},{"index":10,"title":"Negatif Tam Sayılarla İşlemler","list":{"type":"unordered","items":["İki basamaklı üç negatif tam sayının toplamı en çok olduğunda, sıfıra yakın olan negatif sayılar seçilir.","İki basamaklı birbirinden farklı iki tam sayının toplamı en az olduğunda, en büyük negatif sayı (eksi doksandokuz) ve en küçük negatif sayı (eksi doksansekiz) seçilir."]},"beginTime":1485,"endTime":1608,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=1485&ask_summarization=1"},{"index":11,"title":"Rakamları Toplamı Belirli Sayılar","list":{"type":"unordered","items":["Rakamları toplamı oniki olan üç basamaklı en büyük doğal sayı 930'dur.","Rakamları toplamı oniki olan üç basamaklı en küçük doğal sayı 129'dur.","Bu iki sayının toplamı 1059'dur."]},"beginTime":1608,"endTime":1718,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=1608&ask_summarization=1"},{"index":12,"title":"İki Basamaklı Sayıların Toplamı","list":{"type":"unordered","items":["İki basamaklı üç doğal sayının toplamı doksanbeş ise, bu sayıların en büyüğü 75'tir.","En büyük sayıyı bulmak için, diğer iki sayının toplamı (10+10=20) çıkarılır."]},"beginTime":1718,"endTime":1778,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=1718&ask_summarization=1"},{"index":13,"title":"İki Basamaklı Sayıların Toplamı","list":{"type":"unordered","items":["İki basamaklı üç farklı doğal sayının toplamı 95 ise, bu sayıların en büyüğü en çok 74 olabilir.","Toplamları verip çarpımının en büyük veya en küçük değerini isteyen sorular standart soru tarzıdır."]},"beginTime":1779,"endTime":1853,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=1779&ask_summarization=1"},{"index":14,"title":"Toplamları Verilip Çarpımlarının En Büyük Değeri","list":{"type":"unordered","items":["Toplamları 20 olan iki doğal sayının çarpımının en büyük değerini bulmak için sayılar birbirine yakın olmalıdır.","Toplamları verilip çarpımları en küçük değerini bulmak için sayılar birbirine uzak olmalıdır.","Birbirinden farklı doğal sayılar için çarpımların en büyük değerini bulmak için sayılar birbirine yakın olmalıdır."]},"beginTime":1853,"endTime":2069,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=1853&ask_summarization=1"},{"index":15,"title":"Çarpımları Verilip Toplamlarının En Büyük ve En Küçük Değeri","list":{"type":"unordered","items":["Çarpımları 12 olan iki doğal sayının toplamının en büyük değeri 13, en küçük değeri 7'dir.","Çarpımları verip toplamlarının en büyük değerini bulmak için sayılar birbirine uzak olmalıdır.","Çarpımları verip toplamlarının en küçük değerini bulmak için sayılar birbirine yakın olmalıdır."]},"beginTime":2069,"endTime":2153,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=2069&ask_summarization=1"},{"index":16,"title":"Tam Sayılar İçin Çarpımlar ve Toplamlar","list":{"type":"unordered","items":["Tam sayılar için çarpımları 12 olan iki sayının toplamının en küçük değeri -13, en büyük değeri 13'tür.","Tam sayılar için çarpımları 12 olan iki sayının toplamının en küçük değeri negatif tam sayılar olmak üzere -13'tür.","Tam sayılar için çarpımları 12 olan iki sayının toplamının en büyük değeri pozitif tam sayılar olmak üzere 13'tür."]},"beginTime":2153,"endTime":2279,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=2153&ask_summarization=1"},{"index":17,"title":"Birden Fazla Çarpım ve Toplam","list":{"type":"unordered","items":["a×b=12 ve b×c=16 olan üç doğal sayının toplamının en küçük değeri 11'dir.","a×b=12 ve b×c=16 olan üç doğal sayının toplamının en büyük değeri 29'dur.","a×b=12 ve b×c=16 olan üç doğal sayının toplamının en küçük değerini bulmak için sayılar birbirine yakın olmalıdır."]},"beginTime":2279,"endTime":2379,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=2279&ask_summarization=1"},{"index":18,"title":"Çarpanlar ve Denklemler","list":{"type":"unordered","items":["a çarpı b 12, b çarpı c 16 denklemi için a, b ve c'nin birbirinden farklı olması durumunda a=6, b=2, c=8 alınabilir ve toplamları 16 olur.","Konu zor değil ancak çok farklı soru tarzları var ve çok fazla soru çözülmesi gerekiyor.","Negatiflikler sıfırdan farklı olduğu için dikkat edilmeli."]},"beginTime":2390,"endTime":2467,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=2390&ask_summarization=1"},{"index":19,"title":"Ortak Kat Problemi","list":{"type":"unordered","items":["2a=3b ve 4b=5c eşitlikleri için b sayısı 2'nin katı ve 5'in katı olmak zorunda, bu nedenle en küçük ortak kat olan 10 bulunur.","b=10 alındığında, 2a=30 denkleminden a=15, 4b=5c denkleminden c=8 bulunur.","a+b+c'nin en küçük değeri 15+10+8=33'tür."]},"beginTime":2467,"endTime":2588,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=2467&ask_summarization=1"},{"index":20,"title":"Pozitif Tam Sayılar Problemi","list":{"type":"unordered","items":["a+2b=15 koşulunu sağlayan pozitif tam sayılar için, 15 sayısının 2'nin tam katı olan en büyük değeri 14'tür.","İlk çözüm (a=1, b=14) bulunduktan sonra, küçük sayıyı diğer sayının katına ekleyip, büyük sayıyı diğer sayının katından çıkararak diğer çözümler bulunur.","Pozitif tam sayılar için b sayısı 1, 2, 3, 4, 5, 6, 7 olmak üzere toplam 7 farklı değer alabilir."]},"beginTime":2588,"endTime":2756,"href":"/video/preview/356677748255401539?parent-reqid=1767292552671661-8442508682102393366-balancer-l7leveler-kubr-yp-vla-49-BAL&text=7%25+Solution+-+Topic&t=2588&ask_summarization=1"},{"index":21,"title":"Son Örnek","list":{"type":"unordered","items":["3x+5y=25 denklemi için, 5'in katı olan 5 değeri bulunur.","5×5=25 olduğundan, x=0 ve y=5 olarak 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