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Video, birinci bölümün sonunda kısa bir ara verileceği bilgisiyle sona ermektedir."]},"endTime":3558,"title":"Matematik Dersi: Temel Kavramlar ve Sayı Problemleri","beginTime":0}],"fullResult":[{"index":0,"title":"Temel Kavramlar ve Rakamlar","list":{"type":"unordered","items":["Temel kavramlarda en önemli konu tanım kümeleridir.","Rakamlar, sayıları ifade eden sembollerdir ve 0'dan 9'a kadar olan sembollerdir.","En son bulunan rakam sıfırdır ve bu sayıyı Harezmi bulmuştur."]},"beginTime":29,"endTime":100,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=29&ask_summarization=1"},{"index":1,"title":"Sıfırın Matematikteki Önemi","list":{"type":"unordered","items":["Sıfırın matematikteki karşılığı o dönemlerde hiçlik ve yokluk anlamına gelmiştir.","Sıfırın bulunması matematikte devrim niteliğinde bir gelişmedir ve bilgisayar algoritmalarının temelidir.","Sıfır çarpma işleminde yutan elemandır, toplamada ise etkisiz elemandır."]},"beginTime":100,"endTime":155,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=100&ask_summarization=1"},{"index":2,"title":"Sıfırın Tarihsel Yansımaları","list":{"type":"unordered","items":["Bir dönem Floransa'da sıfır yasaklanmıştır çünkü Hristiyanlıkta şeytanı temsil ettiği düşünülmüştür.","Matematikçiler bir dönem sıfırla işlem yapmamışlardır.","Sıfırın bulunması matematik ve mühendislikte inanılmaz gelişmeler sağlamıştır."]},"beginTime":155,"endTime":216,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=155&ask_summarization=1"},{"index":3,"title":"Rakamlarla İlgili Bir Soru","list":{"type":"unordered","items":["\"a, b, c birbirinden farklı rakamlardır\" tanım kümesine göre bir soru çözülmektedir.","\"2a+b-c\" ifadesinin alabileceği en büyük değer 26, en küçük değer -8'dir.","En büyük ve en küçük değerlerin toplamı 18'dir."]},"beginTime":216,"endTime":410,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=216&ask_summarization=1"},{"index":4,"title":"Rakamlarla İlgili İkinci Bir Soru","list":{"type":"unordered","items":["a, b, c rakamları kullanılarak oluşturulan bir şekilde, alttaki karelerdeki sayıların toplamı üstteki karedeki sayıya eşittir.","a+b=c koşulu altında a+b+c toplamının en büyük değeri 36'dır.","Tanım kümesine göre çözüm yapmak önemlidir."]},"beginTime":410,"endTime":565,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=410&ask_summarization=1"},{"index":5,"title":"Rakamlarla İlgili Üçüncü Bir Soru","list":{"type":"unordered","items":["a ve b rakam olmak üzere a/b=2/3 koşuluna göre a+b toplamının alabileceği farklı değerlerin sayısı sorulmaktadır.","a/b=2/3 eşitliğini sağlayan rakam değerleri (2,3), (4,6) ve (6,9) olabilir.","a+b toplamının alabileceği farklı değerler 5, 10 ve 15 olup, toplamda 3 farklı değer vardır."]},"beginTime":565,"endTime":690,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=565&ask_summarization=1"},{"index":6,"title":"Sayı Tutma Oyunu Problemi","list":{"type":"unordered","items":["Buket ve Eren arasında bir sayı tutma oyunu oynanıyor; Eren'den 1 ile 9 arasında üç rakam tutması, birinci rakamı 2 ile, üçüncü rakamı 3 ile çarpması ve tüm sayıları toplaması isteniyor.","Eren'in bulduğu toplam 20 olduğunda, Eren'in aklından tuttuğu üç rakamın toplamının en az kaç olabileceği soruluyor.","Problemin çözümünde, c'ye en büyük değer (6) verilerek 18 elde edilir, geriye 2 kalır; a'ya 2, b'ye 1 verilerek toplam 8 elde edilir, bu en küçük toplam değeridir."]},"beginTime":695,"endTime":974,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=695&ask_summarization=1"},{"index":7,"title":"Doğal Sayılar ve Sıfır","list":{"type":"unordered","items":["Doğal sayılar, sıfırdan başlayıp bir, iki, üç, dört, beş şeklinde giden bir kümedir ve N harfiyle gösterilir.","Sıfır, toplamada etkisiz eleman, çarpmada ise yutan elemandır.","Sıfırın tanımı \"hiçbir şeyde bir şeydir\" olarak ifade edilir ve Hint mitolojisinden gelir.","Bir sayının sıfıra bölümü tanımsızdır, ancak sıfırın sıfıra bölümü belirsizdir ve bu konu limit kavramının konusu olur."]},"beginTime":974,"endTime":1220,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=974&ask_summarization=1"},{"index":8,"title":"Doğal Sayılar ve Çarpım Problemleri","list":{"type":"unordered","items":["Doğal sayılar konusunda önemli olan sıfırı unutmamaktır.","Toplamları verilen iki doğal sayının çarpımının en büyük olması için sayıların birbirine yakın veya eşit olması gerekir.","Toplamları verilen sayıların çarpımlarının en büyük olması için sayılar birbirine yakın olmalı, eşit olabiliyorsa tamamlar."]},"beginTime":1222,"endTime":1420,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=1222&ask_summarization=1"},{"index":9,"title":"Denklem Çözümü ve Çarpım Problemi","list":{"type":"unordered","items":["\"a ve b doğal sayılar olmak üzere a×b biçiminde tanımlanan ifade\" sorusunda, toplamları verilen sayıların çarpımının en büyük değerini bulmak için sayıları birbirine yakın tutmak gerekir.","Denklem çözümünde, bir değişkenin değeri artarken diğer değişkenin değeri azalmaya başlar.","Çarpımın en büyük değeri, sayıların birbirine yakın olduğu durumda elde edilir."]},"beginTime":1420,"endTime":1691,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=1420&ask_summarization=1"},{"index":10,"title":"Toplamları Verilen Sayıların Çarpımı","list":{"type":"unordered","items":["Toplamları verilen iki doğal sayının çarpımının en büyük olması için sayıların birbirine yakın olması ya da eşit olması gerekir.","Çarpımın en küçük olması için sayılar uzak olmalı, çarpımın büyük olması için sayılar birbirine yakın olmalıdır.","Bu kuralı ezberlemek yerine yorumlamak gerekir."]},"beginTime":1691,"endTime":1871,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=1691&ask_summarization=1"},{"index":11,"title":"Temel Kavramlar ve Problem Çözümü","list":{"type":"unordered","items":["Bir soruda, kısa kenarı a tane, uzun kenarı b tane birim karelere ayrılan bir bahçede her karenin ortasına bir fidan dikiliyor ve toplam 48 fidan dikiliyor.","Soruda a×b=48 eşitliği bulunuyor ve bahçenin çevresinde alınabilecek en küçük değer soruluyor.","Çevre hesabı 2×(a+b) formülüyle yapılıyor ve en küçük değer 28 birim olarak bulunuyor."]},"beginTime":1878,"endTime":2170,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=1878&ask_summarization=1"},{"index":12,"title":"Tam Sayılar Kavramı","list":{"type":"unordered","items":["Sıfırın bulunması negatif sayıların varlığını ortaya çıkarmış ve tam sayılar eksi sonsuzdan artı sonsuza doğru giden sayılardır.","Tam sayılar negatif tam sayılar, pozitif tam sayılar ve sıfır (isaretsiz tam sayı) olmak üzere üç gruba ayrılır.","Negatif olmayan en küçük sayılar 0, 1, 2; pozitif olmayan en büyük sayılar -1, -2, -3; pozitif en küçük sayılar 1, 2, 3; negatif en büyük sayılar -1, -2, -3'dür."]},"beginTime":2170,"endTime":2349,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=2170&ask_summarization=1"},{"index":13,"title":"Tam Sayılarla İşlemler","list":{"type":"unordered","items":["a ve b tam sayı olmak üzere a×b=12 olduğunda, a+b toplamının en büyük değeri 13, en küçük değeri -13 olarak bulunuyor.","Tam sayılarla işlem yaparken negatif değerler de dikkate alınmalı ve en büyük değerin eksi işaretli hali en küçük değerdir.","En büyük değer (13) ile en küçük değer (-13) toplamı sıfırdır."]},"beginTime":2349,"endTime":2518,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=2349&ask_summarization=1"},{"index":14,"title":"Kare ve Daire Problemi","list":{"type":"unordered","items":["Bir problemde her kutuya pozitif tam sayılar yerleştirilir ve her karenin içindeki sayı, kendisine komşu olan iki dairenin içindeki sayıların çarpımına eşittir.","Kırmızı renkli karenin içindeki sayının en küçük değeri 12'dir, bu değeri bulmak için dairelerin içindeki sayılar 3 ve 4 olarak seçilmiştir.","En küçük değeri bulmak için, dairelerin içindeki sayıların en büyük ortak böleni seçilmesi gerekir."]},"beginTime":2521,"endTime":2697,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=2521&ask_summarization=1"},{"index":15,"title":"En Büyük-En Küçük Değer Problemi","list":{"type":"unordered","items":["En büyük-en küçük sorularında tanım kümesine dikkat edilmeli, tam sayı derse negatif sayılar da düşünülmelidir.","x, y, z tam sayı olmak üzere x×y=16 ve y×z=24 koşullarında x+y+z toplamının en küçük değeri -41'dir.","Ortak ifade büyüdükçe toplam küçülür, pozitif tam sayılar için en küçük değer 13'tür, ancak tam sayı dediği için negatif değerler de düşünülmeli."]},"beginTime":2697,"endTime":2924,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=2697&ask_summarization=1"},{"index":16,"title":"Negatif Tam Sayı Problemi","list":{"type":"unordered","items":["a, b ve c negatif tam sayılar olmak üzere a×b=24 ve b×c=18 koşullarında a+b+c toplamının en büyük değeri -13'tür.","Ortak ifadeyi büyüterek negatif sayıların toplamını en büyük değerlere yaklaştırmak gerekir.","Negatif tam sayılar için en büyük değer, ortak ifadelerin en büyük ortak böleni seçilerek bulunur."]},"beginTime":2924,"endTime":3053,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=2924&ask_summarization=1"},{"index":17,"title":"Tam Sayı Toplamı Problemi","list":{"type":"unordered","items":["x, y, z birer tam sayı olmak üzere x×y=8 ve y×z=-24 koşullarında x+y+z toplamının en büyük değeri 5'tir.","En büyük değeri bulmak için negatif sayılardan en küçük mutlak değerli olanlar seçilir.","Ortadaki elemana en küçük değer verildiğinde toplamın en büyük değeri elde edilir."]},"beginTime":3053,"endTime":3225,"href":"/video/preview/17576585077672951941?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=3053&ask_summarization=1"},{"index":18,"title":"Matematik Problemi Çözümü","list":{"type":"unordered","items":["Eğitmen, bir sorunun düzeltildiğini belirtiyor ve şıkların farklı olabileceğini söylüyor.","Soruda bir karenin her kutucuğunda bir sayı bulunuyor ve her satır ve köşegenin sayılarının toplamı aynı sabit sayıya eşit.","Mavi renk ile boyalı kutuların içindeki sayıların toplamı 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Try this new app: http://m.onelink.me/611953f Want to learn the piano? Here is the quickest and easiest way: http://bit.do/oyster-flowkey Check out TubeBuddy to be able to perform bulk...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4046066/d96ff8a93fe5afc6477787f86a33bde9/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/x4_xKwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"17","reqid":"1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D1YtnxTcdSzQ","linkTemplate":"/video/preview/18278167742323915191?parent-reqid=1769516372441406-6744843072806354873-balancer-l7leveler-kubr-yp-vla-182-BAL&text=TYTOf2ndness&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"How to play The 2nd Law : Unsustainable by Muse on 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