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Öğretmen, \"RM tayfa\" olarak adlandırdığı izleyicilere hitap etmektedir.","Videoda işçi problemlerinin çözüm yöntemleri adım adım gösterilmektedir. Öğretmen, oran-orantı mantığını kullanarak çeşitli işçi problemlerini çözmekte, işçilerin birim zamanda yaptığı işi hesaplamak için ortak sayılar seçmekte ve denklem kurma tekniklerini açıklamaktadır. Video, farklı işçi problemlerinin çözümüyle ilerleyerek, bir sonraki videoda hız problemlerine geçileceğini belirtmektedir.","Videoda Arda, Onur, Reyhan, Merve, Murat, Gökhan, Mehmet, Orkun, Kenan gibi karakterlerin çalışma kapasiteleri üzerinden çeşitli problemler çözülmektedir. Ayrıca makinelerin üretim hızları ve eşit güçte bir grup işçi tarafından gerçekleştirilen işler de ele alınmaktadır. Öğretmen, rasyonel ifadelerle uğraşmadan kesirli sayılarla işlem yapmanın daha kolay olduğunu ve problem çözmenin anahtarı eşitlik kurmanın olduğunu vurgulamaktadır."]},"endTime":1865,"title":"İşçi Problemleri Matematik Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"İşçi Problemleri Kampı Tanıtımı","list":{"type":"unordered","items":["Mehmet hocanın 15. tatilinde bir problem kampı düzenleniyor ve bir kitabın tamamı soruları paylaşılacak.","İşçi problemleri son dört yıldır ÖSYM'nin soru dağarcığı içerisinde gelmiyor, fakat oran orantı soruları içerisinde yer alıyor.","Bu soruların neredeyse tamamı oran orantı mantığıyla çözülecek."]},"beginTime":0,"endTime":44,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=0&ask_summarization=1"},{"index":1,"title":"Kamp Programı","list":{"type":"unordered","items":["Dördüncü gün işçi problemleri konusu ele alınacak ve hemen arkasından karma test gelecek.","Toplamda sekiz soru çözülecek, diğer tüm sorular ödev olarak verilecek."]},"beginTime":44,"endTime":93,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=44&ask_summarization=1"},{"index":2,"title":"İşçi Problemleri Çözüm Yöntemi","list":{"type":"unordered","items":["İşçi problemlerinde önce işçileri ve işin tamamını yazarak çözüm yapılıyor.","İşçilerin günde yaptığı iş miktarı, işin tamamı ile işçilerin bitirme sürelerinin en küçük ortak katı (48) kullanılarak hesaplanıyor.","İşçi problemlerinde en kolay yöntem, işçilerin günde yaptığı iş miktarını bulup, toplam iş miktarı ile karşılaştırma yapmaktır."]},"beginTime":93,"endTime":273,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=93&ask_summarization=1"},{"index":3,"title":"İşçi Problemleri Çözüm Yöntemi","list":{"type":"unordered","items":["Rasyonel ifadelerde çözüm yöntemleri olsa da, alıştırma olarak bu yöntemi öğrenmek daha faydalıdır.","İşçi-emekçi problemleri aslında oran orantıya dayanmaktadır ve son dört yıldır ÖS'de tek başına soru sorulmamaktadır.","Rasyonel ifadelerle uğraşmak yerine, rasyonel sayılardan ve kesirli sayılardan uzak kalmak daha kolay bir çözüm yöntemidir."]},"beginTime":277,"endTime":308,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=277&ask_summarization=1"},{"index":4,"title":"Örnek Soru Çözümü","list":{"type":"unordered","items":["Arda'nın çalışma kapasitesi Onur'un çalışma kapasitesinin üç katı, Reyhan'ın çalışma kapasitesinin üç çeyrek'ü kadardır.","Reyhan'ın çalışma kapasitesi dört'e bölünebilen bir sayı olarak (örneğin 4) seçilirse, Arda'nın çalışma kapasitesi 3 olur.","Arda ve Onur bir işin yarısını bitirdiğinde, Onur işi bırakıp Reyhan çalışmaya başlar ve işin tamamı kırkdört saatte bittiği belirtilir."]},"beginTime":308,"endTime":459,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=308&ask_summarization=1"},{"index":5,"title":"Matematiksel Çözüm","list":{"type":"unordered","items":["X ile y arasında bir bağıntı bulunur ve x ile y'nin toplamı kırkdört saate eşittir.","X ve y değerleri k katına eşit olarak alınır ve k'nin değeri 4 olarak bulunur.","Reyhan tek başına işin tamamını ellialtı saatte bitirebilir."]},"beginTime":459,"endTime":586,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=459&ask_summarization=1"},{"index":6,"title":"Duvar Boyama Problemi","list":{"type":"unordered","items":["Duvar problemi için duvar on eşit parçaya bölünüyor ve her parça bir metrekare olarak kabul ediliyor.","Bir kişi altı saatte üç metrekare boyayabiliyor, bu da iki saatte bir metrekare boyadığını gösteriyor.","Merve ikinci duvarı boyarken hızını üç katı kadar artırıyor, bu durumda iki saatte dört metrekare, bir saatte ise iki metrekare boyayabiliyor."]},"beginTime":598,"endTime":730,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=598&ask_summarization=1"},{"index":7,"title":"Geometri Kullanımı","list":{"type":"unordered","items":["Dikdörtgende yukarıdaki kenarda seçilen bir nokta, aşağıdaki köşelerle birleştirildiğinde oluşan alan, bütün alanın yarısı kadardır.","Duvarın yarısı 5 metrekare olduğunda, Merve bunu 2,5 saatte boyayabilir.","ÖSYM'nin işçi problemlerinde enteresan soruları olduğunu belirtiyor."]},"beginTime":730,"endTime":811,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=730&ask_summarization=1"},{"index":8,"title":"İşçi Problemi","list":{"type":"unordered","items":["Murat tek başına A saatte, Gökhan tek başına 2A saatte, Mehmet ise 3A saatte bir işi bitirebiliyor.","Birim zamanda yapılan iş: Murat 6V/A, Gökhan 3V/A, Mehmet 2V/A kadar iş yapıyor.","Üç kişi birlikte çalıştığında işi K saatte bitiriyorlar ve K değeri 6A/11 olarak bulunuyor."]},"beginTime":811,"endTime":975,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=811&ask_summarization=1"},{"index":9,"title":"Eşitsizlik Çözümü","list":{"type":"unordered","items":["K'nin 4'ten küçük olması için A'nın alabileceği en büyük tam sayı değeri 7'dir.","K'nin 5'ten büyük olması için A'nın alabileceği en küçük tam sayı değeri 9'dur.","Sorunun cevabı B seçeneği olarak belirleniyor."]},"beginTime":975,"endTime":1028,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=975&ask_summarization=1"},{"index":10,"title":"Gerçek RM Tayfa Daveti","list":{"type":"unordered","items":["Gerçek RM tayfa, videoyu izlerken önce videoyu beğenip, reklamları izleyip, abone değilse abone olmalıdır.","Video bittikten sonra soruları çözmeli ve yorumlara yorum yazmalıdır.","Gerçek RM tayfa, videoyu beğenip, abone olup, video bittikten sonra yorum yazarak selamlaşmalıdır."]},"beginTime":1030,"endTime":1101,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=1030&ask_summarization=1"},{"index":11,"title":"İşçi Problemi Çözümü","list":{"type":"unordered","items":["Orkun ve Kenan bir işi birlikte 10 saatte bitirirken, Orkun 2 saat ve Kenan 3 saat çalıştığında işin 1/4'ü bitmiş olur.","İşçi problemlerinde, bir kişinin bir saatte x kadar iş, diğerinin bir saatte y kadar iş yapması şeklinde çözümleme yaparak problem kolayca çözülebilir.","Çözüm sonucunda Orkun ve Kenan'ın çalışma hızlarının birbirine eşit olduğu bulunmuştur."]},"beginTime":1101,"endTime":1212,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=1101&ask_summarization=1"},{"index":12,"title":"Makine Oran Orantı Problemi","list":{"type":"unordered","items":["K makinesi bir saatte 30 parça, L makinesi bir saatte 36 parça üretmektedir.","K makinesi ilk 30 dakika çalışıp 30 dakika dinlenir, sonrasında her 40 dakikalık çalışma sonrası 10 dakika dinlenir.","L makinesi 20 dakika çalışıp 15 dakika dinlenir."]},"beginTime":1212,"endTime":1298,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=1212&ask_summarization=1"},{"index":13,"title":"Makine Çalışma Süreleri Hesaplama","list":{"type":"unordered","items":["K makinesi 180 dakikalık süreçte toplam 130 dakika çalışarak 65 parça üretir.","L makinesi 180 dakikalık süreçte toplam 105 dakika çalışarak 63 parça üretir.","İki makine birlikte 3 saatte toplam 128 parça üretir."]},"beginTime":1298,"endTime":1536,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=1298&ask_summarization=1"},{"index":14,"title":"İşçi Problemi Çözümü","list":{"type":"unordered","items":["Eşit güçte bir grup işçi bir iş anlaşması yapıyor ve işin başlangıç gününden itibaren her akşam üç işçi işten ayrıldığını söylüyor.","Sadece sondan bir önceki iş gününde kimse işten ayrılmıyor ve iş, anlaşmaya göre bitmesi gereken günden üç gün geç, sekiz günde tamamlanıyor.","Beş günde bitmesi gereken iş sekiz günde bitiyor çünkü sürekli işçilere ayrılma oluyor."]},"beginTime":1546,"endTime":1616,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=1546&ask_summarization=1"},{"index":15,"title":"Matematiksel Çözüm Süreci","list":{"type":"unordered","items":["Her gün çalışan işçi sayısı ve çalışılan süre (v) ile iş miktarı hesaplanıyor: 1. gün xv, 2. gün (x-3)v, 3. gün (x-6)v şeklinde devam ediyor.","Sondan bir önceki iş gününde kimse işten ayrılmıyor, bu nedenle 7. ve 8. günlerde (x-18)v çalışılıyor.","Denklem kurularak x değeri 27 olarak bulunuyor, yani toplam 27 işçi var."]},"beginTime":1616,"endTime":1764,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=1616&ask_summarization=1"},{"index":16,"title":"Orantı Hesaplama ve Sonuç","list":{"type":"unordered","items":["27 işçi işi 5 günde bitirecek şekilde anlaşılıyor.","15 işçi için ters orantı kullanılarak hesaplama yapılıyor: 27x5 = 15xg, g = 9 bulunuyor.","15 işçi işi 9 günde bitirecek."]},"beginTime":1764,"endTime":1803,"href":"/video/preview/80939882727490660?parent-reqid=1773394994742945-2002119638114997001-balancer-l7leveler-kubr-yp-klg-313-BAL&text=ersenbey321&t=1764&ask_summarization=1"},{"index":17,"title":"Dersin Sonu ve Gelecek Konular","list":{"type":"unordered","items":["İşçi problemlerinin çözümü tamamlanıyor ve öğrencilere diğer soruları da çözmeleri isteniyor.","Bir sonraki konu hız problemleri olacak.","Öğrencilere takvim sayfasını açmaları ve rehber sorularını göndermeleri 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