| 1. |
info: 2025-04-26 02:00:08.935 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
19ms [Parameters=[@p7='dd6a514a-ffbf-47e1-b14a-bf190dc4bf0d', @p0='True', @p1='False', @p2='0', @p3='479fb8e8-454a-4c6a-b48d-8f4a19f12360', @p4='86.jpg' (Size = 100), @p5='https://knowledgenest.blob.core.windows.net/scanners/0/[Matematika][Matematika visiems 6 klasė][Vadovėlis 1 dalis]/pages/86.jpg' (Size = 1000), @p6='""
### 5.2.2. Taikome skirstomumo dėsnį
Apskaičiuokime reiškinio (−2/3 + 1/6) · (-3) reikšmę dviem būdais:
1) veiksmus atlikdami iš eilės:
(−2/3 + 1/6) · (-3) = (−4/6 + 1/6) · (-3) = -3/6 · (-3) = -1/2 · (-3) = 3/2 = 1 1/2;
2) pirmiausia iš -3 padauginkime kiekvieną dėmenį atskirai, o tada gautas sandaugas sudėkime:
(−2/3 + 1/6) · (-3) = (-2/3) · (-3) + (1/6) · (-3) = 2 + (-1/2) = 1 1/2.
Pastebėkime, kad abiem atvejais rezultatas nepakito.
Taigi, veiksmams su teigiamaisiais ir neigiamaisiais skaičiais galioja daugybos skirstomumo dėsnis:
(a + b) · c = a · c + b · c, (a - b) · c = a · c - b · c.
Sakome, kad reiškinį (a + b) · c arba (a - b) · c atskliautėme.
Pavyzdžiui: (-2,5 - 3) · 4 = -2,5 · 4 - 3 · 4 = -10 - 12 = -22.
Daugybos skirstomumo dėsnį galima užrašyti ir atvirkščia tvarka:
a · c + b · c = (a + b) · c, a · c - b · c = (a - b) · c.
Tuomet sakome, kad bendrąjį dauginamąjį iškėlėme už skliaustų.
Bendrąjį dauginamąjį galima iškelti ir prieš skliaustus.
Pavyzdžiui, apskaičiuokime iškeldami bendrąjį dauginamąjį prieš skliaustus:
-5 · 3 + 7 · (-5) = -5 · (3 + 7) = -5 · 10 = -50;
-5 · 3 - 7 · (-5) = -5 · (3 - 7) = -5 · (-4) = 20;
5 · (-3) + 7 · 5 = 5 · (-3 + 7) = 5 · 4 = 20;
5 · (-3) - 7 · 5 = 5 · (-3 - 7) = 5 · (-10) = -50;
5 · 3 + 7 · (-5) = 5 · (3 + (-7)) = 5 · (3 - 7) = 5 · (-4) = -20;
5 · 3 - 7 · (-5) = 5 · (3 - (-7)) = 5 · (3 + 7) = 5 · 10 = 50.
---
Ar teisingai apskaičiuota duoto reiškinio reikšmė?
Jei ne, tai pasvarstykite, kur padaryta klaida, o tada apskaičiuokite teisingai.
a) 4 · 3 + 6 · (-3) = 3 · (4 + 6) = 3 · 10 = 30;
b) 4 · 3 - 6 · (-3) = 3 · (4 - 6) = 3 · (-2) = -6.
1. Reiškinio (2/3 - 1/6) · (-6) reikšmė lygi:
A -3 B -1/3 C 1/3 D 3
2. Skaičiuojant reiškinio reikšmę, padaryta klaidų. Ištaisykite jas.
a) -2 · 9 + 6 · (-2) = -2 · (9 + 6) = -2 · 15 = -30;
b) 7 · 4 + 3 · (-7) = 7 · (4 + 3) = 7 · 7 = 49.
3. Sudauginkite taikydami daugybos skirstomumo dėsnį.
a) (1/8 - 3/4) · (-4);
b) (-7,2 + 5,8) · (-5);
c) 6 · (-2 1/2 - 1 2/3).
4. Apskaičiuokite iškeldami bendrąjį dauginamąjį prieš skliaustus.
a) -3 · 18 + 22 · (-3);
b) 7 · 24 + 26 · (-7);
c) 23 · (-6) - 17 · 6.
""' (Size = 4000)], CommandType='Text', CommandTimeout='30']
SET IMPLICIT_TRANSACTIONS OFF;
SET NOCOUNT ON;
UPDATE [ScannerPages] SET [Active] = @p0, [Deleted] = @p1, [Position] = @p2, [ScannerId] = @p3, [StorageMediaName] = @p4, [StorageMediaUrl] = @p5, [Text] = @p6
OUTPUT 1
WHERE [Id] = @p7;
|
| 2. |
info: 2025-04-26 02:00:11.413 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
2ms [Parameters=[@__id_0='457f3cae-6ab4-c087-3a7a-f64ec670c3bc', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [c].[Id], [c].[Active], [c].[Deleted], [c].[Description], [c].[DescriptionBackup], [c].[Left], [c].[ParentId], [c].[Position], [c].[ProcessorGenerateImagePrompt], [c].[Right], [c].[SiteId], [c].[StorageMediaName], [c].[StorageMediaUrl], [c].[Title], [c].[TitleBackup], [c].[TitleSlug], [c].[TotalChildren], [c].[TotalScanners], [c].[TotalYoutubeVideos]
FROM [Categories] AS [c] WITH (NOLOCK)
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id]
|
| 3. |
info: 2025-04-26 02:00:11.430 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
17ms [Parameters=[@__id_0='457f3cae-6ab4-c087-3a7a-f64ec670c3bc', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [c4].[Id], [c4].[Active], [c4].[Deleted], [c4].[Description], [c4].[DescriptionBackup], [c4].[Left], [c4].[ParentId], [c4].[Position], [c4].[ProcessorGenerateImagePrompt], [c4].[Right], [c4].[SiteId], [c4].[StorageMediaName], [c4].[StorageMediaUrl], [c4].[Title], [c4].[TitleBackup], [c4].[TitleSlug], [c4].[TotalChildren], [c4].[TotalScanners], [c4].[TotalYoutubeVideos], [c].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c0].[Id], [c0].[Active], [c0].[Deleted], [c0].[Description], [c0].[DescriptionBackup], [c0].[Left], [c0].[ParentId], [c0].[Position], [c0].[ProcessorGenerateImagePrompt], [c0].[Right], [c0].[SiteId], [c0].[StorageMediaName], [c0].[StorageMediaUrl], [c0].[Title], [c0].[TitleBackup], [c0].[TitleSlug], [c0].[TotalChildren], [c0].[TotalScanners], [c0].[TotalYoutubeVideos]
FROM [Categories] AS [c0] WITH (NOLOCK)
WHERE [c0].[Active] = CAST(1 AS bit) AND [c0].[Deleted] = CAST(0 AS bit)
) AS [c4] ON [c].[Id] = [c4].[ParentId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [c4].[Position], [c4].[Id]
|
| 4. |
info: 2025-04-26 02:00:11.450 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
9ms [Parameters=[@__id_0='457f3cae-6ab4-c087-3a7a-f64ec670c3bc', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [s5].[ScannerId], [s5].[CategoryId], [s5].[Id], [s5].[Active], [s5].[CheatSheet], [s5].[CheatSheet2], [s5].[Deleted], [s5].[FactErrors], [s5].[FactErrorsExplanation], [s5].[ParentCategory2Id], [s5].[ParentCategoryId], [s5].[ProcessorGenerateImagePrompt], [s5].[Prompt], [s5].[Reference], [s5].[ReferenceSlug], [s5].[SiteId], [s5].[SpellingErrors], [s5].[SpellingErrorsExplanation], [s5].[Summary], [s5].[Title], [s5].[TitleBackup], [s5].[TitleSlug], [s5].[TotalCards], [s5].[TotalCards2], [s5].[TotalCategories], [s5].[TotalPages], [s5].[Verified], [c].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c3].[ScannerId], [c3].[CategoryId], [s1].[Id], [s1].[Active], [s1].[CheatSheet], [s1].[CheatSheet2], [s1].[Deleted], [s1].[FactErrors], [s1].[FactErrorsExplanation], [s1].[ParentCategory2Id], [s1].[ParentCategoryId], [s1].[ProcessorGenerateImagePrompt], [s1].[Prompt], [s1].[Reference], [s1].[ReferenceSlug], [s1].[SiteId], [s1].[SpellingErrors], [s1].[SpellingErrorsExplanation], [s1].[Summary], [s1].[Title], [s1].[TitleBackup], [s1].[TitleSlug], [s1].[TotalCards], [s1].[TotalCards2], [s1].[TotalCategories], [s1].[TotalPages], [s1].[Verified]
FROM [CategoryScanners] AS [c3]
INNER JOIN [Scanners] AS [s1] ON [c3].[ScannerId] = [s1].[Id]
WHERE [s1].[Active] = CAST(1 AS bit) AND [s1].[Deleted] = CAST(0 AS bit)
) AS [s5] ON [c].[Id] = [s5].[CategoryId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [s5].[Id], [s5].[ScannerId], [s5].[CategoryId]
|
| 5. |
info: 2025-04-26 02:00:11.459 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
8ms [Parameters=[@__id_0='457f3cae-6ab4-c087-3a7a-f64ec670c3bc', @__site_Id_1='63d6eb4e-8e39-4ac6-8f69-55ee76feccce'], CommandType='Text', CommandTimeout='30']
SELECT [s6].[Id], [s6].[Active], [s6].[Context], [s6].[ContextBackup], [s6].[ContextStorageMediaName], [s6].[ContextStorageMediaUrl], [s6].[Deleted], [s6].[FactErrors], [s6].[FactErrorsExplanation], [s6].[Facts], [s6].[FactsBackup], [s6].[FactsStorageMediaName], [s6].[FactsStorageMediaUrl], [s6].[Position], [s6].[ProcessorGenerateImagePrompt], [s6].[Prompt], [s6].[ScannerId], [s6].[SpellingErrors], [s6].[SpellingErrorsExplanation], [s6].[StorageMediaName], [s6].[StorageMediaUrl], [s6].[Summary], [s6].[SummaryBackup], [s6].[SummaryStorageMediaName], [s6].[SummaryStorageMediaUrl], [s6].[Title], [s6].[TitleSlug], [s6].[TotalFillTheBlankSelectionQuestions], [s6].[TotalMultipleSelectionQuestions], [s6].[TotalOrderingQuestions], [s6].[TotalQuestionPoints], [s6].[TotalQuestions], [s6].[TotalShortAnswerQuestions], [s6].[TotalSingleSelectionQuestions], [s6].[TotalSources], [s6].[TotalTrueFalseQuestions], [s6].[Verified], [s6].[Version], [c].[Id], [s5].[ScannerId], [s5].[CategoryId], [s5].[Id]
FROM [Categories] AS [c] WITH (NOLOCK)
INNER JOIN (
SELECT [c3].[ScannerId], [c3].[CategoryId], [s1].[Id]
FROM [CategoryScanners] AS [c3]
INNER JOIN [Scanners] AS [s1] ON [c3].[ScannerId] = [s1].[Id]
WHERE [s1].[Active] = CAST(1 AS bit) AND [s1].[Deleted] = CAST(0 AS bit)
) AS [s5] ON [c].[Id] = [s5].[CategoryId]
INNER JOIN (
SELECT [s2].[Id], [s2].[Active], [s2].[Context], [s2].[ContextBackup], [s2].[ContextStorageMediaName], [s2].[ContextStorageMediaUrl], [s2].[Deleted], [s2].[FactErrors], [s2].[FactErrorsExplanation], [s2].[Facts], [s2].[FactsBackup], [s2].[FactsStorageMediaName], [s2].[FactsStorageMediaUrl], [s2].[Position], [s2].[ProcessorGenerateImagePrompt], [s2].[Prompt], [s2].[ScannerId], [s2].[SpellingErrors], [s2].[SpellingErrorsExplanation], [s2].[StorageMediaName], [s2].[StorageMediaUrl], [s2].[Summary], [s2].[SummaryBackup], [s2].[SummaryStorageMediaName], [s2].[SummaryStorageMediaUrl], [s2].[Title], [s2].[TitleSlug], [s2].[TotalFillTheBlankSelectionQuestions], [s2].[TotalMultipleSelectionQuestions], [s2].[TotalOrderingQuestions], [s2].[TotalQuestionPoints], [s2].[TotalQuestions], [s2].[TotalShortAnswerQuestions], [s2].[TotalSingleSelectionQuestions], [s2].[TotalSources], [s2].[TotalTrueFalseQuestions], [s2].[Verified], [s2].[Version]
FROM [ScannerCards] AS [s2]
WHERE [s2].[Active] = CAST(1 AS bit) AND [s2].[Deleted] = CAST(0 AS bit)
) AS [s6] ON [s5].[Id] = [s6].[ScannerId]
WHERE [c].[Id] = @__id_0 AND [c].[SiteId] = @__site_Id_1 AND [c].[Active] = CAST(1 AS bit) AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Id], [s5].[Id], [s5].[ScannerId], [s5].[CategoryId], [s6].[TitleSlug], [s6].[Id]
|
| 6. |
info: 2025-04-26 02:00:11.802 RelationalEventId.CommandExecuted[20101] (Microsoft.EntityFrameworkCore.Database.Command)
8ms [Parameters=[@__site_Id_0='63d6eb4e-8e39-4ac6-8f69-55ee76feccce', @__item_Left_1='4428', @__item_Right_2='4429'], CommandType='Text', CommandTimeout='30']
SELECT [c].[Id], [c].[Active], [c].[Deleted], [c].[Description], [c].[DescriptionBackup], [c].[Left], [c].[ParentId], [c].[Position], [c].[ProcessorGenerateImagePrompt], [c].[Right], [c].[SiteId], [c].[StorageMediaName], [c].[StorageMediaUrl], [c].[Title], [c].[TitleBackup], [c].[TitleSlug], [c].[TotalChildren], [c].[TotalScanners], [c].[TotalYoutubeVideos]
FROM [Categories] AS [c] WITH (NOLOCK)
WHERE [c].[SiteId] = @__site_Id_0 AND [c].[Left] <= @__item_Left_1 AND [c].[Right] >= @__item_Right_2 AND [c].[Deleted] = CAST(0 AS bit)
ORDER BY [c].[Left]
|
| 63 ms |
