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Monday, March 31, 2008

Article on DBA Interviews - SQL Server Central dot com

I was just looking through the session list at PASS this year and I noticed something a little different. There are professional development tracks. These are sessions on how to be a successful DBA, change management, etc. Personally, I'm really glad to see that someone is finally taking some interest in helping DBAs in areas other than just technical. Don't get me wrong, plenty of us could still use plenty of help in that area (more on that in a minute), but there's really more to being a good DBA than just sitting in your cube with the lights out watching Spotlight with a bottle of lotion in one hand, and a Kleenex in the other.

Today's DBAs are expected to give presentations to management, teach users, make recommendations based off of business requirements (not just technical), and be a shoulder to cry on when someone loses data. This is a huge responsibility and I urge a lot of you to take advantage of some of these sessions. I'll be there.

On the other side… it's time for a little fun. I promised you to talk about getting help in the technical area, so here it is. I'm in the process of finding another DBA and I recently finished another round of interviewing. Here are some of the answers I got from my esteemed interviewees. I'm not going to give you the correct answers, but compare your answers with theirs, and if you answer the same, similarly, or can't see why the answer is wrong, SEEK HELP RIGHT AWAY!! Ok, here goes:


Q: What is TempDB?

A: The database used for guest accounts. You give a guest user access to TempDB so that he can have access to your system without having rights to anything he could harm.

Experience: This DBA has 10yrs in a production environment.


Q: What's the different between char() and varchar()?

A: char() only holds letters while varchar() holds letters and numbers.

Experience: This DBA has 8yrs.


Q: What's the different between char() and varchar()?

A: char() only holds 1 character while varchar() holds as many as you like.

Experience: This DBA has 12yrs and considers himself an expert in writing SPs.


Q: What is fill factor?

A: Fill factor controls the size of the transaction log. The higher the fill factor, the longer the system waits to checkpoint.

Experience: This DBA has 12yrs and considers himself an expert in writing SPs.


Q: What is checkpointing?

A: Checkpointing is the point at which the system checks to see if the transaction log needs to be truncated.

Experience: This DBA has 12yrs and considers himself an expert in writing SPs.


Q: How much memory does SQL use on startup?

A: That's a trick question because SQL doesn't use memory, it stores its information on disk (I guess he got me on that one).

Experience: This DBA has 5yrs.


Q: What is an acceptable disk queue?

A: 15%.

Experience: This DBA has 10yrs in a production environment.


Q: What's a page fault?

A: A corrupt data page caused by trying to write something you shouldn't like writing int to varchar().

Experience: This DBA has 10yrs in a production environment.


Q: OK, then how do you fix a page fault?

A: I forget the name of it, but there's a DBCC for that.

Experience: This DBA has 10yrs in a production environment.


Q: What's the difference between a full and a differential backup?

A: A full backup fills up the tape, and a differential is different because it removes the data it doesn't really need to save space on the tape.

Experience: This DBA has 5yrs.


Q: How do you restore a single table from a backup?

A: I think it's DBCC PartialRestore, or TableRestore… something like that.

Experience: This DBA has 5yrs.


Q: What is the model DB?

A: It isn't used at all. I usually delete it.

Experience: This DBA has 5yrs.


Q: What is a bookmark lookup?

A: It's what SQL uses to keep track of the next query it needs to run.

Experience: This DBA has 10yrs in a production environment.


Q: What's the difference between delete and truncate?

A: Delete gets rid of the rows in the table for good, and truncate copies them all to a history table first in case you need to get them back.

Experience: This DBA has 10yrs in a production environment.


OK, that was fun. Unfortunately, all of those answers truly did come from candidates with the experience listed. I only wish I could make up fiction like that. The sad part is a lot of these guys are senior level DBAs in very important companies, and if I were to reveal which ones, you would pull your bank accounts, trade in your cell phones, sell your stocks, and shred your credit cards. It's honestly scary the complete incompetence of the people in charge of some of the most important aspects of our lives.

It's very discouraging when a guy who works in a very high transaction environment who claims to do conflict resolution several times a day, can't even tell me what a deadlock is. And this same DBA has never even heard of sp_lock. How is that even possible? I am, of course, just ranting now, but come on guys… pick up a book. We live in an age where information has never been more available than it is right now. When I started doing DBs there weren't that many books, and DBAs didn't part with information very easily. You had to learn everything through trial and error, or find an obscure resource that just happened to mention something. The deeper aspects of DBs and OS systems have been revealed over and over, yet some people just refuse to pick it up. Gone are the days where you can sit on what you know and just collect a paycheck… or are they? I mean, these people are not only making a good living, they're getting job after job. We're all competing against them for every position we go for. And the problem is that the hiring managers don't know the difference.

I don't expect anyone to know everything, but when a 10yr DBA doesn't know the difference between char and varchar… come on. What am I supposed to do with that? If you forget some of the subtle nuances of SQL and have to look something up I understand that… hell, I'm in BOL almost every day looking up something… but there's a base level of knowledge that we should all have. Not knowing some of these basics is like you telling me you've been a DBA for 10yrs and you can't explain to me what SEM is used for. Anyway, that's my rant for now… does anyone have anything to add, or any other interview stories?

221 Microsoft Word Shortcuts

1
Ctrl + Shift + A
AllCaps
Makes the selection all capitals (toggle)

2
Alt + Ctrl + 1
ApplyHeading1
Applies Heading 1 style to the selected text

3
Alt + Ctrl + 2
ApplyHeading2
Applies Heading 2 style to the selected text

4
Alt + Ctrl + 3
ApplyHeading3
Applies Heading 3 style to the selected text

5
Ctrl + Shift + L
ApplyListBullet
Applies List Bullet style to the selected text

6
Alt + F10
AppMaximize
Enlarges the application window to full size

7
Alt + F5
AppRestore
Restores the application window to normal size

8
Ctrl+B
Bold
Makes the selection bold (toggle)

9
Ctrl + PgDn
BrowseNext
Jump to the next browse object

10
Ctrl + PgUp
BrowsePrev
Jump to the previous browse object

11
Alt + Ctrl + Home
BrowseSel
Select the next/prev browse object

12
Esc
Cancel
Terminates an action

13
Ctrl+E
CenterPara
Centers the paragraph between the indents

14
Shift+F3
ChangeCase
Changes the case of the letters in the selection

15
Left arrow
CharLeft
Moves the insertion point to the left one character

16
Shift + Left arrow
CharLeftExtend
Extends the selection to the left one character

17
Rt arrow
CharRight
Moves the insertion point to the right one character

18
Shift + Rt arrow
CharRightExtend
Extends the selection to the right one character

19
Alt + Shift + C
ClosePane
Closes the active window pane (if you are in Normal View and have, for example, the Footnote pane open)

20
Alt+Drag (or press Ctrl + Shift + F8 and drag, but Alt + Drag is far easier!)
ColumnSelect
Selects a columnar block of text

21
Ctrl +Shift+C
CopyFormat
Copies the formatting of the selection

22
Shift + F2
CopyText
Makes a copy of the selection without using the clipboard (press Return to paste)

23
Alt + F3
CreateAutoText
Adds an AutoText entry to the active template

24
Ctrl+ Backspace
DeleteBackWord
Deletes the previous word without putting it on the Clipboard

25
Ctrl + Del
DeleteWord
Deletes the next word without putting it on the Clipboard

26
Ctrl+W, Ctrl+F4
DocClose
Prompts to save the document and then closes the active window. (But doesn't intercept the menu command)

27
Ctrl + F10
DocMaximize
Enlarges the active window to full size

28
Ctrl + F7
DocMove
Changes the position of the active window

29
Ctrl + F5
DocRestore
Restores the window to normal size

30
Ctrl + F8
DocSize
Changes the size of the active window

31
Alt + Ctrl + S
DocSplit
Splits the active window horizontally and then adjusts the split

32
Alt + Shift + F9
DoFieldClick
Executes the action associated with macrobutton fields

33
Ctrl + Shift + D
DoubleUnderline
Double underlines the selection (toggle)

34
Alt R, G
DrawGroup
Groups the selected drawing objects

35
Alt R, I
DrawSnapToGrid
Sets up a grid for aligning drawing objects

36
Alt R, U
DrawUngroup
Ungroups the selected group of drawing objects

37
Ctrl+Shift+F5 (Or: Alt I, K)
EditBookmark
Brings up the bookmark dialog

38
Del
EditClear
Performs a forward delete or removes the selection without putting it on the Clipboard

39
Ctrl+C
EditCopy
Copies the selection and puts it on the Clipboard

40
Ctrl+X
EditCut
Cuts the selection and puts it on the Clipboard

41
Ctrl+F
EditFind
Finds the specified text or the specified formatting

42
F5, Ctrl+G
EditGoTo
Jumps to a specified place in the active document

43
Alt E, K
EditLinks
Allows links to be viewed, updated, opened, or removed

44
Ctrl+V
EditPaste
Inserts the Clipboard contents at the insertion point

45
Alt E, S
EditPasteSpecial
Inserts the Clipboard contents as a linked object, embedded object, or other format

46
Alt + Shift + Backspc
EditRedo
Redoes the last action that was undone

47
F4
EditRedoOrRepeat
Repeats the last command, or redoes the last action that was undone (unfortunately, doesn't work for as many commands in Word 2000 as in Word 97 and below, but this is still one of Word's most useful shortcuts, if not the most useful)

48
Ctrl+H
EditReplace
Finds the specified text or the specified formatting and replaces it

49
Ctrl+A
EditSelectAll
Selects the entire document

50
Ctrl+Z
EditUndo
Reverses the last action

51
Alt + PageDn (to select to end of column, use Alt + Shift + PgDn)
EndOfColumn
Moves to the last cell in the current table column

52
Ctrl+Shift+End
EndOfDocExtend
Extends the selection to the end of the last line of the document

53
Ctrl+End
EndOfDocument
Moves the insertion point to the end of the last line of the document

54
End
EndOfLine
Moves the insertion point to the end of the current line

55
Shift+End
EndOfLineExtend
Extends the selection to the end of the current line

56
Alt+End
EndOfRow
Moves to the last cell in the current row

57
Alt + Ctrl + PgDn
EndOfWindow
Moves the insertion point to the end of the last visible line on the screen

58
Shift + Alt + Ctrl + PgDn
EndOfWindowExtend
Extends the selection to the end of the last visible line on the screen

59
F8 (press Esc to turn off)
ExtendSelection
Turns on extend selection mode and then expands the selection with the direction keys

60
Alt + F4 (<9>)
FileCloseOrExit
Closes the current document, or if no documents are open, quits Word. Horrible command, as it makes it a long winded business to quit Word. But there's a simple solution - assign Alt+F4 to FileExit instead.

61
Alt + F4 (Word 97)
FileExit
Quits Microsoft Word and prompts to save the documents (does intercept the menu item, but not the keyboard shortcut, or the x button. An AutoExit macro is usually a better way of intercepting this).

62
NOT Ctrl+N!!
FileNew
Creates a new document or template (brings up the dialog). Note that: Word pretends that Ctrl+N is assigned to FileNew but it isn't, it's assigned to FileNewDefault You can fix this in Word 2000 by assigning Ctrl+N to the FileNewDialog command. In Word 97 the only way to fix it is to create a macro called FileNew (to do this, press Alt + F8, type "FileNew" without the quotes and Click "Create". The macro will automatically contain the code needed to make it work).

63
Ctrl+N
FileNewDefault
Creates a new document based on the Normal template.

64
Ctrl+O
FileOpen
Opens an existing document or template

65
Alt F, U
FilePageSetup
Changes the page setup of the selected sections

66
Ctrl + P
FilePrint
Prints the active document (brings up the dialog)

67
Ctrl+F2
FilePrintPreview
Displays full pages as they will be printed

68
Alt F, I
FileProperties
Shows the properties of the active document

69
Ctrl+S
FileSave
FileSave

70
Alt F, A (or F12)
FileSaveAs
Saves a copy of the document in a separate file (brings up the dialog)

71
Ctrl+Shift+F
Font
Activates the Fonts listbox on the formatting toolbar

72
Ctrl+Shift+P
FontSizeSelect
Activates the Font Size drop-down on the formatting toolbar

73
Alt + Ctrl + K
FormatAutoFormat
Automatically formats a document (or sometimes, automatically screws it up)

74
Alt O, B
FormatBordersAndSha ding
Changes the borders and shading of the selected paragraphs, table cells, and pictures

75
Alt O, E
FormatChangeCase
Changes the case of the letters in the selection

76
Alt O, C
FormatColumns
Changes the column format of the selected sections (brings up the dialog)

77
Alt O, D
FormatDropCap
Formats the first character of current paragraph as a dropped capital (must select it first)

78
Ctrl+D
FormatFont
Brings up the Format + Font dialog

79
Alt + Shift + R
FormatHeaderFooterL ink
Links the current header/footer to the previous section (but does not intercept the button on the Header Footer toolbar)

80
Alt O, P
FormatParagraph
Brings up the Format Paragraph dialog

81
Alt O, S
FormatStyle
Applies, creates, or modifies styles

82
Alt O, T
FormatTabs
Brings up the Format Tabs dialog

83
Shift + F5
GoBack
Returns to the previous insertion point (goes back to up to 3 points, then returns to where you started; this is one of the most useful shortcuts of them all. Also useful when opening a document, if you want to g straight to where you were last editing it)

84
Ctrl + >
GrowFont
Increases the font size of the selection

85
Ctrl + ]
GrowFontOnePoint
Increases the font size of the selection by one point

86
Ctrl + T (or drag the ruler)
HangingIndent
Increases the hanging indent

87
F1
Help
Microsoft Word Help

88
Shift + F1
HelpTool
Lets you get help on a command or screen region or examine text properties

89
Ctrl + Shift + H
Hidden
Makes the selection hidden text (toggle)

90
Click on it
HyperlinkOpen
Connect to a hyperlink's address

91
Ctrl + M (or drag the ruler)
Indent
Moves the left indent to the next tab stop

92
Alt + Ctrl + M (or Alt I, M)
InsertAnnotation
Inserts a comment

93
F3
InsertAutoText
Replaces the name of the AutoText entry with its contents

94
Alt I, B
InsertBreak
Ends a page, column, or section at the insertion point

95
Alt I, C
InsertCaption
Inserts a caption above or below a selected object

96
Ctrl + Shift + Return
InsertColumnBreak
Inserts a column break at the insertion point

97
Alt + Shift + D
InsertDateField
Inserts a date field

98
Alt + Ctrl + D
InsertEndnoteNow
Inserts an endnote reference at the insertion point without displaying the dialog

99
Alt I, F
InsertField
Inserts a field in the active document

100
Ctrl+F9
InsertFieldChars
Inserts an empty field with the enclosing field characters

101
Alt I, L
InsertFile
Inserts the text of another file into the active document

102
Alt I, N
InsertFootnote
Inserts a footnote or endnote reference at the insertion point

103
Alt + Ctrl + F
InsertFootnoteNow
Inserts a footnote reference at the insertion point without displaying the dialog

104
Ctrl + K
InsertHyperlink
Insert Hyperlink

105
Alt I, D
InsertIndexAndTable s
Inserts an index or a table of contents, figures, or authorities into the document

106
Alt + Ctrl + L
InsertListNumField
Inserts a ListNum Field

107
Alt + Shift + F
InsertMergeField
Brings up a dialog to insert a mail merge field at the insertion point. (It does not intercept the button on the Mail merge. toolbar)

108
Ctrl + Return
InsertPageBreak
Inserts a page break at the insertion point

109
Alt + Shift + P
InsertPageField
Inserts a page number field

110
Ctrl + Shift + F3
InsertSpike
Empties the spike AutoText entry and inserts all of its contents into the document

111
Alt + Shift + T
InsertTimeField
Inserts a time field

112
Ctrl + I
Italic
Makes the selection italic (toggle)

113
Ctrl + J
JustifyPara
Aligns the paragraph at both the left and the right indent

114
Ctrl + L
LeftPara
Aligns the paragraph at the left indent

115
Down arrow
LineDown
Moves the insertion point down one line

116
Shift + down arrow
LineDownExtend
Extends the selection down one line

117
Up arrow
LineUp
Moves the insertion point up one line

118
Shift + up arrow
LineUpExtend
Extends the selection up one line

119
Ctrl + F11
LockFields
Locks the selected fields to prevent updating

120
Alt + Shift + K
MailMergeCheck
Checks for errors in a mail merge

121
Alt+Shift+E
MailMergeEditDataSo urce
Lets you edit a mail merge data source

122
Alt + Shift + N
MailMergeToDoc
Collects the results of the mail merge in a document

123
Alt Shift + M
MailMergeToPrinter
Sends the results of the mail merge to the printer

124
Alt + Shift + I
MarkCitation
Marks the text you want to include in the table of authorities

125
Alt + Shift + X
MarkIndexEntry
Marks the text you want to include in the index

126
Alt + Shift + O
MarkTableOfContents Entry
Inserts a TC field (but it is far better to use Heading Styles to generate your Table of Contents instead)

127
Alt or F10
MenuMode
Makes the menu bar active

128
Alt + Shift + F11
MicrosoftScriptEdit or
Starts or switches to Microsoft Development Environment application, allowing you to view the HTML/XML source code that would be behind the document if it were in ..htm format (or that is behind it if it already is in .htm format).

129
Alt + Ctrl + F1
MicrosoftSystemInfo
Execute the Microsoft System Info application

130
F2
MoveText
Moves the selection to a specified location without using the clipboard (press Return to execute the more)

131
Tab
NextCell
Moves to the next table cell

132
F11
NextField
Moves to the next field

133
Alt + F7
NextMisspelling
Find next spelling error

134
Alt + down arrow
NextObject
Moves to the next object on the page

135
Ctrl + F6
NextWindow
Switches to the next document window, equivalent to selecting a document from the Window menu.

136
Ctrl+Shift+N
NormalStyle
Applies the Normal style

137
Ctrl + 0
OpenOrCloseUpPara
Sets or removes extra spacing above the selected paragraph

138
F6
OtherPane
Switches to another window pane in Normal View (for instance, if you have if you have a Footnotes pane open in Normal view and want to switch to the main document and back without closing the pane).

139
Alt + _
OutlineCollapse
Collapses an Outline in Outline View by one level

140
Alt+Shift+rt arrow
OutlineDemote
Demotes the selected paragraphs one heading level

141
Alt + +
OutlineExpand
Expands an Outline in Outline View by one level

142
Alt+Shift+down arrow
OutlineMoveDown
Moves the selection below the next item in the outline

143
Alt+Shift+up arrow
OutlineMoveUp
Moves the selection above the previous item in the outline

144
Alt+Shift+left arrow
OutlinePromote
Promotes the selected paragraphs one heading level

145
Alt + Shift + L
OutlineShowFirstLin e
Toggles between showing the first line of each paragraph only or showing all of the body text in the outline

146
Ins
Overtype
Toggles the typing mode between replacing and inserting

147
PgDn
PageDown
Moves the insertion point and document display to the next screen of text

148
Shift+ PgDn
PageDownExtend
Extends the selection and changes the document display to the next screen of text

149
PgUp
PageUp
Moves the insertion point and document display to the previous screen of text

150
Shift + PgUp
PageUpExtend
Extends the selection and changes the document display to the previous screen of text

151
Ctrl + down arrow
ParaDown
Moves the insertion point to the beginning of the next paragraph

152
Shift + Ctrl + down arrow
ParaDownExtend
Extends the selection to the beginning of the next paragraph

153
Ctrl + up arrow
ParaUp
Moves the insertion point to the beginning of the previous paragraph

154
Shift + Ctrl + up arrow
ParaUpExtend
Extends the selection to the beginning of the previous paragraph

155
Ctrl+Shift+V
PasteFormat
Applies the previously copied formatting to selection

156
Shift + Tab
PrevCell
Moves to the previous table cell

157
Shift + F11
PrevField
Moves to the previous field

158
Alt + up arrow
PrevObject
Moves to the previous object on the page

159
Ctrl + Shift + F6
PrevWindow
Switches back to the previous document window

160
Sfift+F4
RepeatFind
Repeats Go To or Find to find the next occurrence

161
Ctrl+Spacebar
ResetChar
Makes the selection the default character format of the applied style

162
Ctrl+Q
ResetPara
Makes the selection the default paragraph format of the applied style

163
Ctrl +R
RightPara
Aligns the paragraph at the right indent

164
Ctrl + *
ShowAll
Shows/hides all nonprinting characters

165
Alt + Shift + A
ShowAllHeadings
Displays all of the heading levels and the body text in Outline View

166
Ctrl + <>

Vedic Maths (Truely amazing)

Use the formula ALL FROM 9 AND THE LAST FROM 10 to perform instant subtractions.

  • For example 1000 - 357 = 643

We simply take each figure in 357 from 9 and the last figure from 10.

So the answer is 1000 - 357 = 643

And thats all there is to it!

This always works for subtractions from numbers consisting of a 1 followed by noughts: 100; 1000; 10,000 etc.

  • Similarly 10,000 - 1049 = 8951
  • For 1000 - 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 83 is 083.

So 1000 - 83 becomes 1000 - 083 = 917



Try some yourself:

1) 1000 - 777

=

2) 1000 - 283

=

3) 1000 - 505

=

4) 10,000 - 2345

=

5) 10000 - 9876

=

6) 10,000 - 1101

=

7) 100 - 57

=

8) 1000 - 57

=

9) 10,000 - 321

=

10) 10,000 - 38

=

Total Correct

=


Tutorial 2

Using VERTICALLY AND CROSSWISE you do not need to the multiplication tables beyond 5 X 5.

  • Suppose you need 8 x 7

8 is 2 below 10 and 7 is 3 below 10.
Think of it like this:

The answer is 56.
The diagram below shows how you get it.

You subtract crosswise 8-3 or 7 - 2 to get 5,
the first figure of the answer.
And you multiply vertically: 2 x 3 to get 6,
the last figure of the answer.

That's all you do:

See how far the numbers are below 10, subtract one
number's deficiency from the other number, and
multiply the deficiencies together.

  • 7 x 6 = 42

    Here there is a carry: the 1 in the 12 goes over to make 3 into 4.



Multply These:

1) 8
8 x

2) 9
7 x

3) 8
9 x

4) 7
7 x

5) 9
9 x

6) 6
6 x

Total Correct =

Here's how to use VERTICALLY AND CROSSWISE for multiplying numbers close to 100.

  • Suppose you want to multiply 88 by 98.

Not easy,you might think. But with
VERTICALLY AND CROSSWISE you can give
the answer immediately, using the same method
as above.

Both 88 and 98 are close to 100.
88 is 12 below 100 and 98 is 2 below 100.

You can imagine the sum set out like this:

As before the 86 comes from
subtracting crosswise: 88 - 2 = 86
(or 98 - 12 = 86: you can subtract
either way, you will always get
the same answer).
And the 24 in the answer is
just 12 x 2: you multiply vertically.
So 88 x 98 = 8624

This is so easy it is just mental arithmetic.



Try some:

1) 87
98 x

2) 88
97 x

3) 77
98 x

4) 93
96 x

5) 94
92 x

6) 64
99

7) 98
97 x

Total Correct =

Multiplying numbers just over 100.

  • 103 x 104 = 10712

The answer is in two parts: 107 and 12,
107 is just 103 + 4 (or 104 + 3),
and 12 is just 3 x 4.

  • Similarly 107 x 106 = 11342

107 + 6 = 113 and 7 x 6 = 42

Again, just for mental arithmetic



Try a few:

1) 102 x 107 =

1) 106 x 103 =

1) 104 x 104 =

4) 109 x 108 =

5) 101 x123 =

6) 103 x102 =

Total Correct =


Tutorial 3

The easy way to add and subtract fractions.

Use VERTICALLY AND CROSSWISE to write the answer straight down!

Multiply crosswise and add to get the top of the answer:
2 x 5 = 10 and 1 x 3 = 3. Then 10 + 3 = 13.
The bottom of the fraction is just 3 x 5 = 15.
You multiply the bottom number together.

So:

Subtracting is just as easy: multiply crosswise as before, but the subtract:



Try a few:







Total Correct =


Tutorial 4

A quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE.

  • 752 = 5625

752 means 75 x 75.
The answer is in two parts: 56 and 25.
The last part is always 25.
The first part is the first number, 7, multiplied by the number "one more", which is 8:
so 7 x 8 = 56

  • Similarly 852 = 7225 because 8 x 9 = 72.



Try these:

1) 452 =

2) 652 =

3) 952 =

4) 352 =

5) 152 =

Total Correct =

Method for multiplying numbers where the first figures are the same and the last figures add up to 10.

  • 32 x 38 = 1216

Both numbers here start with 3 and the last
figures (2 and 8) add up to 10.

So we just multiply 3 by 4 (the next number up)
to get 12 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 to
get the last part of the answer.

Diagrammatically:

  • And 81 x 89 = 7209

We put 09 since we need two figures as in all the other examples.



Practise some:

1) 43 x 47 =

2) 24 x 26 =

3) 62 x 68 =

4) 17 x 13 =

5) 59 x 51 =

6) 77 x 73 =

Total Correct =


Tutorial 5

An elegant way of multiplying numbers using a simple pattern.

  • 21 x 23 = 483

This is normally called long multiplication but
actually the answer can be written straight down
using the VERTICALLY AND CROSSWISE
formula.

We first put, or imagine, 23 below 21:

There are 3 steps:

a) Multiply vertically on the left: 2 x 2 = 4.
This gives the first figure of the answer.
b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8
This gives the middle figure.
c) Multiply vertically on the right: 1 x 3 = 3
This gives the last figure of the answer.

And thats all there is to it.

  • Similarly 61 x 31 = 1891

  • 6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1



Try these, just write down the answer:

1) 14
21 x

2) 22
31 x

3) 21
31 x

4) 21
22 x

5) 32
21 x

Total Correct =

Multiply any 2-figure numbers together by mere mental arithmetic!

If you want 21 stamps at 26 pence each you can
easily find the total price in your head.

There were no carries in the method given above.
However, there only involve one small extra step.

  • 21 x 26 = 546

The method is the same as above
except that we get a 2-figure number, 14, in the
middle step, so the 1 is carried over to the left
(4 becomes 5).

So 21 stamps cost �5.46.



Practise a few:

1) 21
47 x

2) 23
43 x

3) 32
53 x

4) 42
32 x

5) 71
72 x

Total Correct =

  • 33 x 44 = 1452

There may be more than one carry in a sum:

Vertically on the left we get 12.
Crosswise gives us 24, so we carry 2 to the left
and mentally get 144.

Then vertically on the right we get 12 and the 1
here is carried over to the 144 to make 1452.



6) 32
56 x

7) 32
54 x

8) 31
72 x

9) 44
53 x

10) 54
64 x

Total Correct =

Any two numbers, no matter how big, can be
multiplied in one line by this method.


Tutorial 6

Multiplying a number by 11.

To multiply any 2-figure number by 11 we just put
the total of the two figures between the 2 figures.

  • 26 x 11 = 286

Notice that the outer figures in 286 are the 26
being multiplied.

And the middle figure is just 2 and 6 added up.

  • So 72 x 11 = 792



Multiply by 11:

1) 43 =

2) 81 =

3) 15 =

4) 44 =

5) 11 =

Total Correct =

  • 77 x 11 = 847

This involves a carry figure because 7 + 7 = 14
we get 77 x 11 = 7147 = 847.



Multiply by 11:

1) 88 =

2) 84 =

3) 48 =

4) 73 =

5) 56 =

Total Correct =

  • 234 x 11 = 2574

We put the 2 and the 4 at the ends.
We add the first pair 2 + 3 = 5.
and we add the last pair: 3 + 4 = 7.



Multiply by 11:

1) 151 =

2) 527 =

3) 333 =

4) 714 =

5) 909 =

Total Correct =


Tutorial 7

Method for diving by 9.

  • 23 / 9 = 2 remainder 5

The first figure of 23 is 2, and this is the answer.
The remainder is just 2 and 3 added up!

  • 43 / 9 = 4 remainder 7

The first figure 4 is the answer
and 4 + 3 = 7 is the remainder - could it be easier?



Divide by 9:

1) 61 = remainder

2) 33 = remainder

3) 44 = remainder

4) 53 = remainder

5) 80 = remainder

Total Correct =

  • 134 / 9 = 14 remainder 8

The answer consists of 1,4 and 8.
1 is just the first figure of 134.
4 is the total of the first two figures 1+ 3 = 4,
and 8 is the total of all three figures 1+ 3 + 4 = 8.



Divide by 9:

6) 232 = remainder

7) 151 = remainder

8) 303 = remainder

9) 212 = remainder

10) 2121 = remainder

Total Correct =

  • 842 / 9 = 812 remainder 14 = 92 remainder 14

Actually a remainder of 9 or more is not usually
permitted because we are trying to find how
many 9's there are in 842.

Since the remainder, 14 has one more 9 with 5
left over the final answer will be 93 remainder 5



Divide these by 9:

1) 771 = remainder

2) 942 = remainder

3) 565 = remainder

4) 555 = remainder

5) 777 = remainder

6) 2382 = remainder

7) 7070 = remainder

Total Correct =