Math Workshop Klang
Transcript of Math Workshop Klang
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COMPLEMENTS
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Complements
In the number system there are only
nine numbers and a zero. With thesewe can display all multiplicity. In
counting, once we are past the number
ten then the numbers repeatthemselves
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Complements
The simple formula relates anynumber to the next base of ten above.
For example, with the number 86, thenearest base of ten which is more than86 is 100.
86 is 14 less than 100. 14 is called thecomplement of 86.
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Complements
Example 1
To obtain the
complement of 783
we take each of the
digits from 9 and the
last from ten
Complement is 217
783
217
7 from 9 =2
8 from 9 =1
3 from 10 = 7
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Complements
Example 2
503700496300
5 from 9 = 40 from 9 = 9
3 from 9 = 6
7 from 10 = 3The final noughts are
brought straight down.
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Complements
Example 2 : Complement of 743
Example 3 : Complement of 8532
Example 4 : Complement of 70843
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Exercise 112/17/2012Infinite Learning Academy
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No Question Answer
1 87
2 94
3 36
4 42
5 886 75
7 903
8 1340
9 3564
10 8004
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No Question Answer
1 87 13
2 94 06
3 36 64
4 42 58
5 88 126 75 25
7 903 097
8 1340 8660
9 3564 6436
10 8004 1996
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Using Complement inCalculation
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Using Complement inCalculation
What we want to do is to convert BIG no
to SMALL no and do arithmetic operationon it.
For example 1000 - 643= 357
We simply take each figure in 357 from 9and the last figure from 10.
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Using Complement inCalculation
Example 2
Similarly 1000 - 649 = 351
1000 - 6 4 9
| | |3 5 1
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Using Complement inCalculation
Only the last number subtracted
from 10, and all other numbers
must be subtracted from 9
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Using Complement inCalculation
Example 3
Similarly 10 000 - 1249 = 8751
10 000 - 1 2 4 9
| | | |
8 7 5 1
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Using Complement inCalculation
Example 4
For 1000 - 83, in which we have morezeros than figures in the numbers being
subtracted, we simply suppose 83 is
083.So 1000 - 83 becomes 1000 - 083 = 917
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Exercise 2
10 MINUTES
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Exercise 2
1) 100 - 36 = _________
2) 100 - 74 = _________
3) 1000 - 236 = _________4) 1000 - 472 = _________
5) 1000 - 618 = _________
6) 10 000 - 6381 = _________
7) 10 000 - 7395 = _________
8) 100 000 - 71095 = _________
9) 100 000 - 93286 = _________
10) 100004825 = _________
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Exercise 2
1) 100 - 36 = 64
2) 100 - 74 = 26
3) 1000 - 236 = 7644) 1000 - 472 = 528
5) 1000 - 618 = 382
6) 10 000 - 6381 = 3419
7) 10 000 - 7395 = 2605
8) 100 000 - 71095 = 28905
9) 100 000 - 93286 = 6714
10) 10 0004825 = 5175
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SPEED SUBTRACTIONSubtraction Using complement
(2 Digit Subtract 2 Digit)
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Speed Subtraction
For most of us, it is easier to add than to
subtract. But if you, continue to computefrom left to right and to break down
problems into simpler components,
subtraction can become almost as easy asaddition.
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Speed Subtraction
How would you minus
63- 37 = ____
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Speed Subtraction
Example 1
62
- 37
_________
_________
2 - 7 = - 5 that means
it is 5 short of 10 since
there was negativeresult from subtraction
operation in units
place, it means that wehave to reduce 6 by 1
and hence 5 - 3 = 2 .
Answer would be 25
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Speed Subtraction
Example 2
52
- 26
_________
_________
2 - 6 = - 4 that means it
is 6 short of 10 since
there was negativeresult from subtraction
operation in units place,
it means that we have to
reduce 5 by 1 and hence4 - 2 = 2 . Answer
would be 26
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Speed Subtraction
Example 3
4 5 3
- 8 7
_________
_________
3 - 7 = -4 that means it is 6short of 10 since there wasnegative result from
subtraction operation in unitsplace . It means that we have toreduce 5 by 1 hence 4 - 8 = -4 .That means it is 6 short of 10there was negative result fromsubtraction operation in unitplace it means that we have to
reduce 4 by 1 and hence 4 - 1= 3.
Answer would be 366
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Speed Subtraction
Exercise 3 10 minutes
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82
- 57
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91
- 52
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70
- 69
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53
- 25
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81
- 44
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37
- 29
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72
- 64
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90
- 79
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90
- 51
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72
- 33
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57
- 19
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80
- 71
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61
- 25
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93
- 86
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90
- 73
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41
- 15
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--------
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MULTIPLY BY 9
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Multiply By 9
Can you multiply this with a
calculatora) 342 x 999
b) 34 x 99c) 5642 x 9999
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Multiply by 9
Example : 342 x 999
We divide our answer in two parts, the LHS and RHS Step 1 : LHS We write one less than the
multiplicand 342 -1 + 341
Step 2 : RHS We write the complement of themultiplicand using "All from 9 last
from 10" complement for 342 = 658
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Multiply By 9
Example : 34 x 99
Step 1 : LHS 34 -1 = 33
Step 2 : RHS Complement for 34 = 66Step 3 : Answers 3366
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Multiply By 9
Example : 5642 X 9999
Step 1 : LHS 5642 -1 = 5641
Step 2 : RHS Complements for 5642 =
4358
Answers 56414358
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No Question
1 56 X 99
2 46 X 99
3 74 X 99
4 65 X 99
5 34 X 99
6 67 X 99
7 23 X 99
8 87 X 999 73 X 99
10 92 X 99
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CROSSWISE AND VERTICAL
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CROSSWISE and VERTICAL12/17/2012Infinite Learning Academy
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CROSSWISE and VERTICAL
Step 1
The ones place of the product is determined vertically,
by computing 68. The result, 48, tells us the onesplace of the product is an 8, and we have an additional
4 tens to keep track of.
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CROSSWISE and VERTICAL
Step 2
The tens place of the product is determined crosswise,by taking both the product 67 and also the product38, plus the extra 4 tens we have from above.
This yields 42+24+4=70 tens, so the tens place of theproduct is 0, and we have an additional 7 hundreds to
keep track of.
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CROSSWISE and VERTICAL
Step 3
Finally, the hundreds place of the product is
determined vertically, by computing 37, plus the7 extra hundreds from above. That gives 21+7=28hundreds. Putting it all together, we have 2808 asthe product.
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CROSSWISE and VERTICAL
21
X 32
------
2____
21
X 32
------
72____
21
X 32
------
672____
Starting from the
RHS, multiply the
digit on vertically
multiply 1 x 2, We
get 2
Cross multiply
2 x 2 = 41 x 3 = 3
4 + 3 = 7
Vertically
left column2 x 3
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Example 2 : 21 x 32
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CROSSWISE and VERTICAL
42X 13
--------
6--------
42X 13
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146--------
42X 13
--------
546--------
Step 1 : RHS,
multiply
vertically
2 x 3 = 6
Step 2 :
4 x 3 = 12
2 x 1 = 2Add 2 + 12 = 14
We put 4 and
carry over 1
Step 3
4 x 1 = 4
4 + 1 (carry) =
5
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Example 3 : 42 x 13
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CROSSWISE and VERTICAL
Example 4 : 46 x 27
4 6
x 2 7
--------------
12 44 42--------------
Example 5 : 57 x 83
5 7x 8 3
-----------
47 73 21------------
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Exercise
1) 24
x 56---------
---------
2) 43
x 29---------
---------
3) 76
x 24-------
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Bar ModelAlternatives Method to ProblemSolving Strategy
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Here is a math problem you can solve
easily:
A man sold 230 balloons at a fun fair in the
morning. He sold another 86 balloons in
the evening. How many balloons did hesell in all?
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And here is one you cant
Lauren spent 20 percent of her money on a dress.
She spent 2/5 of the remainder on a book. She had
$72 left. How much money did she have at first?
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How to Solve ProblemSolving Question
What is model drawing
Model drawing means translating a
word problem into diagrams ormodels.
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How to Solve Problem Solving
Question
Why use model drawing A picture ( or a diagram) is worth a
thousand words
Younger children find equation andabstract calculations difficult to
understand
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How to Solve Problem Solving
Question
Why use model drawing Model drawing helps to convert the data
provided in a problem into concrete visual
images
It enables students to comprehend andconvert problem situations into relevant
mathematical expression or number sentences
and to solve them
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Other Problem SolvingStrategies
Draw a Picture
Look for a Pattern Guess and Check
Make a systematic List
Logical Reasoning Work Backwards
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2 Types of Bar Models
Part - Whole Model
Used to find the whole given the parts or
the parts given the whole.Comparison Bars
Used to compare two objects to eachother.
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PartWhole Models
On Tuesday, Cole ran 6 miles. On Thursday, he ran 8
miles. How many miles did he run altogether?
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8 mi
? mi
6 mi
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Comparison Bar Models
Laina is 13 years old. Her sister is 22 years old. Find
the difference in age between them.
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?
22
13
Laina
Sister
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Bar Model
Question 2
Tom, Dean and Harry have a total ofRM850. Dean has RM 120 more than
Tom and Harry has RM190 more thanDean. How much money does Harryhave ?
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Tom, Dean and Harry have a total of RM850. Dean has
RM 120 more than Tom and Harry has RM190 more
than Dean. How much money does Harry have ?
1) Who has the least
amount of money?
Tom
Tom of course
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Tom, Dean and Harry have a total of RM850. Dean has
RM 120 more than Tom and Harry has RM190 more
than Dean. How much money does Harry have ?
1) Who has the least
amount of money?
Tom
Dean
Tom of course
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Tom, Dean and Harry have a total of RM850. Dean has
RM 120 more than Tom and Harry has RM190 more
than Dean. How much money does Harry have ?
1) Who has the least
amount of money? Tom of course
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Tom, Dean and Harry have a total of RM850. Dean has
RM 120 more than Tom and Harry has RM190 more
than Dean. How much money does Harry have ?
1) Who has the least
amount of money? Tom of course
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Tom, Dean and Harry have a total of RM850. Dean has
RM 120 more than Tom and Harry has RM190 more
than Dean. How much money does Harry have ?
3 units + 120 +120 + 190= 850
3 units = 850430
1 unit = 420 divide 3
= 140
Harry has = 10 + 120 +
190
Harry has 450
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Bar Model
Question 2Charlie, Sally and Eddie have a total of
RM570. Charlie has RM 80 more than Sally
and Eddie has 5 times as much as Sally.How much does of them have?
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Bar Model
Charlie, Sally and Eddie have a total of
RM570. Charlie has RM 80 more than
Sally and Eddie has 5 times as much asSally. How much does of them have?
Sally
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Bar Model
Charlie, Sally and Eddie have a total of
RM570. Charlie has RM 80 more than
Sally and Eddie has 5 times as much as
Sally. How much does each of themhave?
Charlie
Sally
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Bar Model
Charlie, Sally and Eddie have a total of
RM570. Charlie has RM 80 more than
Sally and Eddie has 5 times as much as
Sally. How much does each of themhave?
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7 equal units = 80 = 570
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Charlie, Sally and Eddie have a total of RM570. Charlie has RM 80
more than Sally and Eddie has 5 times as much as Sally. How
much does of them have?
7 equal units = 57080
= 490
1 unit = 490 divide 7= 70
Sally has 70
Charlie has 70 + 80 = 150Eddie has 5 x 70 = 350
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Bar Model
Question 3
Each admission ticket for a concert cost RM 25. A total
of RM30,000 was collected from ticket sales for
Saturday and Sunday. If 300 more tickets were sold on
Sunday than on Saturday, how many tickets were sold
on Sunday
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Each admission ticket for a concert cost RM 25. A total of RM30,000 was
collected from ticket sales for Saturday and Sunday. If 300 more tickets
were sold on Sunday than on Saturday, how many tickets were sold on
Sunday
1) Find the total number of tickets sold for 2 days
(how many RM 25 tickets can you buy with RM 30,000)
2) Subtract 300 tickets from the total number of tickets sold.
3) Divide the answer (from step 3) by 2 to find ticket sold on
Sat.
4) To find no of ticket sold on Sunday add 300 to Saturday's no.
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Each admission ticket for a concert cost RM 25. A total ofRM30,000 was collected from ticket sales for Saturday and
Sunday. If 300 more tickets were sold on Sunday than on
Saturday, how many tickets were sold on Sunday
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Shakuntala Devi: Thats Incalculable!
In 1976 theNew York Times reported that an Indian
woman named Shakuntala Devi (b. 1939) added
25,842 + 111,201,721 + 370,247,830 + 55,511,315,and then multiplied that sum by 9,878 for a correct total of
5,559,369,456,432 all in less than twenty seconds
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Her greatest claimed accomplishmentthe timedmultiplication of two thirteen digit numbers on paperhas appeared in the Guinness Book of World Records as
an example of a Human Computer. The time of thecalculation, however, is questionable at best. Devi, amaster of the criss-cross method, reportedly multiplied7,686,369,774,870 x 2,465,099,745,799 numbersrandomly generated at the computer department of
Imperial College, London, on June 18, 1980. Her correctanswer of18,947,668,177,995,426,773,730 wasgenerated in an incredible twenty seconds.
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