Math Workshop Klang

7/30/2019 Math Workshop Klang

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12/17/2012Infinite Learning Academy


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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





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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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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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Example 2

Similarly 1000 - 649 = 351

1000 - 6 4 9

| | |3 5 1



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Only the last number subtracted

from 10, and all other numbers

must be subtracted from 9



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Example 3

Similarly 10 000 - 1249 = 8751

10 000 - 1 2 4 9

| | | |

8 7 5 1



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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

--------

--------

91

- 52

--------

-------

70

- 69

--------

--------

53

- 25

--------

--------

81

- 44

--------

--------

37

- 29

--------

--------

72

- 64

--------

--------

90

- 79

--------

--------



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90

- 51

--------

--------

72

- 33

--------

--------

57

- 19

--------

--------

80

- 71

--------

--------

61

- 25

--------

--------

93

- 86

--------

--------

90

- 73

--------

--------

41

- 15

--------

--------



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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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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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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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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


Example 2 : 21 x 32


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42X 13

--------

6--------

42X 13

--------

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


Example 3 : 42 x 13


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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

Infinite Learning Academy 12/17/2012


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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.

Infinite Learning Academy

12/17/2012


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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?


8 mi

? mi

6 mi

12/17/2012


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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.


?

22

13

Laina

Sister

12/17/2012


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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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amount of money?

Tom

Dean

Tom of course



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amount of money? Tom of course



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amount of money? Tom of course



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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



Sally and Eddie has 5 times as much as

Sally. How much does each of themhave?

Charlie

Sally



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Bar Model



Sally and Eddie has 5 times as much as

Sally. How much does each of themhave?


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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Math Workshop Klang