# MSC 2 – All from 9 and the Last from 10 Subtraction

As in Addition, we were taught to subtract from right to left. But when computing money, we struggle mentally with left to right computation.  If we paid for a P347.25 purchase with a P1,000 bill, for example, our mental process goes on like this:

1. 1000 minus 300 is 700 but my purchase is more than 300
so my change is less than 700, or 600+.
2. It is not 660, because we bought more than 340, so it must be 650+.
3. It is not 653, because we bought more than 347, so it must be 652+.
4. Aha!, we know that the change for .25 is .75, so we have our final change of P652.75

In Vedic Math, they have a nice Sutra or word formulafor this: “All from 9 and the Last from 10” , which means that when subtracting from a power of 10, we subtract, starting from the leftmost digit, all the digit from 9 except the last digit which we will subtract from 10.

Example 2.1 : How much change do I get if I pay for my P347.25 purchase with a P1,000 bill?

We are used to writing subtraction like this:

 ``` 1,000.00  -347.25 ``` ``` 1,000.00 -347.25 652.75 ```
1. Starting from the left, subtract every digit of the subtrahend, except the last,  from 9
2. Subtract the last digit from 10.

Some find it easier to add than to subtract. Using the same example above, we can readily announce the change:

1. “My change is” (what should I add to 3 hundred to make 9?)six hundred
2. (What should I add to 4 to make 9?) fifty
3. (What should I add to 7 to make 9?) two pesos and
4. (What should I add to 2 to make 9?) seventy
5. (What should I add to 5 to make 10?) five

When the subtrahend ends in zero(es), we make a slight modification in our procedure

Example 2.2 : How much change do I get if I pay for my P340.00 purchase with a P1,000 bill?

 ``` 1,000.00 -340.00 ``` ``` 1,000.00 -340.00 660.00 ```
1. Momentarily disregard the  three ending zeroes.
2. Apply the “All from 9 and the last from 10” only to 34 to get 66.

When the subtrahend contains less digits than the number of zeroes in the minuend

Example 2.3

 ```1,000.00 - 8.55 ``` ```1,000.00 - 008.55 99 ``` ```1,000.00 - 008.55 991.45 ```
1. Pad the given number with zeroes to the left so that it has as many digits as the power of 10 has zeroes.
2. Apply the “all from 9” procedure.

When the minuend is not a power of ten

Example 2.4:

 ``` 500.00 -68.95 ``` ``` 500.00 - 068.95 4 ``` ``` 500.00 - 68.95 431.05 ```
1. Subtract 1 from the leftmost digit.
2. Apply the “All from 9 and the last from10” to the rest of the digits.

When subtracting from a power of ten, the difference is called the ten’s complement of the subtrahend. When the minuend is not specified, it is assumed to be the next higher power of 10.

The 10’s complement of 8 is 2, of 286 is 714, and of 889 is 111. The ten’s complement of 2 with respect to 1000 is 998.

Exercise 2.1 : What change will you get when you pay P1,000 for the following purchases?

a)     P 347. 25
b)     P 489.80
c)     P 700.11
d)     P 826.35
e)     P 899.01

Exercise 2.2:

a)     P500.00 – 123.45 =
b)     P200.00 – 73.20 =
c)     P700.00 – 622.98 =
d)     P350.00 – 325.25 =
e)     P800.00 – 749.98 =

Exercise 2.3: Find the ten’s complement of the following numbers.
a)     76
b)     21
c)     97
d)     288
e)     898
f)       232
g)     1001
h)     6789
i)        9929
j)        9878

Discover the 25 Math Short Cuts!

# Our Philosophy:

This we believe:
Each child is a unique individual whose immense potentials must be brought to full flowering. Each child must grow – without surrendering his individuality – into a critical thinker, a socially sensitive, self-directed, creative, responsible and caring adult.

This we believe:
The development of a child is the shared responsibility of equally concerned and equally loving parents and teachers in the warmth of home and a child-friendly school.

This we believe:
The Child is Today.
The Child is Tomorrow. ## Our Mission:

To provide each child with superlative environment for physical, moral, spiritual, emotional and intellectual growth through a variety of meaningful experiences designed for the child’s total development.

## Our Vision:

Each child is a growing individual – with the independence, the sense of responsibility, the intellectual and emotional maturity demanded by a world continuously getting complex. Each child growing into a good human being – with the courage, the ability and the confidence to face the realities of his world.

Each child, a family’s pride.

# 25 Years Ago – How MSC Started

By Ike Prudente

On Dec 4, 1989, we started the MSC Computer training center.

Over the years, we branched into all sorts of ventures, from computer hardware to  computer supplies to internet services to business applications and unrelated courses. We gave thousands of scholarships to financially challenged but deserving students. As we look back, we realized our greatest contribution to society are the fine citizens in the community who we helped educate and train these 25 years.

We are now in our new garden site in San Gabriel, refocusing our efforts in our core strengths in education. We now proudly re-introduce ourselves: we are MSC Institute of Technology – THE Math, Science and Computing School.

Start of MSC
MSC is best known as an educational institution. However, MSC started out as a computer software company, not a school.

In June 1989, Jorge Tanalega and I, together with our Cobol Instructor/ STI Center administrator Danny Lopez thought of forming a software development company because we were informed that a local utility wanted to computerize its billing system. With some friends, we brainstormed for a name which can be easily remembered. We thought that SMC (San Miguel Corporation) was very popular so we thought that jumbling the initials would be a good idea.

We thought of MSC and the name Management Systems Consultants. But when we tried to register it with the Department of Trade and Industry as a single proprietorship business entity, it was rejected because all the words in the proposed company name are common, generic words. So we added my initials VYP (for Virgilio Y. Prudente). Thus, VYP-Management Systems Consultants was registered.

When I was given the specifications for the billing systems requirement, I thought that I could easily finish it in a few days so I submitted a quotation of P8,000. They did not bother to contact us back. I found out later that a large company quoted P80,000 for the system.

A couple of unforeseen events led us to seriously consider the direction of a new company. In a planning session, Danny Lopez asked us “who do you think are the best programmers in San Pablo?” Of course, I pointed to Jorge Tanalega, Danny and Myself. And so Danny suggested that we establish a computer school. With two other friends from the Kiwanis Club of Lake City, Louie Perlas and Tony Celestino who believed in us, we decided to put up the MSC Computer Training Center.

Several days later, on Dec 4, 1989, on the mezzanine (above what is now LBC) of the Magcase Building on Barleta St., with a classroom with 9 chairs and a laboratory of 5 computers bought with borrowed money, or donated by family and friends, we conducted our first class with our first four students: Arnel Eneria, Christopher Catapia, Jonathan Romo and Noel Baldores – the WE WEH boys!

Our first course , Fundamentals of Computer Operations (FCO) was of course, handled by the teacher among us, Danny Lopez. But since Danny’s expertise is in teaching programming logic and COBOL, he needed help in preparing for his lessons in using the basic software – DOS, Wordstar, Lotus, dBase III.

Our software department headed by Gigi Tanalega doubled as the research department. Research then was very different from research now. Without Internet or books on the popular software, the team of Gigi spent hours, discovering tricks and short cuts using our AT 286, double diskette drive computers (without hard disk) which Danny could teach to our FCO students. This training proved beneficial to Gigi’s boys. Jonald Aguila is now a software developer based in Maryland USA and Edgar Cauyan is now president of CARD MRI Information Technology, Inc.

Anticipating the need for more instructors, we recruited Aniles Aquino (now Mrs. Duma, a professor at the Laguna State Polytechnic University and currently pursuing her doctorate in Education) and Gemma Pangilinan (now Mrs. Dimaano, the registrar of MSC).

In January 1990, a team from the Department of Education Culture and Sports came and told us that we were operating without a permit. Apparently, some not so friendly elements reported us to the DECS. After showing them our facilities which is certainly not below the minimum requirements for a school, I told them that we are awaiting our transfer to our new site before we submit our application for a school. I invited them to view a vacant space in the second floor of a nearby building, which I told them would be the future site of our new school. We also invited them to the “blessing” of our new site on April 1, 1990.

# More Robotics Programming at MSC High

We will have more time for Computer Programming Lessons this school year at MSC High School, including robotics programming using the latest state-of-the-art Lego MindStorm EV3 robotics set. MSC Institute of Technology High School students at all levels will have two hours of computer programming lessons per week beginning this school year. Programming “is the new ‘superpower’ that isn’t taught in 90% of US schools” During the previous years, MSC students started programming once a week using the Lego Mindstorms NXT 2.0 Robotics Kits.

This year the students will have, in addition to their Robotics classes, an additional hour of programming using a high level language like Python. This will prepare the MSC students for high- paying jobs in the 2020s.

Just this December, 2013, computer industry leaders like Bill Gates and Mark Zuckerberg organized the Code.org to encourage schools in the US to offer programming courses at all level because they feared that “1 million of the best jobs in America may go unfilled” in 2020 because only “1 out of ten schools in America teach children how to code”. They project that by that date about 1.4 million programming jobs will be open and the American educational system can only produce 400,000 programmers if the other schools will not include programming in their curriculum.

Moreover, according to Steve Jobs, the late founder of Apple, Inc. and the creator of IPad and IPhone, “Everybody (in this country) should learn how to program a computer, because it teaches you how to think”.

Watch this video clip: What Most Schools Don’t Teach

Believing that knowledge of programming will have a great positive impact on the future of its students, the MSC administration not only decided to have the additional hour of computer programming instruction, but also acquired the latest and most advanced Lego Mindstorms Kit, the EV3 for Evolution – Third generation for use of their students.

And, to make sure that MSC students will have the best possible training in computer programming, MSC founder and President, Virgilio “ Sir Ike” Prudente will personally handle the classes.

# MSC 25th Foundation Day

by Ike Prudente

On Dec. 4, 2014, we will be celebrating our 25th Foundation Day. In line with this, we are preparing some activities in addition to whatever plans the Alumni Association has.

First is the Search for Outstanding MSC Alumni. We will be awarding 25 Tech-Voc, 25 High School and 25 Short Course (FCO, ACO, Caregiving and Call Center) graduates during our Foundation Day. The criteria will be announced in early June.

Second is the 25 MSC – 25 Math Short Cuts. Every week, we will send a very useful math technique to all subscribers of the 25 MSC Newsletter which will come out beginning the second week of June. This Newsletter will be available to all – to MSC Alumni, your friends and relatives. Anyone who wishes to subscribe to this newsletter can fill out the form on the right of this page, or click on this link, just send a email with “Subscribe” on the subject line to msc@msc.edu.ph.

Third is the MSC Directory. We would like to keep track of all former
MSC students so we will start to gather data for an MSC directory which will be made accessible to all MSC alumni.

Fourth but not the least and surely not the last is the creation of an MSC Scholarship Fund. MSC has given many MSC scholarships to deserving students in the past, but we have not institutionalized it. With the creation of the MSC Scholarship Fund we hope to have more donors and more scholars.

# 25 Math Short Cuts Answer Key

by Ike Prudente

This is the answer key to all the exercises in the 25 Math Short Cuts

MSC 1 – Addition by Creating Zeroes
Exercise 1.
a) 25
b) 27
c) 30
d) 32
e) 184
f)1267
g) 157
h) 1071
i) 925
j) 1,666,666

MSC 2 – All from 9 and the Last from 10 Subtraction

Exercise 2.1: What change will you get when you pay P1,000 for the following purchases?

a) P 1,000 – P 347.25 = P 652.75
b) P 1,000 – P 489.80 = P 510.20
c) P 1,000 – P 700.11 = P 299.89
d) P 1,000 – P 826.35 = P 173.65
e) P 1,000 – P 899.01 = P 100.99

Exercise 2.2:

a) P500.00 – 123.45 = P 376.55
b) P200.00 – 73.20 = P 126.80
c) P700.00 – 622.98 = P 77.02
d) P350.00 – 325.25 = P 24.75
e) P800.00 – 749.98 = P 50.02

Exercise 2.3:  Find the ten’s complement of the following numbers.
a) 76 → 24
b) 21 → 79
c) 97 → 3
d) 288 → 712
e) 898 → 102
f) 232 → 768
g) 1001 → 8999
h) 6789 → 3211
i) 9929 → 71
j) 9878 → 122

MSC 3 – Subtraction without Borrowing

Exercise 3.1

a)     724 – 698 =  26
b)     1, 256 – 994 = 262
c)     3, 534 – 1, 985 = 1,549
d)     5, 463 – 2, 778 = 2,685
e)     25, 647 – 8678 = 16,969

Exercise 3.2:

a)     525 –  496 = 29
b)     847 – 293 = 554
c)     5,743 – 1,976 = 3,767
d)     7,352 – 2,684 = 4,668
e)     17, 437 – 9, 689 =  7,748

Exercise 3.3:

a)     452 – 357 = 95
b)     843 – 255 =588
c)     2, 336 – 1,448 = 888
d)     1, 234 – 365 = 869
e)     8, 745 – 6, 849 = 1,89

MSC 4 – Multiplication by 11

Exercises 4.1: Perform the following multiplication:

1.        52 x 11 = 572
2.        36 x 11 = 396
3.       245 x 11 = 2,695
4.     7,261 x 11 = 79,871
5.   435,263 x 11 = 4,787,893

Exercise 4.2. Perform the following multiplication

1. 46 x 11 = 506
2. 75 x 11 = 825
3. 567 x 11 = 6,237
4. 7,856 x 11 = 86,416
5. 29,586 x 11 = 325,446

MSC 5 – Multiplication by 2
Exercise 5.1: Double the following  numbers

1.   2,343 = 4,686
2.   2,535 = 5,070
3.   4,527 = 9,054
4.   3,552 = 7,104
5.   5,555 = 11,110
6.   8,477 = 16,954
7.   6,386 = 12,772
8.   3,099 = 6,198
9.   3,909 = 7,818
10.   7,896 = 15,972

Exercise 5.2: Find the following products:

1.    142 x 4 = 568
2.    357 x 4 = 1,428
3.    568 x 4 = 2,272
4.    742 x 4 = 2,968
5. 2,468 x 4 = 9,872
6.    214 x 8 = 1,712
7.    455 x 8 = 3,640
8.    773 x 8 = 6,184
9.    894 x 8 = 7,152
10. 3,152 x 8 = 25,216

MSC 6 – Dividing  by 2
Exercise 6: Halve the following numbers

1.         468 ÷ 2 = 234
2.      1,264 ÷ 2 =  632
3.      3,456 ÷ 2 =  1728
4.      2,752 ÷ 2 =  1376
5.      2,526 ÷ 2 =  1263
6.      7,338 ÷ 2 =  3669
7.      5,372 ÷ 2 =  2686
8.      6,784 ÷ 2 =  3392
9.      8,357 ÷ 2 =  4178.5
10. 101,303 ÷ 2 =  50,651.5

MSC 7 – Doubling and Halving
Exercise 7: Compute the following using halving and doubling

1.       16 x 4 = 64
2.       18 x 3 = 54
3.       36 x 22 = 792
4.       62 x 22 = 1,364
5.       160 x 3.5 = 560
6.       1.5 x 24 =36
7.       55% of 1800 = 990
8.       125 x 48 = 6,000
9.       1.75 x 32 = 56
10.       55 x 64 = 3,520

Exercise 8; Use (10-1) in multiplying by 9

1. )      6 x 9 = 54
2. )      9 x 9 = 81
3. )      35 x9 = 315
4. )      49 x 9 = 441
5. )      82 x 9 = 738
6. )      148 x 9 = 1332
7. )      285 x 9 = 2511
8. )      0. 9 x 68 = 61.2
9. )      90% of 675 = 60.75
10. )  45% of 740 = 333

MSC 9 – Dividing by 5, 50, 0.5, etc.
Exercise 9: Compute the following:

1. )     370 ÷ 5 = 74
2. )     535 ÷ 5 = 107
3. )     2,367 ÷ 5 = 473.4
4. )     9,898 ÷ 5 = 1,979.6
5. )     4,656 ÷ 50 = 931.2
6. )     24,579 ÷ 50 = 491.58
7. )     5,836 ÷ 500 = 11.672
8. )     34,785 ÷ 500 = 69.570
9. )     4,524 ÷ 0.5 = 9,048
10. )    3,645 ÷ 0.05 = 72,900

MSC 10 – Multiplying by 5, 50, 5%, etc
Exercise 10: compute for the following products:

1. ) 864 x 5 = 4,320
2. ) 748 x 5 = 3,740
3. ) 356 x 5 = 1,780
4. ) 475 x 5 = 2,375
5. ) 2,357 x 5 = 11,785
6. ) 685 x 50 = 34,250
7. ) 873 x 50 = 43,650
8. ) 347 x 500 = 173,500
9. ) 5% of 739 = 36.95
10. ) 5% of 95.5 = 4.775

MSC 11 – Division by 9
Exercise 11: Divide the following numbers by 9

1. )      134 / 9 = 14 r 8
2. )      215 / 9 = 23 r 8
3. )      2231 / 9 = 247 r 4
4. )      4202  / 9 = 466 r 8
5. )      625   / 9 = 69 r 4
6. )      3030 / 9 = 336 r 6
7. )      7135 / 9 = 792 r 7
8. )      5672 / 9 = 630 r 2
9. )      3692 / 9 = 410 r 2
10. )      46893 / 9 = 5210 r 3

MSC 12 – Division by 4 and 8
Exercise 12:

1. )  456 ÷ 4 = 114
2. )  527 ÷ 4 = 131.75
3. )  983 ÷ 4 = 245.75
4. )  2,538 ÷ 4 = 634.5
5. )  6,789 ÷ 4 = 1,697.25
6. )  745 ÷ 8 = 93.125
7. )  1,278 ÷ 8 = 159.5
8. )  3,684 ÷ 8 = 460.5
9. )  6,454 ÷ 8 = 806.75
10. )  10,522 ÷ 8 = 1,315.25

Exercise 13:

1.    36 x 25 = 900
2.    78 x 25 = 1,950
3.    67 x 25 = 1,675
4.    256 x 125 = 32,000
5.    55 x 125 = 6,875
6.    123 x 250 =40,750
7.    466 x 2.5 = 1,165
8.    3599 x 25% = 899.75
9.    2468 x 2.5% = 61.7
10.    2552 x 1.25% = 31.9

Exercise 14:

1. ) 1050 ÷ 25 = 42
2. ) 6025÷ 25 = 241
3. ) 8375 ÷ 25 = 335
4. ) 12,400 ÷ 250 = 49.6
5. ) 71000÷ 125 = 568
6. ) 5,125÷ 125 = 41
7. ) 3,475÷ 250 = 13.9
8. ) 830÷ 12.5 = 66.4
9. ) 2475÷ 2.5 = 990
10. ) 5264÷ 0.25 = 21,056

Exercise 15:     Find the square of the following numbers

1. )   45 = 2,025
2. )   95 = 9025
3. )   195 = 38,025
4. )   10,005 = 100,100,025
5. )   10.5 = 110.25
6. )   7.5 = 56.25
7. )   6 ½ = 42 1/4  ( or 42.25 )
8. )   9 ½ = 90 1/4  ( or 90.25 )
9. )   100.5 = 10,100.25
10. )   0.025 = 0.000625

Exercise 16:

1. ) 24 x 26 = 624
2. ) 73 x77 = 5,621
3. ) 81 x 89 = 7,209
4. ) 998 x 992 = 99,016
5. ) 4.3 x 4.7 = 20.21
6. ) 7.4 x 7.6 =  56.24
7. ) 3 3/7 x 3 4/7 = 12 12/29
8. ) 4 1/6 x 4 5/6 = 20 6/36
9. ) 2 4/9 x 2 5/9 = 6 20/81
10. ) 297 x 203 = 60,291

Exercise 17: Find the following products using base multiplication

1. 12 x 13 = 156
2. 14 x 17 = 238
3. 15 x 18 =270
4. 108 x 101= 10,908
5. 116 x 102 = 11,832
6. 108 x 112 = 12,096
7. 112 x 114= 12,768
8. 123 x 106 = 13,038
9. 1021 x 1006 = 1,027,126
10. 1432 x 1002 = 1,434,864

Exercise 18:      Find the following products using the base method.

1. 6 x 9 = 54
2. 99 x 98 = 9,702
3. 98 x 93 = 9,114
4. 88 x 98 = 8,624
5. 75 x 97 = 7,275
6. 87 x 88 = 7,656
7. 97 x 67 = 6,499
8. 94 x 91 = 8,554
9. 995 x 975 = 970,125
10. 997 x 778 = 775,666

Exercise 19: Find the following products using the base method

1. ) 12 x 9 = 108
2. ) 103 x 98 = 10,094
3. ) 102 x 97 = 9,894
4. ) 102 x 98 = 9,996
5. ) 103 x 97 = 9,991
6. ) 105 x 93 = 9,765
7. ) 75 x 103 = 7,725
8. ) 112 x 89 = 9,968
9. ) 1012 x 991 = 1,002,892
10. ) 1125 x 995 = 1,119,375

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Discover 25 Math Short Cuts!

# MSC 1 – Addition by Creating Zeroes

By Ike Prudente

Addition with zeroes is very simple so to simplify addition we must create numbers with zeroes.

1)Add number pairs or groups totalling to ten or multiples of ten first

Example 1.1: 3 + 4 + 6 + 8 + 5 + 9 =

 3 + 4 + 6 + 8 + 5 + 9 Add 4 and 6 first to get 10 = 3 +  (4 + 6 ) + 8 + 5 + 9 = 3 + 10 + 8 + 5 + 9 Next we add 3, 8 and 9 to get 20 for a total of 30 = 10 + ( 3 + 8 + 9 ) + 5 = (10 + 20) + 5 = 30 + 5 Only the 5 remains to be added so we have a total of 35. = 35

Example 1.2: 4 + 67 + 276 + 20 =

 4 + 67 + 276 + 20 Add 4 to 276 first to get 280 = (4+276) + 67 + 20 =  280 + 67 + 20 Then add the 20 to get 300 = (280 + 20) + 67 = 300 + 67 Finally add the 67 to get 367 = 367

2) Mentally create zeroes by transferring

Example 1.3:  34 + 56 =

 34 + 56 Mentally transfer 4 from 34 to 56 = 30 + (4 + 56) = 30 + 60 Addition then become a simple 30 + 60 exercise. = 90

Example 1.4:              65 + 97 =

 65 + 97 Mentally transfer 3 from 65 to 97 to make it 100. = 62 + (3 + 97) = 62 + 100 65 becomes 62, so the answer is 162. = 162

Example 1.5:  137 + 245 + 489 =

 137 + 245 + 489 = Transfer 11 from 137 to 489 to make it 500. = (137 – 11) + (11+489) + 245= (137 – 11) + 500 + 245 Transfer 5 from 137 to 245 to make it 250. = (137  – 11 – 5 ) + 500 + (245 + 5)= (137  – 11 – 5 ) + 500 + 250 Then we have 500 + 250 = 750 = (137  – 11 – 5 ) + 750 Finally we add 121 (137-11-5) to 750 to get 871. = 121 + 750= 871

3) Sometimes it is easier to add a round number first before deducting the excess.

Example 1.6   376 + 995 =

 376 + 995 Add 1000 to 376 to get 1376 = 376 + (1000 – 5)= 376 + 1000 – 5 = (376 + 1000 ) – 5 = 1376 – 5 Deduct 5 which is the excess of 1000 from 995 to get1371 = 1371

Why it works.

This is not rocket science, but in case you are wondering, we are just using the associative and commutative properties of addition.

Exercises

a)   2 + 5 + 4 + 8 + 6 =

b)   1 + 6 + 9 + 4 + 7 =

c)   5 + 6 + 7 + 8 + 4 =

d)   8 + 4 + 9 + 8 + 3 =

e)   86 + 98 =

f)     989 + 278 =

g)   24 + 67 + 66 =

h)   287 + 471 + 313 =

i)     734 + 40 + 125 + 26 =

j)     999,967 + 666,699 =