Author Archives: Roberto Prudente

Issue 1 : Creating Zeroes – 25 Math Short Cuts

25 Math Short Cuts - Be a Mathemagician! June 12, 2014 Issue 1

25th MSC Foundation Day

On Dec. 4, 2014, we will be celebrating our 25th Foundation Day. In line with this, we have lined up many activities leading up to the Foundation Day celebration. One initiative is this newsletter, 25 Math Short Cuts. Every week, we will feature a very useful math technique in this Newsletter. This Newsletter will be available to all – to MSC/MATH-Inic students/parents/faculty, MSC Alumni, your friends and relatives. We encourage you to forward this newsletter to anyone who you think would benefit from it. Just click here to subscribe, or just send an email with “Subscribe” on the subject line to msc@msc.edu.ph . Read more….

MSC Scholarships

In MSC, we believe in bringing out the best in every student and make each one a life long learner. We are passionate about teaching Math, Science and Computing. We believe that we should help deserving students get the quality education despite financial difficulties. Hence we, philanthropic individuals and institutions join hands in providing scholarships to as many students as possible. Read more…

25 Math Short Cuts

Everyone can learn math short cuts. We launched the MATH-Inic program because we believe everyone, from pre-school children to the young at heart can learn speed math techniques after a few hours in our class. Last May 17, 2014, 6-year-old Khallel showed us how to solve 5 math problems in 47 seconds!
Learning to be a Mathemagician like Khallel is easy but one has to learn short cuts one by one, and we begin by teaching you 25 math short cuts. Just make sure you subscribe to this newsletter. I have selected what I think will be most useful for everyone, whether you are students, teachers, professionals or plain folks who need to calculate every day. Much of the hard work in compiling this work is not in researching for materials, because I know these short cuts by heart, but in selecting what short cuts to include. Read More…

MSC 1 – Addition by Creating Zeroes

From our grade school years, many of us have learned many ways of simplifying calculations. I am sure that for most of us, “multiplying by 10” is one of the first math short cut we have learned. And we continue to use it, which is the reason why I did not include it here. But note that in math, zeroes and ones are usually our best friends. The simplest addition problem involves zero. Anything plus zero equals the same thing. Wouldn’t it be cool to simplify addition problems by creating numbers with zeroes? How quickly ( and easily) can you solve:

2 + 5 + 4 + 8 + 6 =
1 + 6 + 9 + 4 + 7 =
5 + 6 + 7 + 8 + 4 =
8 + 4 + 9 + 8 + 3 =
86 + 98 =
989 + 278 =
24 + 67 + 66 =
287 + 471 + 313 =
734 + 40 + 125 + 26 =
999,967 + 666,699 =

In the Next Issue

MSC History
MATH-Inic Speed Math System
MSC 2 – All from 9 and the Last from 10 Subtraction

Every week, for 25 weeks up to December 4, 2014 when we celebrate our 25th Foundation day, this newsletter will feature one math short cut. We will progress from the simplest to the simple. Believe you can do it! Just proceed one step ( short cut ) at a time, and be pleasantly surprised to discover none of the math short cuts are difficult! Forward this newsletter to your friends, relatives, and young kids. Subscribe to the 25 Math Short Cuts Newsletter today!

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:

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

Exercise 4.2. Perform the following multiplication

46 x 11 = 506
75 x 11 = 825
567 x 11 = 6,237
7,856 x 11 = 86,416
29,586 x 11 = 325,446

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

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

Exercise 5.2: Find the following products:

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

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

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

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

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

MSC 8 – Multiplying by 9

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

) 6 x 9 = 54
) 9 x 9 = 81
) 35 x9 = 315
) 49 x 9 = 441
) 82 x 9 = 738
) 148 x 9 = 1332
) 285 x 9 = 2511
) 0. 9 x 68 = 61.2
) 90% of 675 = 60.75
) 45% of 740 = 333

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

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

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

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

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

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

MSC 12 – Division by 4 and 8
Exercise 12:

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

MSC 13 – Multiplying by 25, 250, 125

Exercise 13:

36 x 25 = 900
78 x 25 = 1,950
67 x 25 = 1,675
256 x 125 = 32,000
55 x 125 = 6,875
123 x 250 =40,750
466 x 2.5 = 1,165
3599 x 25% = 899.75
2468 x 2.5% = 61.7
2552 x 1.25% = 31.9

MSC 14 – Dividing by 25, 250, 125

Exercise 14:

) 1050 ÷ 25 = 42
) 6025÷ 25 = 241
) 8375 ÷ 25 = 335
) 12,400 ÷ 250 = 49.6
) 71000÷ 125 = 568
) 5,125÷ 125 = 41
) 3,475÷ 250 = 13.9
) 830÷ 12.5 = 66.4
) 2475÷ 2.5 = 990
) 5264÷ 0.25 = 21,056

MSC 15: Squaring Numbers Ending in 5

Exercise 15: Find the square of the following numbers

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

MSC 16 – Multiplying Complementary Numbers

Exercise 16:

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

MSC 17 – Base Multiplication: Multiplying “Teen” Numbers and Others

Exercise 17: Find the following products using base multiplication

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

MSC 18: Base Multiplication – Numbers Below the Base

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

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

MSC 19: Base Multiplication: One Number Above and One Number Below the Base

Exercise 19: Find the following products using the base method

) 12 x 9 = 108
) 103 x 98 = 10,094
) 102 x 97 = 9,894
) 102 x 98 = 9,996
) 103 x 97 = 9,991
) 105 x 93 = 9,765
) 75 x 103 = 7,725
) 112 x 89 = 9,968
) 1012 x 991 = 1,002,892
) 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 =

See Answers

Discover the 25 Math Short Cuts!

25 Math Short Cuts

By Ike Prudente

This collection of 25 Math Short Cuts is published in commemoration of the 25th Foundation Day of MSC Institute of Technology.

I have selected what I think will be most useful for everyone, whether you are students, teachers, professionals or plain folks who need to calculate every day. Much of the hard work in compiling this work is not in researching for materials because I know these short cuts by heart but in selecting what short cuts to include.

From our grade school years, many of us have learned many ways of simplifying calculations. I am sure that for most of us, “multiplying by 10” is one of the first math short cut we have learned. And we continue to use it, which is the reason why I did not include it here. Unfortunately, most of us have forgotten most of the short cuts we have been taught in the past. As for my case, I am somewhat “lazy” at calculations so that I always looked for easier ways of computing. From my grade four teacher, I learned “squaring numbers ending in 5’ To this was added some more techniques which I picked-up from various books. I developed more short cuts by applying what I learned in algebra to simplify arithmetic computations. Then there were also some “tricks” I learned when I began to study “Vedic Math” in 2003, when they became available in the Internet.

$Math Short Cuts$

Even very young children can learn math short cuts, even adding left-to-right ( versus the traditional right to left )

I observed that my students enjoyed the short cuts that I shared with them and many came to love Math and actually improved their grades in the subject. I am also sure that these short cuts helped countless of my students pass the Philippine Science High School, UP Rural High School and UP entrance examinations.

Realizing that most readers like me, don’t want to read explanations, I will try to present the techniques in the form of examples, avoiding long explanations as much as possible. But sometimes we will cite Sutras or “word formulas” used in Vedic Math, which are very useful in remembering the short cuts.

We hope that with these shortcuts you will eventually be able to do most calculations mentally. However, we also realize that many will have to write down the answer first before reciting it. So we will explain the procedures to arrive at a written answer using a mental solution. With a little practice, many can dispense with the written answer.

Math Short Cuts (MSC)

We will add one short cut every week until Foundation Day 2014

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Author Archives: Roberto Prudente

MSC 25th Foundation Day

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25 Math Short Cuts Answer Key

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MSC 1 – Addition by Creating Zeroes

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25th MSC Foundation Day

MSC Scholarships

25 Math Short Cuts

MSC 1 – Addition by Creating Zeroes

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