# 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 =