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

MSC 8 – Multiplying by 9

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

 

MSC 13 – Multiplying by 25, 250, 125

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

MSC 14 – Dividing by 25, 250, 125

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

MSC 15:  Squaring Numbers Ending in 5

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

 

MSC 16 – Multiplying Complementary Numbers

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

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

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

MSC 18: Base Multiplication – Numbers Below the Base

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

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

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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