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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