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Art. 9. To multiply a number by 25: Multiply 4 of the number by 100. Why?

48 x 25 1 of 48 x 100 = 1200
49 x 25 of 49 x 100 = 1225

Multiply :
36 by 25 32 by 25 33 by 25
40 by 25 28 by 25 29 by 25
24 by 25 16 by 25 19 by 25

52 by 25 48 by 25 50 by 25

(i) Find the sum of the twelve products. Art. 10. To multiply a number by 26: Take 25 times the number, to which add the number itself. Why?

36 x 26 25 times 36 = 900 900 + 36 = 936
37 x 26 25 times 37 = 925 925 + 37 = 962

Multiply:
36 by 26 48 by 26 45 by 26
28 by 26 24 by 26 25 by 26
44 by 26 32 by 26 35 by 26
52 by 26 16 by 26

18 by 26 (j) Find the sum of the twelve products. Art. 11. To multiply a number by 27: Take 25 times the number, to which add twice the number. Why?

36 x 27 25 times 36 = 900 900 + 72= 972
37 x 27 25 times 37 = 925 925 + 74= 999

Multiply:
48 by 27 52 by 27 37 by 27
32 by 27 16 by 27 17 by 27
28 by 27 24 by 27 26 by 27

44 by 27 56 by 27 35 by 27
(k) Find the sum of the twelve products.

Art. 12. To multiply a number by 24: Take 25 times the number, from which subtract the number itself. Why?

32 x 24 25 times 32 = 800 800 – 32= = 768
33 x 24 25 times 33 = 825 825 - 33 = 792

Multiply:
24 by 24 16 by 24 17 by 24
44 by 24 36 by 24 37 by 24
28 by 24 32 by 24 35 by 24

48 by 24 52 by 24 54 by 24

(1) Find the sum of the twelve products. Art. 13. To multiply a number by 20: Multiply } of the number by 100. How may a number be multiplied by 21 ? by 22? by 19 ? 35 x 21 20 times 35= 700 700 + 35 = 735

Multiply:
45 by 21 45 by 22 45 by 19
35 by 21 35 by 22 35 by 19
36 by 21 36 by 22 36 by 19

27 by 21 27 by 22 27 by 19

(m) Find the sum of the twelve products. Art. 14. To multiply a number by 16: Multiply d of the number by 100. How may a number be multiplied by 173 ? by 183? by 15? 24 x 17

163 times 24 = 400 400 + 24 = 424

Multiply:
18 by 17 18 by 183 18 by 15
30 by 173 30 by 183 30 by 15ş
36 þy 17

36 by 183 36 by 15%
42 by 17% 42 by 183 42 by 153
(n) Find the sum of the twelve products.

Art. 15. To multiply a number by 121: Multiply of the number by 100. How may a number be multiplied by 131? by 141? by 111? 32 x 131

121 times 32= 400 400 + 32=432

Multiply:
24 by 131
24 by 141

24 by 111
16 by 13

16 by 143 16 by 111 40 by 131 40 by 141 40 by 111 48 by 133 48 by 14) 48 by 111

(0) Find the sum of the twelve products. Art. 16. To multiply a number by 125: Multiply s of the number by 1000. How may a number be multiplied by 126? by 127 ? by 124 ?

96 x 125 of 96 x 1000 = 12000
96 x 126. 125 times 96 = 12000 12000 + 96 = 12096

Multiply:
120 by 126 120 by 127 120 by 124
320 by 126 320 by 127 320 by 124
240 by 126 240 by 127 240 by 124

(p) Find the sum of the nine products. Art. 17. To multiply a number by 250: Multiply 1 of the number by 1000. How may a number be multiplied by 251? by 252 ? by 249 ?

48 x 250 of 48 x 1000= 12000
48 x 251 250 times 48 = 12000 12000 + 48= 12048

Multiply:
60 by 251 60 by 252 60 by 249
72 by 251 72 by 252 72 by 249
96 by 251 96 by 252 96 by 249
(q) Find the sum of the nine products.

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Art. 18. To square 21, 31, 41, etc. : Multiply the integer by the integer plus 1, and add 1 to the product.

21 x 21 = 2 times 2+ 2 times 1 + 1 of 2 + 1 of 1
But 2 times 1 + 1 of 2=1 time 2; and 1 of 1 = 1
Hence, 21 x 21 = 2 x 3+1= 61
34 x 31 = 3 x++1=127

Multiply:
41 by 41 51 by 51 61 by 61
7} by 71 81 by 81 91 by 91
17 by 11 21 by 21 31 by 32
(r) Find the sum of the nine products.

Art. 19. To square 25, 35, 45, etc.: Multiply the tens' figure* by the tens' figure increased by 1; regard the product as hundreds, to which add 25.

To explain this rule, think of 25 as 2 tens and 1 of a ten, and apply the explanation given under Art. 18.

25 x 25 = 2 X 3 hundred and 25 = 625
35 x 35= 3 X 4 hundred and 25 = 1225
45 x 45=4 x 5 hundred and 25 = 2025

Multiply:
55 by 55 65 by 65 75 by 75
85 by 85 95 by 95 15 by 15
(s) Find the sum of the six products.

* The author is aware that the expressions “Multiply the tens' figure" and "the tens' figure increased by 1,” are tabooed by the hypercritical. But it is believed that neither obscurity nor misconception will arise from this use of the word figure. The word as here used clearly means the form value of the figure - the number which the figure by virtue of its shape represents.

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Art. 20. To multiply 24 by 24, 31 by 34, etc. : Multiply the integer by the integer plus 1, and to the product add the product of the fractions.

Observe that this rule will apply only when the integer of the multiplicand and the integer of the multiplier are the same, and the sum or the fractions is 1.

21 by 24 = 2 times 2 + 2 times 1 + $ of 2+ 8 of 1
But 2 times 1 + 4 of 2 =1 time 2, and 1 of 1 = 16

Hence 24 x 24 = 2 x 3 + 4 of

31 x 34 = 3 x 4 +of }=122
24 x 24 = 2 x 3 + of = 63

Multiply :
4} by 43 51 by 54 6} by 63
77 by 7 8j by 83 91 by 94

(t) Find the sum of the six products. Art. 21. To multiply 24 by 26, 33 by 37, etc.: Multiply the tens' figure by the tens' figure increased by 1; regard the product as hundreds, to which add the product of the units' figures.

Observe that this rule will apply only when the tens' figure of the multiplicand and the tens' figure of the multiplier are alike, and the sum of the units' figures is 10.

22 x 28 = 2 x 3 hundred and 16 = 616
33 x 37 = 3 X 4 hundred and 21 = 1221
44 x 46 = 4 x 5 hundred and 24 = 2024

Multiply :
21 by 29 23 by 27 24 by 26
31 by 39 32 by 38 34 by 36

41 by 49 42 by 48 43 by 47
(u) Find the sum of the nine products.

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