विनजीत वैदिक अंकगणित पुस्तक || 1 || अध्याय 14.05 || 11 के गुणज से गुणा (Type 1C)
Vinjeet Vedic Arithmetic Book || 1 || Chapter 14.05 || Multiplication by multiples of 11 (Type 1C)
Author
ॐ जितेन्द्र सिंह तोमर
(M.A., B. Ed., MASSCOM, DNYS )
(Specialist in Basic and Vedic Maths)
अध्याय 14.05
गुण्यांक = गुणकांक 11 या 11 के गुणज
Multiplicand = Multiplayer 11 Or Multiple of 11
पिछले भाग में हमने संख्या 11 से किसी भी संख्या का गुणा करना सीखा। इसके लिए सबसे अच्छा मेथड स्लैशिंग मेथड रहा ।
चलिए हम अब इस अध्याय में 11 और उसके गुणजों अर्थात मल्टीपल्स (11, 22, 33, 44, 55, 66, 77, 88, 99, 110 आदि) से गुणा करना सीखेंगे।
11 से गुणा करने का स्लाइसिंग मेथड इस प्रकार है।
In the previous section we learned how to multiply any number by the number 11. The best method for this was slashing method.
Let us now learn to multiply by 11 and its multiples i.e. multiples (11, 22, 33, 44, 55, 66, 77, 88, 99, 110 etc.) in this chapter.
The slashing method of multiplying by 11 is as follows.
01. स्लैशिंग तथा बैलेंसिंग द्वारा
01. By Slashing And Balancing Method
AB × 11 = A/(A+B)/B
ABC × 11 = A/(A+B)/(B+C)/C
ABCD × 11 = A/(A+B)/(B+C)/(C+D)/D
आदि द्वारा।
अब थोड़ा सा ध्यान यदि हमें 22 से गुणा करने हैं तो हम स्लैशिंग टूल का ही उपयोग कर सकते हैं। कैसे नीचे देखें और समझे।
Now pay a little attention, if we have to multiply by 22 then we can use slashing tool only, see below and understand how.
★ 22 से गुणा करने के लिए
★ to multiply by 22
AB × 22
= AB × 2 × 11
= 2 (AB × 11)
=2 [ A/(A+B)/B ]
★ 33 से गुणा करने के लिए
★ to multiply by 33
AB × 33
= AB × 3 × 11
= 3 (AB × 11)
= 3 [ A/(A+B)/B ]
★ 44 से गुणा करने के लिए
★ to multiply by 45
AB × 44
= AB × 4 × 11
= 4 (AB × 11)
= 4 [ A/(A+B)/B ]
★ 55 आदि से गुणा करने के लिए
★ to multiply by 55
AB × 55
= AB × 5 × 11
= 5 (AB × 11)
= 5 [ A/(A+B)/B ]
Practice Time 01
11से गुणा करना हम पिछले अध्याय 14.03 में सीख चुके हैं। इस अध्याय को करने से पहले 14.03 अध्याय अवश्य कर लें।
We have learned how to multiply by 11 in the previous chapter 14.03. Before doing this chapter, make sure to do chapter 14.03.
(1) 12 × 11
(2) 99 × 11
(3) 23 × 11
(4) 87 × 11
(5) 34 × 11
(6) 167 × 11
(7) 256 × 11
(8) 346 × 11
(9) 432 × 11
(10) 579 × 11
(11) 1274 × 11
(12) 3473 × 11
(13) 4558 × 11
(14) 7896 × 11
(15) 9236 × 11
Sol. (1) 12 × 11
= 1/(1+2)/2
= 1/3/2
= 132
Sol. (8) 167 × 11
= 1/(1+6)/(6+7)/7
= 1/7/¹3/7
= 1837
Sol. (15) 1274 × 11
= 1/(1+2)/(2+7)/(7+4)/4
= 1/3/9/¹1/4
= 14014
Practice Time 02
(1) 12 × 22
(2) 99 × 22
(3) 23 × 22
(4) 87 × 22
(5) 34 × 22
(6) 167 × 22
(7) 256 × 22
(8) 346 × 22
(9) 432 × 22
(10) 579 × 22
(11) 1274 × 22
(12) 3473 × 22
(13) 4558 × 22
(14) 7896 × 22
(15) 9236 × 22
Sol. (1) 12 × 22
= 12 × 11 × 2
= 2 × 12 × 11
= 2 [ 12 × 11 ]
= 2 [1/(1+2)/2]
= 2 [1/3/2]
= 2 [132]
= 264
Sol. (6) 167 × 22
= 167 × 11 × 2
= 2 × 167 × 11
= 2 [ 167 × 11 ]
= 2 [1/(1+6)/(6+7)/7]
= 2 [1/7/¹3/7]
= 2 [1837]
= 3674
Sol. (11) 1274 × 22
= 1274 × 11 × 2
= 2 × 1274 × 11
= 2 [ 1274 × 11 ]
= 2 [1/(1+2)/(2+7)/(7+4)/4]
= 2 [1/3/9/¹1/4]
= 2 [14014]
= 28028
Practice Time 03
(1) 12 × 33
(2) 99 × 33
(3) 23 × 33
(4) 87 × 33
(5) 34 × 33
(6) 167 × 33
(7) 256 × 33
(8) 346 × 33
(9) 432 × 33
(10) 579 × 33
(11) 1274 × 33
(12) 3473 × 33
(13) 4558 × 33
(14) 7896 × 33
(15) 9236 × 33
Sol. (1) 12 × 33
= 12 × 11 × 3
= 3 × 12 × 11
= 3 [ 12 × 11 ]
= 3 [1/(1+2)/2]
= 3 [1/3/2]
= 3 [132]
= 396
Sol. (6) 167 × 33
= 167 × 11 × 3
= 3 × 167 × 11
= 3 [ 167 × 11 ]
= 3 [1/(1+6)/(6+7)/7]
= 3 [1/7/¹3/7]
= 3 [1837]
= 5511
Sol. (11) 1274 × 33
= 1274 × 11 × 3
= 3 × 1274 × 11
= 3 [ 1274 × 11 ]
= 3 [1/(1+2)/(2+7)/(7+4)/4]
= 3 [1/3/9/¹1/4]
= 3 [14014]
= 42042
Practice Time 04
(1) 12 × 44
(2) 99 × 44
(3) 23 × 44
(4) 87 × 44
(5) 34 × 44
(6) 167 × 44
(7) 256 × 44
(8) 346 × 44
(9) 432 × 44
(10) 579 × 44
(11) 1274 × 44
(12) 3473 × 44
(13) 4558 × 44
(14) 7896 × 44
(15) 9236 × 44
Sol. (1) 12 × 44
= 12 × 11 × 4
= 4 × 12 × 11
= 4 [ 12 × 11 ]
= 4 [1/(1+2)/2]
= 4 [1/3/2]
= 4 [132]
= 528
Sol. (6) 167 × 44
= 167 × 11 × 4
= 4 × 167 × 11
= 4 [ 167 × 11 ]
= 4 [1/(1+6)/(6+7)/7]
= 4 [1/7/¹3/7]
= 4 [1837]
= 7348
Sol. (11) 1274 × 44
= 1274 × 11 × 4
= 4 × 1274 × 11
= 4 [ 1274 × 11 ]
= 4 [1/(1+2)/(2+7)/(7+4)/4]
= 4 [1/3/9/¹1/4]
= 4 [14014]
= 56056
Practice Time 05
(1) 12 × 55
(2) 99 × 55
(3) 23 × 55
(4) 87 × 55
(5) 34 × 55
(6) 167 × 55
(7) 256 × 55
(8) 346 × 55
(9) 432 × 55
(10) 579 × 55
(11) 1274 × 55
(12) 3473 × 55
(13) 4558 × 55
(14) 7896 × 55
(15) 9236 × 55
Sol. (1) 12 × 55
= 12 × 11 × 5
= 5 × 12 × 11
= 5 [ 12 × 11 ]
= 5 [1/(1+2)/2]
= 5 [1/3/2]
= 5 [132]
= 660
Sol. (6) 167 × 55
= 167 × 11 × 5
= 5 × 167 × 11
= 5 [ 167 × 11 ]
= 5 [1/(1+6)/(6+7)/7]
= 5 [1/7/¹3/7]
= 5 [1837]
= 9185
Sol. (11) 1274 × 55
= 1274 × 11 × 5
= 5 × 1274 × 11
= 5 [ 1274 × 11 ]
= 5 [1/(1+2)/(2+7)/(7+4)/4]
= 5 [1/3/9/¹1/4]
= 5 [14014]
= 70070
Practice Time 02
(1) 3242 × 11
(2) 9913 × 22
(3) 4343 × 33
(4) 8723 × 44
(5) 5456 × 55
(6) 7965 × 66
(7) 4789 × 77
(8) 6767 × 88
(9) 5867 × 99
(10) 4765 × 110
(11) 23923 × 11
(12) 37191 × 22
(13) 46232 × 33
(14) 58343 × 44
(15) 67545 × 55
(16) 127434 × 66
(17) 235587 × 77
(18) 349767 × 88
(19) 453568 × 99
(20) 568967 × 110
Sol. (1) 3242 × 11
= 3/(3+2)/(2+4)/(4+2)/2
= 3/5/6/6/2
= 35662
Sol. (11) 23923 × 11
= 2/(2+3)/(3+9)/(9+2)/(2+3)/3
= 2/5/¹2/¹1/5/3
= 2/6/3/1/5/3
= 263154
Sol. (16) 127434 × 66
= 1274 × 11 × 6
= 6 × 1274 × 11
= 6 [1/(1+2)/(2+7) /(7+4)/ (4+3)/ (3+4)/4]
= 6 [1/3/9/¹1/7/7/4]
= 6 [1401664]
= 8409984
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