Transcript How_To_Multiply - DEP

• Though this text is collection of
facts/ tricks but I am happy to tell
you that some new tricks are also
introduced in this text which are
not written earlier anywhere with
best of my knowledge.I hope that
learners of mathematics will
find it interesting and will enjoy
it. I dedicate this piece of work to
all lovers of mathematics.
U.C. Pandey
Lecturer in Mathematics
G.I.C.Dinapani Almora (U.A.)
• 1-To multiply two digit numbers with 11.
• 2-To multiply two digit numbers having tenth place digits
same and the sum of unit place numbers are 10.
• 3-Multiplying two , two digit numbers ,where difference
between them is 10 & 5 in their unit place.
• 4-To multiply two digit numbers in which either unit
place or tenth place numbers are same.
• 5-To doing square of any two digit number.
• 6-Doing square of the number where 5 is in unit place.
• 7-More about “How To Multiply”.
To multiply two digit numbers with 11
14 x 11 =
25 x 11 =
62 x 11 =
56 x 11= 5(5+6) 6 =
1 (1+4) 4 = 154
2 (2+5) 5 = 275
6 (6+2) 2 = 682
5 11 6 = 5+1 1 6 = 6 1 6
•Trick(1)- Write the number.
(2)- Put sum of the digits between these
numbers. If sum comes more than 10,
add carry in the left side digit.
Formula – ab x 11 = a a+b b
To multiply two digit numbers having tenth place
numbers same and the sum of unit place numbers are10.
48 x 42 = (4)x(4+1) 8 x2
= 4 x 5 16 = 2016
53 x 57 = (5)x (5+1) 3 x 7 = 5 x 6 21 = 3021
62 x 68 = (6)x (6+1) 2 x 8 = 6x7 16 = 4216
84 x 86 = (8)x (8+1) 4x6 = 7224
61 x 69 = (6)x(7) 1x9 = 4209
Trick-1- Multiply the unit place numbers.
2- Multiply tenth place number(which is common) with its next
number.Put it left of the former.(ab) (ac)= (a)(a+1) (b)(c) ,where b+c=10
Multiplying two , two digit numbers where
difference between them is 10 & 5 is in their
unit place.
35 x 45 = (3x4)+3 75 = 1575
45 x 55 = (4x5)+4 75 = 2475
65 x 75 = (6x7)+6 75 = 4875
85 x 95 = (8x9)+8 75 = 8075
Trick 1-Put 75 in the right of the column.
2-Multiply tenth place numbers and add lower digit
(whichever be in these two).Put that in the left of the
column. (a5 x b5) + a = axb+a 75 (here a < b)
To multiply two digit numbers in which either
unit place or tenth place numbers are same.
45 x 65 = 4x6 5(4+6) 5x5= 24 50 25 =24 50+2 5
= 245 2 5 = 24+5 2 5 =2925
36 x 34 = 3x3 3(6+4) 6x4 = 9 30 24 = 9 (30+2) 4
=9 32 4 =9+3 2 4 = 1224
72 x 32 = 7x3 2(7+3) 2x2 = 21 20 4 = 2304
Trick(1)- Multiply the unit place numbers.
(2)- Add the numbers which are different in both & multiply
them with the common number.Put it in the middle.
(3)- Multiply the tenth place digits & put them in the extreme left.
(4)- Now add carrys from right to left.
To doing square of any two
digit number.
342 = 32 2(3+4) 22 = 9 14 4 = 9+1 4 4 = 10 4 4
542 = 52 2x5x4 42 =25 40 16 = 25 40+1 6 =2916
432 = 42 2(4+3) 32 =16 14 9 = 1749
712 = 72 2(7x1) 12 = 49 14 1 = 5041
Trick1- Do square of the unit place number.
2- Multiply both digits by 2.
3- Do square of tenth place number.
4- Add carrys from right to left.
Doing square of the number
where 5 is in unit place.
252 =
352 =
652 =
1152=
2x(2+1) 52 =
3x(3+1) 52 =
6x(6+1) 52 =
11x12 52 =
6 25
1225
4225
13225
Trick1- Do square of 5 i.e. 25.
2- Multiply tenth place digit with its next
digit.Write it left of former.
Formula -:(a5)2= (a)(a+1) 25
Relation of calculation efficiency
with "How To Multiply"
100
Efficiency 50
0
1
Relation with
"How To
Multiply"
Calculation
efficiency before
using "How To
Multiply"
Calculation
efficiency After
using "How To
Multiply"
More about “How To Multiply”
• How to do cube of any
two digit number.
• How to do general
multiplications easily.
• How to find cube root
and square root of any
number.
• How to multiply two
numbers nearer to 100
,1000 etc .
• Many other tricks of
multiplication.For detail,
see book “How To multiply”.
Gratitude
• I am grateful to old Indian
mathematicians who gave
me clues to work on How
To Multiply.
The end