How To Multiply

1. How To Multiply

2. Preface • 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.)

3. Index • 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”.

4. To multiply two digit numbers with 11 14 x 11 = 1 (1+4) 4 = 154 25 x 11 = 2 (2+5) 5 = 275 62 x 11 = 6 (6+2) 2 = 682 56 x 11= 5(5+6) 6 = 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

5. 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

6. 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)

7. 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.

8. 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 Trick- 1- 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.

9. Doing square of the number where 5 is in unit place. 252 = 2x(2+1) 52 = 6 25 352 = 3x(3+1) 52 = 1225 652 = 6x(6+1) 52 = 4225 1152= 11x12 52 = 13225 Trick- 1- 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

11. 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”.

12. Gratitude • I am grateful to old Indian mathematicians who gave me clues to work on How To Multiply. The end