On multiply by formula of Nikhilam :
(i) 12 × 13
Hints :
(a) Multiple number 12 = 10 + 2 which is 2 more than 10 and 13 = 10 + 3, which is 3 more than 10. We write + 2, + 3 as in form of deviation.
(b) Write the numbers up and down and deviation in front of them.
(c) Product of deviation (+ 2 × + 3) = 6, would be written on the right side of slanted line.
(d) Write 12 + 3 or 13 + 2 = 15 on left side.
(e) Product is 156 after removing the diagonal line.
(ii) 11 × 19
Hints :
(a) Multiple number 11 = 10 + 1, which is 1 more than 10, and 19 = 10 + 9, which is 9 more than 10, we write it as + 1, + 9 as in form of deviation.
(b) Write the number up and down and deviation in front of them.
(c) Product of deviation (+ 1) × (+ 9) = 9, would be written on the right side of slanted line.
(d) Write 11 + 9 or 19 + 1 = 20 on left side.
(e) Product is 209 after removing the diagonal lines.
(iii) 13 × 15
Hints :
(a) Multiple 13 = 10 + 3, which is 3 more than 10, and 15-10 + 5 which is 5 more than 10, we write + 3 and + 5 as in form of deviation.
(b) Write the numbers up and down and deviation in front of them.
(c) Product of deviations (+ 3) × (+ 5) = 15 is written on the right side of the diagonal lines.
(d) Write in the left side (13 + 5) or (15 + 3) = 18.
(e) There will be only one number on the right hand side because in base 10, there is one zero.
(f) In the product of deviation (15) unit digit 5 on R.H.S. and add 1 on the left side. (In form of base 10)
(g) On L.H.S. 18 + 1 = 19.
(h) On removing slanted line product is 195.
(iv) 8 × 7
Hints :
(a) Multiple 8 = 10 – 2, which is 2 less than 10 and 7 = 10 – 7, which is 3 less than 10, we write – 2, – 3 as in form of deviation.
(b) Write the numbers up and down and deviation in front of them.
(c) Product of deviation (- 2 × – 3) = 6, would be written on the right side of the slanted line.
(d) Write in the left side (8 – 3) or (7 – 2) = 5.
(e) On removing slanted line product is 56.
(v) 6 × 9
Hints :
(a) Multiple 6 = 10 – 4 which is 4 less than 10 and 9 = 10 – 1 which is 1 less than 10. We write – 4 and – 1 as in the form of deviation.
(b) Write the numbers up and down and deviation in front of them.
(c) Product of deviation (- 4) × (-1) = 4, would be written on the right side of the slanted line.
(d) Write in the left side (6 – 1) or ( 9 – 4) = 5.
(e) On removing slanted line product is 54.
(vi) 8 × 12
Hints :
(a) Multiple 8 = 10 – 2, which is 2 less than 10, and 12 = 10 + 2, which is 2 more than 10. We write – 2 and + 2 as in form of deviation.
(b) Write numbers up and down and deviation in front of them.
(c) Product of deviation (- 2) × (+ 2) = 4, would be written on the right of the slanted line.
(d) Write in the left side (8 + 2) or (12 – 2) = 10.
(e) The product of deviation is negative on the right hand side, for converting it into positive take 1 from left side as 1 × 10 = 10 towards right hand side.
(f) There would be 10 – 1 = 9 on the left hand side.
(g) On right hand side 10 – 4 = 6.
(h) On removing slanted line, product is 96.
(vii) 102 × 104
Hints :
(a) Multiple 102 = 100 + 02 , which is 2 more than 100 and 104 = 100 + 4 which is 4 more than 100, we write + 2 and + 4 as in form of deviation.
(b) Write the numbers up and down and deviation in front of them.
(c) Product of deviation (+ 02) × (+ 04) = 08, would be written on the right of the slanted line.
(d) Write in the left side (102 + 04) or (104 + 02) = 106.
(e) Multiplication of deviation is + 8 on the right hand side (two zeroes in 100). Therefore, there must be 2 digits on right side. So, write 08 instead of + 8.
(f) On removing slanted line, product is 10608.
