(i) 106 × 107
Hints :
(a) Multiple 106 = 100 + 06, which is 6 more than 100 and 107 = 100 + 7 which is 7 more than 100, we write + 06 and + 07 as in form of deviation.
(b) Write the numbers up and down and their deviation in front of them.
(c) Product of deviation + 06 × + 07 = + 42, would be written on the right side of the diagonal line.
(d) Write on the left side (106 + 07) or (107 + 06) = 113.
(e) Product of multiplication of deviation on the right hand side is + 42 and there are two zeroes in base number 100. Therefore, two digits on the right hand side.
(f) On removing slanted line, product is 11342.
(ii) 112 × 109
Hints :
(a) Multiple 112 = 100 + 12, which is 12 more than 100 and 109 = 100 + 9 which is 9 more than 100, we write 12 and + 09 as in form of deviation.
(b) Write the numbers up and down and their deviation in front of them.
(c) Product of deviation (+ 12 × + 09) = + 108 would be written on the right side of the diagonal line.
(d) Write on the left side (112 + 09) or (109 +12) = 121.
(e) On the right side multiplication of deviation is 108 (two zeroes in base 100) therefore their will be two digits in right side i.e., 08. Add 1 to the left side.
(f) On left side 121 + 1 = 122.
(g) On removing slanted line, product is 12208.
(iii) 91 × 98
Hints :
(a) Multiple 91 = 100 – 09 which is 9 less than 100 and 98 = 100 – 2, which is 2 less than 100, we write – 09 and — 02 as in form of deviation.
(b) Write the numbers up and down and their deviation in front of them.
(c) Product of deviation – 09 × – 02 = + 18, would be written on the right side of the diagonal line.
(d) Write on the left side (91 – 02) or (98 – 09) = 89.
(e) Product of deviation on right side is + 18 and there are two zeroes in base number 100. Therefore, two digits on the right hand side.
(f) On removing slanted line, product is 8918.
(iv) 96 × 94
Hints :
(a) Multiple 96 = 104 – 4 which is 4 less than 100 and 94 = 100 – 06 which is 6 less than 100. Write – 04 and – 06 as in form of deviation.
(b) Write numbers up and down and their deviation in front of them.
(c) Product of deviation – 4 × – 6 = 24, would be written on the right side of the diagonal line.
(d) Write on left side (96 — 6) or (94 – 4) = 90.
(e) Product of deviation on right side as + 24 and their are two zeroes in base number 100. Therefore, two digits on the right hand side.
(f) On removing slanted line, product is 9024.
(v) 98 × 104
Hints :
(a) Multiple 98 = 100 – 2 which is 2 less than 100 and 104 = 100 + 4 which is 4 more than 100. Write (- 2) and (+ 4) as in form of deviation.
(b) Write numbers up and down and their deviation in front of them.
(c) Product of deviation (- 2) × (4) = – 8, would be written on the right side of diagonal line.
(d) On left side right (98 + 4) or (104 – 2) = 102.
(e) Multiplication of deviation is negative on right hand side. For converting it into positive, take 1 from left side in form of 1 × 100 = 100, towards right hand side.
(f) 102 – 1 = 101, would be remainder in left side.
(g) On right side, 100 – 8 = 92.
(h) On removing slanted line, product is 10192.
(vi) 85 × 93
Hints :
(a) Multiple 85 = 100 – 15 which is less than 100 and 93 = 100 – 07 which is 7 less than 100. Write (- 15) and (- 07) as in form of deviation.
(b) Write the numbers up and down and their deviation in front of them.
(c) Product of deviation -15 × – 07 = 105, would be written on the right side of diagonal line.
(d) Write (85 – 07) or ( 93 – 15) = 78 on the left side.
(e) On the right side product of deviation is 105 (two zeroes in base 100), therefore there will be two digits in right side i.e., 05. Add 1 to the left side.
(f) Now, on left side 78 + 1 = 79.
(g) On removing slanted line, product is 7905.
