Multiplication -1
Same Base Method :
When both the numbers are more than the same base. This method is extension of the above method i.e.
we are going to use same sutra here and applying it to larger numbers.
When both the numbers are more than the same base. This method is extension of the above method i.e.
we are going to use same sutra here and applying it to larger numbers.
Example 1: 12 × 14
Step 1: Here base is 10
12 + 2 [12 is 2 more than 10 also called surplus]
14 + 4 [14 is 4 more than 10also called surplus]
Step 2: Cross add: 12 + 4 =16 or 14 + 2 = 16,(both same) which gives first part of answer = 16
Step 3: Vertical multiplication: 2 × 4 = 8
So, 12 + 2
14 +4
16 / 8So, 12 × 14 = 168
(14 + 2 = 12 + 4)
Step 1: Here base is 10
12 + 2 [12 is 2 more than 10 also called surplus]
14 + 4 [14 is 4 more than 10also called surplus]
Step 2: Cross add: 12 + 4 =16 or 14 + 2 = 16,(both same) which gives first part of answer = 16
Step 3: Vertical multiplication: 2 × 4 = 8
So, 12 + 2
14 +4
16 / 8So, 12 × 14 = 168
(14 + 2 = 12 + 4)
Example 2:105x 107
Step1: Here base is 100
105 + 05 [105 is 5 more than 100 or 5 is surplus]
107 + 07 [107 is 7 more than 100 or 7 is surplus]
Base here is 100 so we will write 05 in place of 5and 07 in place of 7
Step 2: Cross add: 105 + 7 = 112 or 107 + 5 = 112 which gives first part of the answer = 112
Step 3: Vertical multiplication: 05 × 07 = 35 (two digits are allowed)
As the base in this problem is 100 so two digits are allowed in the second part.
So, 105 × 107 = 11235
Step1: Here base is 100
105 + 05 [105 is 5 more than 100 or 5 is surplus]
107 + 07 [107 is 7 more than 100 or 7 is surplus]
Base here is 100 so we will write 05 in place of 5and 07 in place of 7
Step 2: Cross add: 105 + 7 = 112 or 107 + 5 = 112 which gives first part of the answer = 112
Step 3: Vertical multiplication: 05 × 07 = 35 (two digits are allowed)
As the base in this problem is 100 so two digits are allowed in the second part.
So, 105 × 107 = 11235
Example 3: 112 x 115
Step 1: Here base is 100
112 + 12 [2 more than 100 i.e. 12 is surplus]
115 + 15 [15 more than 100 i.e. 15 is surplus]
Step 2: Cross add: 112 + 15 = 127 = 115 + 12 to get first part of answer
i.e.127
Step 3: Vertical multiplication 12 × 15 = ? Oh, my god!It’s such a big number. How to get product of this? Again use the same method to get the product.
12 + 2
15 + 5
12 + 5 = 15 + 2 = 17/ (1) 0, 17 + 1 / 0 = 180 i.e. 12 × 15 = 180
But only two digits are allowed here, so 1 is added to 127 and we get (127 + 1) = 128
So, 112 × 115 = 128, 80
Step 1: Here base is 100
112 + 12 [2 more than 100 i.e. 12 is surplus]
115 + 15 [15 more than 100 i.e. 15 is surplus]
Step 2: Cross add: 112 + 15 = 127 = 115 + 12 to get first part of answer
i.e.127
Step 3: Vertical multiplication 12 × 15 = ? Oh, my god!It’s such a big number. How to get product of this? Again use the same method to get the product.
12 + 2
15 + 5
12 + 5 = 15 + 2 = 17/ (1) 0, 17 + 1 / 0 = 180 i.e. 12 × 15 = 180
But only two digits are allowed here, so 1 is added to 127 and we get (127 + 1) = 128
So, 112 × 115 = 128, 80
Try these: (i)12 × 14 (ii) 14 × 17 (iii) 17 × 19 (iv) 19 × 11 (v) 11 × 16 (vi) 112 × 113 (vii) 113 × 117 (viii) 117 × 111 (ix) 105 × 109 (x) 109 × 102 (xi) 105 × 108 (xii) 108 × 102 (xiii) 102 × 112 (xiv ) 112 × 119 (xv) 102 × 115
Both numbers less than the same base:
Same sutra applied to bigger numbers which are less than the same base.
Same sutra applied to bigger numbers which are less than the same base.
Example1: 99 × 98
Step 1: Check the base: Here base is 100 so we are allowed to have two digits on the right hand side.
99 – 01 (1 less than 100 ) i.e. 01 deficiency
98 – 02 (2 less than 100) i.e. 0 2 deficiency
Step 2: Cross – subtract: 99 – 02 = 97 = 98 – 01 both same so first part of answer is 97
Step3: Multiply vertically – 01 × – 02 = 02 (As base is 100 so two digits are allowed in second part
So, 99 × 98 = 9702
Step 1: Check the base: Here base is 100 so we are allowed to have two digits on the right hand side.
99 – 01 (1 less than 100 ) i.e. 01 deficiency
98 – 02 (2 less than 100) i.e. 0 2 deficiency
Step 2: Cross – subtract: 99 – 02 = 97 = 98 – 01 both same so first part of answer is 97
Step3: Multiply vertically – 01 × – 02 = 02 (As base is 100 so two digits are allowed in second part
So, 99 × 98 = 9702
Example 2 : 89 × 88
Step1: Here base is 100
So, 89 – 11 (i.e. deficiency = 11)
88 – 12 (i.e. deficiency = 12)
Step2: Cross subtract: 89 – 12 = 77 = 88 – 11(both same)
So, first part of answer can be 77
Step 3:Multiply vertically – 11 × – 12
Again to multiply 11 × 12 apply same rule
11 + 1 (10 + 1)
12 + 2 (10 + 2)
11 + 2 = 13 = 12 + 1 / 1 × 2 = 12 so, 11 × 12 = (1) 32 as only two digits are allowed on right hand
side so add 1to L.H.S.
So, L.H.S. = 77 + 1 = 78
Hence 89 × 88 = 7832
Step1: Here base is 100
So, 89 – 11 (i.e. deficiency = 11)
88 – 12 (i.e. deficiency = 12)
Step2: Cross subtract: 89 – 12 = 77 = 88 – 11(both same)
So, first part of answer can be 77
Step 3:Multiply vertically – 11 × – 12
Again to multiply 11 × 12 apply same rule
11 + 1 (10 + 1)
12 + 2 (10 + 2)
11 + 2 = 13 = 12 + 1 / 1 × 2 = 12 so, 11 × 12 = (1) 32 as only two digits are allowed on right hand
side so add 1to L.H.S.
So, L.H.S. = 77 + 1 = 78
Hence 89 × 88 = 7832
Example 3: 988 × 999
Step 1: As the numbers are near 1000 so the base here is 1000 and hence three digits allowed on the
right hand side
988 – 012 (012 less than 1000) i.e. deficiency = 0 12
999 – 001 (001 less than 1000) i.e. deficiency = 00 1
Step 2: Cross – subtraction: 988 – 001 = 987 = 999 – 012 = 987
So first part of answer can be 987
Step 3: Multiply vertically: –012 xs – 001 = 012 (three digits allowed)
988 × 999 = 987012
Step 1: As the numbers are near 1000 so the base here is 1000 and hence three digits allowed on the
right hand side
988 – 012 (012 less than 1000) i.e. deficiency = 0 12
999 – 001 (001 less than 1000) i.e. deficiency = 00 1
Step 2: Cross – subtraction: 988 – 001 = 987 = 999 – 012 = 987
So first part of answer can be 987
Step 3: Multiply vertically: –012 xs – 001 = 012 (three digits allowed)
988 × 999 = 987012
How to check whether the solution is correct or not by 9 – check method.
Example 1: 99 × 98 = 9702 Using 9 – check method.
As, 99 = 0 Product (L.H.S.) = 0 × 8 = 0 [taking 9 = 0]
98 = 8
R.H.S. = 9702 = 7 + 2 = 9 = 0 9702 = 9 both are same
As both the sides are equal answer may be correct.
As, 99 = 0 Product (L.H.S.) = 0 × 8 = 0 [taking 9 = 0]
98 = 8
R.H.S. = 9702 = 7 + 2 = 9 = 0 9702 = 9 both are same
As both the sides are equal answer may be correct.
Example 2: 89 × 88 = 7832
89 = 8
88 = 8 + 8 = 16 = 1 + 6 = 7 (add the digits)
L.H.S. = 8 × 7 = 56 = 5 + 6 = 11 = 2 (1 + 1)
R.H.S. = 7832 = 8 + 3 = 11 = 1 + 1 = 2
As both the sides are equal, so answer is correct
89 = 8
88 = 8 + 8 = 16 = 1 + 6 = 7 (add the digits)
L.H.S. = 8 × 7 = 56 = 5 + 6 = 11 = 2 (1 + 1)
R.H.S. = 7832 = 8 + 3 = 11 = 1 + 1 = 2
As both the sides are equal, so answer is correct
Example 3: 988 × 999 = 987012
988 = 8 + 8 = 16 = 1 + 6 =7
999 = 0
As 0 × 7 =0 = LHS
987012 = 0 (As 7 + 2 = 9 = 0 , 8 + 1 = 9 = 0 also 9 = 0 )
RHS = 0
As LHS = RHS So, answer is correct.
988 = 8 + 8 = 16 = 1 + 6 =7
999 = 0
As 0 × 7 =0 = LHS
987012 = 0 (As 7 + 2 = 9 = 0 , 8 + 1 = 9 = 0 also 9 = 0 )
RHS = 0
As LHS = RHS So, answer is correct.
Try These:
(i) 97 × 99 (ii) 89 × 89 (iii) 94 × 97 (iv) 89 × 92 (v) 93 × 95 (vi) 987 × 998 (vii) 997 × 988 (viii) 988 × 996 (ix) 983 × 998 (x) 877 × 996 (xi) 993 × 994 (xii) 789 × 993 (xiii) 9999 × 998 (xiv) 7897 × 9997
(xv) 8987 × 9996.
(i) 97 × 99 (ii) 89 × 89 (iii) 94 × 97 (iv) 89 × 92 (v) 93 × 95 (vi) 987 × 998 (vii) 997 × 988 (viii) 988 × 996 (ix) 983 × 998 (x) 877 × 996 (xi) 993 × 994 (xii) 789 × 993 (xiii) 9999 × 998 (xiv) 7897 × 9997
(xv) 8987 × 9996.
Multiplying bigger numbers close to a base: (number less than base)
Example 1: 87798 x 99995
Step1: Base here is 100000 so five digits are allowed in R.H.S.
87798 – 12202 (12202 less than 100000) deficiency is 12202
99995 – 00005 (00005 less than100000) deficiency is 5
Step 2: Cross – subtraction: 87798 -00005 =87793
Also 99995 – 12202 = 87793 (both same)
So first part of answer can be 87793
Step 2 : Multiply vertically: –12202 × – 00005 = + 61010
87798 × 99995 = 8779361010
Checking:
87798 total 8 + 7 + 7 + 8 = 30 = 3 (single digit)
99995 total = 5
LHS = 3 x 5 =15 total = 1 + 5 = 6
RHS = product = 8779361010 total = 15 = 1 + 5 = 6
L.H.S = R.H.S. So, correct answer
Step1: Base here is 100000 so five digits are allowed in R.H.S.
87798 – 12202 (12202 less than 100000) deficiency is 12202
99995 – 00005 (00005 less than100000) deficiency is 5
Step 2: Cross – subtraction: 87798 -00005 =87793
Also 99995 – 12202 = 87793 (both same)
So first part of answer can be 87793
Step 2 : Multiply vertically: –12202 × – 00005 = + 61010
87798 × 99995 = 8779361010
Checking:
87798 total 8 + 7 + 7 + 8 = 30 = 3 (single digit)
99995 total = 5
LHS = 3 x 5 =15 total = 1 + 5 = 6
RHS = product = 8779361010 total = 15 = 1 + 5 = 6
L.H.S = R.H.S. So, correct answer
Example 2 : 88777 × 99997
Step 1: Base have is 100000 so five digits are allowed in R.H.S.
88777 – 11223 i.e. deficiency is 11223
99997 – 00003 i.e. deficiency is 3
Step 2: Cross subtraction: 88777 – 00003 = 88774 = 99997 – 11223
So first part of answer is 88774
Step 3: Multiply vertically: – 11223 × – 00003 = + 33669
88777 × 99997 = 8877433669
Checking: 88777 total 8 + 8 + 7 + 7 + 7 = 37 = + 10 = 1
99997 total = 7
LHS = 1 × 7 = 7
RHS = 8877433669 =8 + 8 + 7 + 7 + 4 = 34 = 3 + 4 = 7
i.e. LHS = RHS So, correct answer
Step 1: Base have is 100000 so five digits are allowed in R.H.S.
88777 – 11223 i.e. deficiency is 11223
99997 – 00003 i.e. deficiency is 3
Step 2: Cross subtraction: 88777 – 00003 = 88774 = 99997 – 11223
So first part of answer is 88774
Step 3: Multiply vertically: – 11223 × – 00003 = + 33669
88777 × 99997 = 8877433669
Checking: 88777 total 8 + 8 + 7 + 7 + 7 = 37 = + 10 = 1
99997 total = 7
LHS = 1 × 7 = 7
RHS = 8877433669 =8 + 8 + 7 + 7 + 4 = 34 = 3 + 4 = 7
i.e. LHS = RHS So, correct answer
Try These:
(i) 999995 × 739984 (ii) 99837 × 99995 (iii) 99998 × 77338 (iv) 98456 × 99993 (v) 99994 × 84321
(i) 999995 × 739984 (ii) 99837 × 99995 (iii) 99998 × 77338 (iv) 98456 × 99993 (v) 99994 × 84321
Multiply bigger number close to base (numbers more than base)
Example 1: 10021 × 10003
Step 1: Here base is 10000 so four digits are allowed
10021 + 0021 (Surplus)
10003 + 0003 (Surplus)
Step 2: Cross – addition 10021 + 0003 = 10024 = 10003 + 0021 (both same)
First part of the answer may be 10024
Step 3: Multiply vertically: 10021 × 0003 = 0063 which form second part of the answer
10021 × 10002 = 100240063
Checking:
10021 = 1+ 2 + 1 + 1 = 4
10003 = 1 + 3 = 4
LHS = 4 × 4 = 16 = 1 + 6 = 7
RHS = 100240063 = 1 + 2 + 4 = 7
As LHS = RHS So, answer is correct
Step 1: Here base is 10000 so four digits are allowed
10021 + 0021 (Surplus)
10003 + 0003 (Surplus)
Step 2: Cross – addition 10021 + 0003 = 10024 = 10003 + 0021 (both same)
First part of the answer may be 10024
Step 3: Multiply vertically: 10021 × 0003 = 0063 which form second part of the answer
10021 × 10002 = 100240063
Checking:
10021 = 1+ 2 + 1 + 1 = 4
10003 = 1 + 3 = 4
LHS = 4 × 4 = 16 = 1 + 6 = 7
RHS = 100240063 = 1 + 2 + 4 = 7
As LHS = RHS So, answer is correct
Example 2: 11123 × 10003
Step 1: Here base is 10000 so four digits are allowed in RHS
11123 + 1123 (surplus)
10003 + 0003 (surplus)
Step 2: Cross – addition: 11123 + 0003 = 11126 = 10003 + 1123 (both equal)
First part of answer is 11126
Step 3: Multiply vertically: 1123 × 0003 = 3369 which form second part of answer
11123 × 10003 = 111263369
Checking:
11123 = 1 + 1 + 1 + 2 + 3 = 8
10003 = 1 + 3 = 4 and 4 × 8 = 32 = 3 + 2 =5
LHS = 5
R.H.S = 111263369 = 1 + 1 + 1 + 2 = 5
As L.H.S = R.H.S So, answer is correct
Step 1: Here base is 10000 so four digits are allowed in RHS
11123 + 1123 (surplus)
10003 + 0003 (surplus)
Step 2: Cross – addition: 11123 + 0003 = 11126 = 10003 + 1123 (both equal)
First part of answer is 11126
Step 3: Multiply vertically: 1123 × 0003 = 3369 which form second part of answer
11123 × 10003 = 111263369
Checking:
11123 = 1 + 1 + 1 + 2 + 3 = 8
10003 = 1 + 3 = 4 and 4 × 8 = 32 = 3 + 2 =5
LHS = 5
R.H.S = 111263369 = 1 + 1 + 1 + 2 = 5
As L.H.S = R.H.S So, answer is correct
Try These:
(i) 10004 × 11113 (ii) 12345 × 111523 (iii) 11237 × 10002 (iv) 100002 × 111523 (v) 10233 × 10005
(i) 10004 × 11113 (ii) 12345 × 111523 (iii) 11237 × 10002 (iv) 100002 × 111523 (v) 10233 × 10005
Numbers near different base: (Both numbers below base)
Example 1: 98 × 9
Step 1: 98 Here base is 100 deficiency=02
9 Base is 10 deficiency = 1
98 – 02 Numbers of digits permitted on R.H.S is 1 (digits in lower base )
Step 2: Cross subtraction: 98-188
It is important to line the numbers as shown because 1 is not subtracted from 8 as usual but from
9 so as to get 88 as first part of answer.
Step 3: Vertical multiplication: (-02) x (-1) = 2 (one digits allowed )
Second part = 2
98 × 9 = 882
Step 1: 98 Here base is 100 deficiency=02
9 Base is 10 deficiency = 1
98 – 02 Numbers of digits permitted on R.H.S is 1 (digits in lower base )
Step 2: Cross subtraction: 98-188
It is important to line the numbers as shown because 1 is not subtracted from 8 as usual but from
9 so as to get 88 as first part of answer.
Step 3: Vertical multiplication: (-02) x (-1) = 2 (one digits allowed )
Second part = 2
98 × 9 = 882
Checking:
(Through 9 – check method)
98 = 8 , 9 = 0, LHS = 98 × 9 = 8 × 0 = 0
RHS = 882 = 8 + 8 + 2 = 18 = 1 + 8 = 9 = 0
As LHS = RHS So, correct answer
(Through 9 – check method)
98 = 8 , 9 = 0, LHS = 98 × 9 = 8 × 0 = 0
RHS = 882 = 8 + 8 + 2 = 18 = 1 + 8 = 9 = 0
As LHS = RHS So, correct answer
Example 2: 993 × 97
Step 1: 993 base is 1000 and deficiency is 007
97 base is 100 and deficiency is 03
993 – 007 (digits in lower base = 2 So, 2 digits are permitted on
× 97 – 03 RHS or second part of answer)
Step 2: Cross subtraction:
993– 03
963
Again line the number as shown because 03 is subtracted from 99 and not from 93 so as to get 963
which from first part of the answer.
Step 3: Vertical multiplication: (–007) – (–03) = 21 only two digits are allowed in the second part
of answer So, second part = 21
993 × 97 = 96321
Checking: (through 9 – check method)
993 = 3 97 = 7
L.H.S. = 3 × 7 = 21 = 2 + 1 = 3
R.H.S. = 96321 = 2 + 1 = 3
As LHS =RHS so, answer is correct
Step 1: 993 base is 1000 and deficiency is 007
97 base is 100 and deficiency is 03
993 – 007 (digits in lower base = 2 So, 2 digits are permitted on
× 97 – 03 RHS or second part of answer)
Step 2: Cross subtraction:
993– 03
963
Again line the number as shown because 03 is subtracted from 99 and not from 93 so as to get 963
which from first part of the answer.
Step 3: Vertical multiplication: (–007) – (–03) = 21 only two digits are allowed in the second part
of answer So, second part = 21
993 × 97 = 96321
Checking: (through 9 – check method)
993 = 3 97 = 7
L.H.S. = 3 × 7 = 21 = 2 + 1 = 3
R.H.S. = 96321 = 2 + 1 = 3
As LHS =RHS so, answer is correct
Example 3 : 9996 base is 10000 and deficiency is 0004
988 base is 1000 and deficiency is 012
9996 – 0004 (digits in the lower base are 3 so,3digits
× 988 – 012 permitted on RHS or second part of answer)
Step 2 : Cross – subtraction:
9996– 012
9876
Well, again take care to line the numbers while subtraction so as to get 9876 as the first part of the answer.
Step3 : Vertical multiplication: (–0004) × (–012) = 048
988 base is 1000 and deficiency is 012
9996 – 0004 (digits in the lower base are 3 so,3digits
× 988 – 012 permitted on RHS or second part of answer)
Step 2 : Cross – subtraction:
9996– 012
9876
Well, again take care to line the numbers while subtraction so as to get 9876 as the first part of the answer.
Step3 : Vertical multiplication: (–0004) × (–012) = 048
(Remember, three digits are permitted in the second part i.e. second part of answer = 048
9996 × 988 = 9876048
Checking:(9 – check method)
9996 = 6, 988 = 8 + 8 + = 16 = 1 + 6 = 7
LHS = 6 × 7 = 42 = 4 + 2 = 6
RHS = 9876045 = 8 + 7 = 15 = 1 + 5 = 6
As, LHS =RHS so, answer is correct
9996 × 988 = 9876048
Checking:(9 – check method)
9996 = 6, 988 = 8 + 8 + = 16 = 1 + 6 = 7
LHS = 6 × 7 = 42 = 4 + 2 = 6
RHS = 9876045 = 8 + 7 = 15 = 1 + 5 = 6
As, LHS =RHS so, answer is correct
When both the numbers are above base
Example 1: 105 × 12
Step 1: 105 base is 100 and surplus is 5
12 base is 10 and surplus is 2
105 + 05 (digits in the lower base is 1 so, 1 digit is permitted in the second part of answer )
12 + 2
Step 2: Cross – addition:
105
+ 2
125 (again take care to line the numbers properly so as to get 125 )
First part of answer may be 125
Step 3: Vertical multiplication : 05 × 2 = (1)0 but only 1 digit is permitted in the second part so 1
is shifted to first part and added to 125 so as to get 126
105 × 12 = 1260
Checking:
105 = 1 + 5 = 6 , 12 = 1 + 2 = 3
LHS = 6 × 3 = 18 = 1 + 8 = 9 = 0
RHS = 1260 = 1 + 2 + 6 = 9=0
Example 1: 105 × 12
Step 1: 105 base is 100 and surplus is 5
12 base is 10 and surplus is 2
105 + 05 (digits in the lower base is 1 so, 1 digit is permitted in the second part of answer )
12 + 2
Step 2: Cross – addition:
105
+ 2
125 (again take care to line the numbers properly so as to get 125 )
First part of answer may be 125
Step 3: Vertical multiplication : 05 × 2 = (1)0 but only 1 digit is permitted in the second part so 1
is shifted to first part and added to 125 so as to get 126
105 × 12 = 1260
Checking:
105 = 1 + 5 = 6 , 12 = 1 + 2 = 3
LHS = 6 × 3 = 18 = 1 + 8 = 9 = 0
RHS = 1260 = 1 + 2 + 6 = 9=0
Example 2: 1122 × 104
Step1: 1122 – base is 1000 and surplus is 122
104 – base is 100 and surplus is 4
1122 + 122
104 + 04 (digits in lower base are 2 so, 2-digits are permitted in the second part of answer )
Step 2: Cross – addition
1122
+ 04 (again take care to line the nos. properly so as to get 1162)
1162
40
First part of answer may be 1162
Step 3: Vertical multiplication: 122 × 04 = 4, 88
But only 2 – digits are permitted in the second part, so, 4 is shifted to first part and added to 1162
to get 1166 ( 1162 + 4 = 1166 )
1122 × 104 = 116688
Can be visualised as: 1122 + 122
104 + 04
1162 / (4) 88 = 116688
+ 4 /
Checking:
1122 = 1 + 1 + 2 + 2 + = 6, 104 = 1 + 4 =5
LHS = 6 × 5 = 30 = 3
RHS = 116688 = 6 + 6 = 12 = 1 + 2 = 3
As LHS = RHS So, answer is correct
Step1: 1122 – base is 1000 and surplus is 122
104 – base is 100 and surplus is 4
1122 + 122
104 + 04 (digits in lower base are 2 so, 2-digits are permitted in the second part of answer )
Step 2: Cross – addition
1122
+ 04 (again take care to line the nos. properly so as to get 1162)
1162
40
First part of answer may be 1162
Step 3: Vertical multiplication: 122 × 04 = 4, 88
But only 2 – digits are permitted in the second part, so, 4 is shifted to first part and added to 1162
to get 1166 ( 1162 + 4 = 1166 )
1122 × 104 = 116688
Can be visualised as: 1122 + 122
104 + 04
1162 / (4) 88 = 116688
+ 4 /
Checking:
1122 = 1 + 1 + 2 + 2 + = 6, 104 = 1 + 4 =5
LHS = 6 × 5 = 30 = 3
RHS = 116688 = 6 + 6 = 12 = 1 + 2 = 3
As LHS = RHS So, answer is correct
Example 3: 10007 × 1003
Now doing the question directly
10007 + 0007 base = 10000
× 1003 + 003 base = 1000
10037 / 021 (three digits per method in this part)
10007 × 10003 = 10037021
Checking : 10007 = 1 + 7 = 8 , 1003 = 1 + 3 = 4
LHS = 8 × 4 = 32 = 3 + 2 = 5
RHS = 10037 021 = 1 + 3 + 1 = 5
As LHS = RHS so, answer is correct
Now doing the question directly
10007 + 0007 base = 10000
× 1003 + 003 base = 1000
10037 / 021 (three digits per method in this part)
10007 × 10003 = 10037021
Checking : 10007 = 1 + 7 = 8 , 1003 = 1 + 3 = 4
LHS = 8 × 4 = 32 = 3 + 2 = 5
RHS = 10037 021 = 1 + 3 + 1 = 5
As LHS = RHS so, answer is correct
Try These:
(i) 1015 × 103 (ii) 99888 × 91 (iii) 100034 × 102 (iv) 993 × 97 (v) 9988 × 98 (vi) 9995 × 96 (vii) 1005 × 103 (viii) 10025 × 1004 (ix) 102 × 10013 (x) 99994 × 95
(i) 1015 × 103 (ii) 99888 × 91 (iii) 100034 × 102 (iv) 993 × 97 (v) 9988 × 98 (vi) 9995 × 96 (vii) 1005 × 103 (viii) 10025 × 1004 (ix) 102 × 10013 (x) 99994 × 95
Reference : SCERT, 2014
Fore more details : Contact : dwivedi0108@gmail.com
Contact No 8989838778
Contact No 8989838778
Comments
Post a Comment