It is always a fun to play with numbers. Aspirants preparing for Bank exams & other competitive exams have to be quick enough to perform calculations within seconds. If they will follow the basic approach for performing calculations, they will lag behind.
Someone has rightly said,
“Effort is important, but knowing where to make an effort makes all the difference”
Calculation is an important part of Quantitative Aptitude section in every competitive exam. Through this blog, we would like to share with our readers Short-tricks on Squares & Multiplication which will definitely help them to perform quick calculations & save time in the upcoming Bank exams.
Shortcut Tricks to solve Squares
Type I: (80-100)
Assume 100 as the base since 80-100 is near to 100.
Example 1: 93^{2}
Base = 100
Step 1: Calculate the difference between base and number
100-93 = 7
Step 2: Subtract the difference from the number
93-7= 86
Step 3: Calculate the square of the difference
7^{2 }= 49
Answer = 8649
Example 2: 82^{2}
In order to calculate the square of 82, we will follow similar steps mentioned in example 1:
Base =100
100-82 =18
82-18= 64
18^{2} = 324
This square is 3 digit no., however, we are calculating from 100, where we assumed base which has 2 zeros,
So, the new no. becomes = 64__324
This 3 will be carried forward and will be added to 64.
Therefore, the correct answer is = (64+3)__24
= 6724
Type II: 100-120
Example 3: 103^{2}
Step 1: Difference between 103 and 100 (i.e 3)
Step 2: Add this difference to the base i.e 100
= 100+3
= 103
Step 3: 103+3
= 106
Step 3: Calculate the square of the difference
3^{2 }= 9
Note: 9 is a single digit no. and we are assuming 100 as base
Therefore, we will add zero before 9 .
Correct answer = 106_09
Example 4: 114^{2}
114+14 = 128
14^{2 }= 196
Square is a 3 digit no., however we are calculating assuming the base to be 100
Therefore, we will carry forward the 1 and add it to 128.
Correct answer = (128+1)__96
= 12996
Type III: 50-70
Base -50
25 + Difference between given no. & 50_Sqaure of the difference |
Example 5: 54^{2}
=(25+4)__4^{2}
=2916
Example 6: 63^{2}
= (25+13)__(13)^{2}
= 38__169
1 will be carried forward and added to 38 to reach the correct answer
= (38+1)__69
= 3969
Type IV: 30-50
Base- 50
25- difference between the given no. & 50_Sqaure of the difference |
Example 7:
47^{2 }
^{ }= (25-3)__3^{2}
= 2209
Example 8:
36^{2}
= (25-14)__14^{2}
= 11_196
We will carry forward 1 and add it to 11
Therefore, the correct answer= 12_96
Example 9:
32^{2}
= (25-18)__18^{2}
= 1024
Type V: 71-79
This category can be calculated assuming both the bases 50 as well as 100.
Example 10: 74^{2}
i.Base 50
(25+24)_24^{2}
49_576 (We will carry forward 5 and add it to 49)
Correct answer =5476
ii.Base 100
(74-26)_26^{2}
48_676
We will carry forward 6 and add it to 48.
Correct answer = 5476
Tricks to solve Multiplications
(A) Multiplication of Numbers having 5 at their unit places
Type I: When the nos. are same
In this if questions, we fix 25 in the end and multiply first digit with the next digit. Let us go through examples to understand it better:
Example 11:
65 *65
=6*7_25
=4225
Example 12:
55 * 55
= 5*6_25
=3025
Example 13:
125*125
=(12*13)_25
= 15625
Type II: When nos. have difference of 10
Example 14:
45*55
(4*6)_75
2475
105*105
= (10*12)_75
=12075
Example 15:
185*195
=(18*20)
=36075
Type III: When nos. have a difference of 20
Example 16:
45*65
= (4*7)_125 (Fix 125 in the last and multiply 4*7)
Note: From 125, we will carry forward 1 to the digits multiplied)
Correct answer = (28+1)_25
= 2925
Example 17:
95*115
=(9*12)_125
=(108+1)25
=10925
Example 18:
185*205
(18*21)_125
(378+1)_25
37925
Type IV: When the difference between the nos. is 30
Example 19:
55*85
Fix 175 in the end and multiply 5 and 9.
(5*9)_175
From this 175, 1 will be carried forward to the digits multiplied to find the correct answer.
Correct answer = 4675
Example 20:
125*155
=(12*16)-175
=19375
(B) Multiplication by 25
Whenever we have to multiply by 25,instead of directly multiplying by 25, we should rather multiply by 100 and divide by 4 in order to follow an easy approach.
Let us understand it with the help of examples:
Example 21
52*25
=52*100/4
=1300
Example 22:
112*25
=112*100/4
=2800
(C) Multiplication by 50
Whenever we have to multiply by 50, we should multiply by 100 and divide by 2 in order to make our calculations easy.
Example 23:
28*50
=28*100/2
=1400
(D) Multiplication using Multiples
Directly multiplying 2 nos. is time consuming, so we must follow multiples approach wherever it is suitable so make our calculations easy.
Example 24:
15*18
=15*6*3 (Here we have split 18 into 6*3)
= 180
(E) Consecutive Number Multiplication
Square of smaller number + Smaller number |
Example 25:
25*26
= (25)^{2} + 25
= 625 + 25
= 650
(F) Rule of Multiply of 100(+)
This rule is used where the nos. to be multiplied are more than 100
Example 26:
105*109
+9 +5 and 9*5=45
(105+9)_(+9)*(+5) OR (109+5)_(+5)*(+9)
114_45 =114_45
11445 =11445
Example 27:
1009*1012
Here, we will take Base as 1000 instead of 100 since the no. is a 4-digit number.
1009* 1012
+12 +9 and 12*9 =108
(1009+12)_(12*9)
1021_108
1021108
(G) Rule of Multiply of 100(-)
Example 28:
94*96
-4 -6 and (-4)*(-6)
(94-4)_24
90_24
=9024
Example 29:
494*483
Here the digits are near 500. So we assume base to be 500
494*483
(-17) (-6) and (-17)*(-6)
(494-17)_102
477_102
Important Note: We have taken Base-500 instead of 100 i.e 5 times of 100. So, now we multiply 477 with 5 which amounts to 2385.
2385_102 (Since the base as 2 zeros we will carry forward 1 from 102 and add it to 2385)
So, the correct answer is (2385+1)_02
=238602
(H) Rule of Multiply of 100(+) and 100 (-)
Example 30:
96*107
(+7) (-4) and (+7)*(-4)
(96+7)_(-28)
103_(-28)
=10300-28
=10272
Example 31:
91*116
+16 -9
(91+16) and (+16)*(-9)
107_(-144)
10700-144
=10556
(I) Unit’s digit 10
We use this approach when the sum of unit’s digit is 10 and ten’s digit is same.
Let us understand it with the help of an example:
Example 32:
46*44
Here the sum of unit’s digits (i.e 6+4 =10) is 10 and tenis digit is same i.e 4.
4*5_6*4 (We have multiplied the units digit with the next consecutive no. and ten’s digit of both the nos.)
20_24
2024
Example 33:
52*58
5*6_2*8
=3016
(I) Multiplication by 11
Type 1: If sum of digits is greater than 10
Example 34:
67*11
=6_7
Therefore, middle no. is 6+7 =13
Since middle no. is more than 10, use 3 and add then add 1 to the first term
737
Type 2: If sum of digits is less than 10
Example 35:
52*11
5_2
Sum of middle terms = 5+2
=7
Place the middle between 5 and 2
Correct answer= 572
We hope we have made it easy for all the aspirants to calculate squares and solve multiplication. It is sincere advice, if you want to use these short-tricks at exam time, keep practicing these tricks on daily basis.
Good Luck
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