Essential Learning Points
The above can be done quickly if one has a familiarity with numbers.
Thus, tables, squares, cubes, fractions and percentages must be learnt by heart.
Tables from 1-10
Table |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
18 |
20 |
3 |
6 |
9 |
12 |
15 |
18 |
21 |
24 |
27 |
30 |
4 |
8 |
12 |
16 |
20 |
24 |
28 |
32 |
36 |
40 |
5 |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |
6 |
12 |
18 |
24 |
30 |
36 |
42 |
48 |
54 |
60 |
7 |
14 |
21 |
28 |
35 |
42 |
49 |
56 |
63 |
70 |
8 |
16 |
24 |
32 |
40 |
48 |
56 |
64 |
72 |
80 |
9 |
18 |
27 |
36 |
45 |
54 |
63 |
72 |
81 |
90 |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
90 |
100 |
11 |
22 |
33 |
44 |
55 |
66 |
77 |
88 |
99 |
110 |
12 |
24 |
36 |
48 |
60 |
72 |
84 |
96 |
108 |
120 |
13 |
26 |
39 |
52 |
65 |
78 |
91 |
104 |
117 |
130 |
14 |
28 |
42 |
56 |
70 |
84 |
98 |
112 |
126 |
140 |
15 |
30 |
45 |
60 |
75 |
90 |
105 |
120 |
135 |
150 |
16 |
32 |
48 |
64 |
80 |
96 |
112 |
128 |
144 |
160 |
17 |
34 |
51 |
68 |
85 |
102 |
119 |
136 |
153 |
170 |
18 |
36 |
54 |
72 |
90 |
108 |
126 |
144 |
162 |
180 |
19 |
38 |
57 |
76 |
95 |
114 |
133 |
152 |
171 |
190 |
20 |
40 |
60 |
80 |
100 |
120 |
140 |
160 |
180 |
200 |
Tables from 11-20
Table |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
1 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
2 |
22 |
24 |
26 |
28 |
30 |
32 |
34 |
36 |
38 |
40 |
3 |
33 |
36 |
39 |
42 |
45 |
48 |
51 |
54 |
57 |
60 |
4 |
44 |
48 |
52 |
56 |
60 |
64 |
68 |
72 |
76 |
80 |
5 |
55 |
60 |
65 |
70 |
75 |
80 |
85 |
90 |
95 |
100 |
6 |
66 |
72 |
78 |
84 |
90 |
96 |
102 |
108 |
114 |
120 |
7 |
77 |
84 |
91 |
98 |
105 |
112 |
119 |
126 |
133 |
140 |
8 |
88 |
96 |
104 |
112 |
120 |
128 |
136 |
144 |
152 |
160 |
9 |
99 |
108 |
117 |
126 |
135 |
144 |
153 |
162 |
171 |
180 |
10 |
110 |
120 |
130 |
140 |
150 |
160 |
170 |
180 |
190 |
200 |
11 |
121 |
132 |
143 |
154 |
165 |
176 |
187 |
198 |
209 |
220 |
12 |
132 |
144 |
156 |
168 |
180 |
192 |
204 |
216 |
228 |
240 |
13 |
143 |
156 |
169 |
182 |
195 |
208 |
221 |
234 |
247 |
260 |
14 |
154 |
168 |
182 |
196 |
210 |
224 |
238 |
252 |
266 |
280 |
15 |
165 |
180 |
195 |
210 |
225 |
240 |
255 |
270 |
285 |
300 |
16 |
176 |
192 |
208 |
224 |
240 |
256 |
272 |
288 |
304 |
320 |
17 |
187 |
204 |
221 |
238 |
255 |
272 |
289 |
306 |
323 |
340 |
18 |
198 |
216 |
234 |
252 |
270 |
288 |
306 |
324 |
342 |
360 |
19 |
209 |
228 |
247 |
266 |
285 |
304 |
323 |
342 |
361 |
380 |
20 |
220 |
240 |
260 |
280 |
300 |
320 |
340 |
360 |
380 |
400 |
Squares and Cubes
Students should learn the squares of numbers up to 32 and cubes upto 12 so that they do not waste time in he exam. Square roots of numbers up to 16 should also be learnt.
Equivalent Percentages of some commonly used Fractions
It is useful to learn these by heart
Fraction |
Equivalent % |
Fraction |
Equivalent % |
Fraction |
Equivalent % |
_{} |
50% |
_{} |
75% |
_{} |
22.22% |
_{} |
33.33% |
_{} |
80% |
_{} |
6.67% |
_{} |
25% |
_{} |
12.5% |
_{} |
5% |
_{} |
20% |
_{} |
8.33% |
_{} |
4% |
_{} |
16.67% |
_{} |
37.5% |
_{} |
2% |
_{} |
40% |
_{} |
62.5% |
_{} |
133.33% |
_{} |
60% |
_{} |
87.5% |
_{} |
125% |
_{} |
66.67% |
_{} |
11.11% |
_{} |
120% |
Units
Units
v 1 Lakh = 1,00,000 = 10^{5}
1 Crore = 1,00,00,000 = 10^{7}
1 Million = 1,000,000 = 10^{6}
1 Billion = 1,000,000,000 = 10^{9}
Ãž 1 Billion = 10 Crores = 1000 Million
1 Million = 10 Lakhs
v 1 Km = 1000 m.
1 m = 100 cms.
1 inch = 2.54 cms.
1 Foot = 12 inch = 30.48 cms.
1 Yard = 3 foot = 36 inch = 91.44 cms.
1 Mile = 1760 yards = 1.6 kms.
### TOPIC###Vedic Maths###
Multiplying Numbers
1. Multiplying numbers
When a 2-digit number is to be multiplied with a two-digit number the following process would be applied. If there were two numbers AB and CD then there product would be calculated as under.
AB
CD
Step 1 : BD (Write only the unitâ€™s digit and carry the rest to the next step).
Step 2 : AD + BC + Carry over (Cross multiply and Add, write a single digit and carry the rest to the next step).
Step 3 : AC + Carry over (Write the complete number because this is the last step).
29
53
Step 1: 9 Â´ 3 = 27 (Write 7 and 2 is carried over to the next step).
Step 2: 2 Â´ 3 + 9 Â´ 5 + 2 (Carried Over) = 53 (Write 3 and 5 is carried over to the next step)
Step 3: 2 Â´ 5 + 5 (Carried Over) = 15 (Write 15 because this is the last step)
Therefore 1537 is the answer
37
73
Step 1: 7 Â´ 3 = 21 ( Write 1 and 2 is carried over to the next step )
Step 2: 3 Â´ 3 + 7 Â´ 7 + 2 (Carried Over) = 60 (Write 0 and 6 is carried over to the next step)
Step 3: 3 Â´ 7 + 6 (Carried Over) = 27 (Write 27 because this is the last step)
Hence 2701 is the answer.
Multiplying a three-digit number by a three-digit number
ABC
DEF
Step 1: CF ( Write only the unitâ€™s digit and carry the rest to the next step)
Step 2: BF + CE + Carried Over (Write only the unitâ€™s digit and carry the rest to the next step)
Step 3: AF + CD + BE + Carried Over ( Write only the unitâ€™s digit and carry the rest to the next step)
Step 4: AE + BD + Carried Over ( Write only the unitâ€™s digit and carry the rest to the next step)
Step 5: AD + Carried Over ( Write the complete number cbecuase this is the last step)
123
456
Step 1: 3 Â´ 6 = 18 ( Write 8 and 1 is carried over to the next step)
Step 2: 2 Â´ 6 + 3 Â´ 5 + 1 (Carried Over) = 28 (Write 8 and 2 is carried over to the next step)
Step 3: 1 Â´ 6 + 3 Â´ 4 + 2 Â´ 5 + 2 (Carried Over) = 30 (Write 0 and 3 is carried over to the next step)
Step 4: 1 Â´ 5 + 2 Â´ 4 + 3 (Carried Over) = 16 (Write 6 and 1 is carried over to the next step)
Step 5: 1 Â´ 4 + 1 (Carried Over) = 5 (Write 5 because this is the last step).
So 56088 is the answer.
243
172
Step 1: 3 Â´ 2 = 6 (Write 6 which is the single digit number)
Step 2: 4 Ã— 2 + 7 Ã— 3 = 29 (Write 9 and 2 is carried over to the next step)
Step 3: 2 Ã— 2 + 1 Ã— 3 + 4 Ã— 7 + 2 (Carried Over) = 37 (Write 7 and 3 is carried over to the next step)
Step 4: 2 Ã— 7 + 4 Ã— 1 + 3 (Carried Over) = 21 (Write 1 and 2 is carried over to the next step)
Step 5: 2 Ã— 1 + 2 (Carried Over) = 4 (Write 4 as this is the last step)
So 41796 is the answer.
Squaring Numbers
2. Squaring Numbers
Part â€“ I: The square of a number will have two parts, the left part and the right part. There is no limit for the left side, but the right side must have as many digits as the number of zeroes in the base i.e. if 100 is taken as base there should be 2 zeroes on the right side and if 1000 is taken as base then the number of digits on RHS should be 3.
Illustration:
Take a number 92. The nearest complete base is 100. The difference between the base and the number given is 8. The square of this difference is 64, which will become the right side.
Difference of 8 is subtracted from the number given i.e. 92 â€“ 8 = 84 and it will become the left side.
Hence the square of 92 is 8464.
Illustration:
While squaring 94, the right side will be (6)^{2} i.e. 36.
The left side would be the number given â€“ difference i.e. 94 â€“ 6 = 88.
So the square of 94 is 8836.
In case, the number of digits is more than needed, then the extra digits are carried to the left side. e.g. take 86. The difference is 14 and the square of the difference is 196, which is a 3-digit number, so the 3^{rd} extra digit 1 would be carried to the left side. The left side is 86 â€“ 14 = 72 + 1 (carried over) = 73.
So the square of the number is
7 2 - -
+ - 1 9 6
7 3 9 6
Part 2
Part â€“ II : If the number to be squared is greater than the base:
In this case, difference between the number and the base is to be added in the number instead of subtracting.
Illustration:
Find the square of 107:
The difference is 7. The right side will have square of difference i.e. (7)^{2} = 49.
The left side will be 107 + 7 = 114
So the square is 11449.
The square of 103 would be: the difference is 3, its square is 9, which is a single digit number, so a 0 would be written with it i.e. 09. Then the left side is 103 + 3 = 106.
The square becomes 10609.