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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 = 105

1 Crore = 1,00,00,000 = 107

1 Million = 1,000,000 = 106

1 Billion = 1,000,000,000 = 109

Þ 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 unit’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 ´ 3 = 27 (Write 7 and 2 is carried over to the next step).

 

Step 2: 2 ´ 3 + 9 ´ 5 + 2 (Carried Over) = 53 (Write 3 and 5 is carried over to the next step)

 

Step 3: 2 ´ 5 + 5 (Carried Over) = 15 (Write 15 because this is the last step)

 

Therefore 1537 is the answer
 

    37

    73

 

 

Step 1: 7 ´ 3 = 21 ( Write 1 and 2 is carried over to the next step )

 

Step 2: 3 ´ 3 + 7 ´ 7 + 2 (Carried Over) = 60 (Write 0 and 6 is carried over to the next step)

 

Step 3: 3 ´ 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 unit’s digit and carry the rest to the next step)

 

Step 2: BF + CE + Carried Over (Write only the unit’s digit and carry the rest to the next step)

 

Step 3: AF + CD + BE + Carried Over ( Write only the unit’s digit and carry the rest to the next step)

 

Step 4: AE + BD + Carried Over ( Write only the unit’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 ´ 6 = 18 ( Write 8 and 1 is carried over to the next step)

 

Step 2: 2 ´ 6 + 3 ´ 5 + 1 (Carried Over) = 28 (Write 8 and 2 is carried over to the next step)

 

Step 3: 1 ´ 6 + 3 ´ 4 + 2 ´ 5 + 2 (Carried Over) = 30 (Write 0 and 3 is carried over to the next step)

 

Step 4: 1 ´ 5 + 2 ´ 4 + 3 (Carried Over) = 16 (Write 6 and 1 is carried over to the next step)   

 

Step 5: 1 ´ 4 + 1 (Carried Over) = 5 (Write 5 because this is the last step).

So 56088 is the answer.
 

243

172


  

Step 1: 3 ´ 2 = 6 (Write 6 which is the single digit number)

 

Step 2: 4 × 2 + 7 × 3 = 29 (Write 9 and 2 is carried over to the next step)

 

Step 3: 2 × 2 + 1 × 3 + 4 × 7 + 2 (Carried Over) = 37 (Write 7 and 3 is carried over to the next step)


Step 4
:
2 × 7 + 4 × 1 + 3 (Carried Over) = 21 (Write 1 and 2 is carried over to the next step)

 

Step 5: 2 × 1 + 2 (Carried Over) = 4 (Write 4 as this is the last step)

So 41796 is the answer.

 

Squaring Numbers

2. Squaring Numbers

 

Part – 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 – 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 – difference i.e. 94 – 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 3rd extra digit 1 would be carried to the left side. The left side is 86 – 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 – 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.

 





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