2. This manual is designed to show second grade school pupils the Vedic Maths
methods for multiplication.
At the end of the manual, pupils will learn alternate methods to check their
school work. It isn’t meant to replace the methods taught at school, but it is
useful in double checking their work using alternate methods.
This manual follows the South African schools’ curriculum.
3. MULTIPLES OF TEN
o You need to know multiples of 10 when you are doing sums.
What are multiples of ten? Multiples of ten end in zeroes, like:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120……
They are called multiples of ten, because you add 10 to the first number
number to get to the next number, for example: 20 + 10= 30. Another word
for them is also bases.
Practice: Colour in the 10 stars in each square below. Then add each group of
stars in tens. How much do you get?
ANSWER: 10, 20, 30
4. o There are five pairs of numbers which add up to 10 shown below. A pair
means ‘two’, like a pair of hands.
1+9=10 or write them the other way 9 + 1=10
2+8= 10 8 + 2=10
3+7= 10 7 + 3=10
4+6= 10 6 + 4=10
5+5= 10
Remember these pairs, as it will help you do your sums.
MULTIPLICATION
Multiplication is another way of adding. It’s an easy way of adding BIG
numbers.
• Example:
Mum buys 8 packets of candy bars for Halloween . The packets each have 7
bars. How many candy bars do you now have altogether?
Calculation: 8x7=?
The nearest base in this example is 10. 8 is 2 away from 10 and 7 is 3 away
from 10. Then write 2 and 3 next to each number as below.
5. 8 - 2
X 7 -3
When numbers are below a base, you cross-subtract to get the first digit
of your answer. Start writing the answer from the left hand side.
You can say 8-3 or 7 -2 and the answer either way is 5.
8 -2
X 7 -3
5
Then multiply 2 x3 to get the second digit of your answer.
8
X 7
56
EXERCISES:
a) 7x9=? b) 8x8=?
c) 7x7=? d) 8x9=?
Answers:
a) 63 b) 64 c) 49 d) 72
o CARRYING OVER A DIGIT
Sometimes there can be a digit you have to carry over in your sums.
For example: 6x7=?
6 is 4 away from 10 and 7 is 3 away from 10. You write the numbers as shown
below.
6 -4
6. X 7 -3
Then you cross-subtract. Either 6-3 or 7-4. The answer either way is 3.
6 -4
X 7 -3
3
Multiply 3x4 and you get 12. Write down 2 and carry the 1 as shown.
6
X 7
312
You add the 1 to the first digit. So the answer is 42.
EXERCISES
a) 7x5=?
b) 6x5=?
c) 6x6=?
d) 9x6=?
Answers:
a) 35 b) 30 c) 36 d) 54
MULTIPYING NUMBERS JUST OVER 10
When numbers are slightly bigger than a base, you cross-add instead of
subtracting.
For example:
12x13=?
7. 12 is 2 higher than 10 and 13 is 3 higher than 10.
12 +2
X 13 +3
Then you cross-add. You add 12+3 or 13+2. The answer is 15.
12 +2
X 13 +3
15
Then multiply 2x3 like before. And you get 6.
12
X 13
156
EXERCISES
a) 13x11=
b) 12x12=
c) 11x15=
d) 13x13=
e) 11x11=
-and with carry overs
f) 13x14=
g) 12x16=
h) 14x14=
i) 16x16=
j) 13x18=
8. Answers:
a) 143 b) 144 c) 165 d) 169 e) 121
f) 182 g) 192 h) 196 i) 256 j) 234
MULTIPLYING BIG NUMBERS CLOSE TO 100
100 is another base or whole number or multiple of ten.
Example 1:
88x98=?
88 is 12 away from 100 and 98 is 2 away from 100.
88 -12
X 98 -2
86
Because the numbers are below the base, you cross-subtract as usual. 88-2 or
98-12.The answer is 86. Then multiply 12x2 and you get 24.
88 -12
X 98 -2
8624
Example 2:
98x97=? 98 is 2 away from 100 and 97 is 3 away from 100.
98 -2
X 97 -3
Then cross-subtract, 98-3 or 97-2. The answer is 95.
98 -2
X 97 -3
95
And multiply 2x3 which equals 6. But because you are working with big
numbers close to 100, you have to put a 0 in between the 95 and 6.
9. 98
X 97
9506
EXERCISES:
a) 94 × 94 =?
b) 97 × 89 =?
c) 87 × 99 =?
d) 87 × 98 =?
e) 87 × 95=?
f) 95 × 95 =?
g) 79 × 96 =?
h) 98 × 96 =?
i) 92 × 99 =?
j) 99 × 99=?
ANSWERS:
a)8836 b) 8633 c) 8613 d) 8526 e) 8265
f) 9025 g) 7584 h) 9408 i) 9108 j) 9801
WHEN THERE IS A CARRY OVER NUMBER
Example 1:
89 X 89=?
89 is 11 away from 100.
89 -11
X 89 -11
Then you cross-subtract, as shown below.
89 -11
X 89 -11
78/
10. And you multiply 11 x 11 which is equal to 121. You write the last 2 digits of
the answer-21 and carry the 1.
89
X 89
781 /21
And the 1 to 78. The answer is 7921.
EXERCISES:
a) 88 × 88 b) 97 × 56 c) 44× 98 d) 97 × 63
ANSWERS:
a) 7744 b) 5432 c) 4312 d) 6111
NUMBERS OVER 100
Example:
103 x 104=?
The closest base for these numbers is 100 but they are bigger than the base, so
that means you have to cross-add.
103 is 3 bigger than 100 and 104 is 4 bigger than 100.
103 +3
X 104 +4
Then cross-add.
103 +3
X 104 +4
107
And multiply 3x4 which equals 12.
103
11. X 104
10712
EXERCISES
a)107 × 104 b) 107 × 108 c) 133 × 103 d) 102 × 104
ANSWERS:
a) 11128 b) 11556 c) 13699 d) 10608
