6. After learning this you will be able to find
square of a number ending with 5 say 25, 35, 45
etc.
Say you want to find square of 85
Do the following:
· Multiply 5 by 5 and put 25 as your right part of
the answer.
· Multiply 8 by the next higher digit i.e. 9 and
put 72 as your left part of the answer.
· Your answer is 7225
You can use this formula to find square of any
number ending with 5.
7. SQUARE ROOT ENDING WITH
0
First digit squaqre & put 00
e.g.
30=900
40=1600
8. Square of other number
Steps.
1. Square of last digit.
2. Both number multiply & double.
3. Square of first digit.
e.g. 48=2304
. 8 square is 64 so put 4 & carry 6
. 4 multiply by 8 & double plus carry
=32+32+6 is 70 so put 0 & 7 carry.
. 4 square is 16 + carry 7 = 23.
9. A man has 49 cows. The first cow gives one
litre milk, the second cow gives 2 litre of
milk, the third cow gives 3 litre milk & so
on up to the forty-ninth cow which gives
49 litre of milk. This man has 7 sons. He
want to divide the 49 cows with his 7 sons
in such a manner that the each child
receives the same number of cows & the
same quantity of milk.
Can you help him to do it?
10. 1) Start middle of right hand.
2) L from all right column to left.
3) L from up column to down column.
4) Next upper column.
5) One step back.
13. TO MULTI- PLY BY THE PROCEDURE
IS THIS:
MULTIPLICATION BY ELEVEN
Add the neighbour.
Each successive number of the
multiplicand is added to its
neighbour at the right.
14. MULTIPLICATION BY TWELVE
Double each number in turn
and add its neighbour.
This is the same as
multiplying by 11 except that
now we double the
"number" before we add its
"neighbour."
18. 3
First step: subtract from 10 and
double, and add 5 if the number is
odd. Middle steps: subtract from 9 and
double, add 5 if the number is odd,
and add "half" the neighbour. Last
step: take "half" the left-hand digit of
the multiplicand and reduce by 2.
19. 4
First step: subtract from 10, and
add 5 if the number is odd. Middle
steps: subtract from 9 and add
"half" the neighbour, plus 5 if the
number is odd. Last step: take
"half" the left-hand of the
multiplicand and reduce by l.
21. 6
Add 5 to the number if the
number is odd; add nothing
if it is even. Add "half" the
neighbour (dropping
fractions, if any).
22. 7
Double the number and
add 5 if the number is
odd, and add "half" the
neighbour.
23. 8
First step: subtract from 10
and double. Middle steps:
subtract from 9, double, and
add the neighbour. Last
step: reduce left-hand digit
of multiplicand by 2.
24. 9
First step: subtract from 10.
Middle steps: subtract from
9 and add the neighbour.
Last step: reduce left-hand
digit of multiplicand by l.
