Art force school in wind tunnel road.

We had conducted the workshop in Arr force school in wind tunnel road for the standard between 8th to 12 and we had the great experience and response from the students. We will be happy to conduct such workshop to teachers and students in near feature.

from fun and activity learning

Speed Maths Session 6

Dear Friends,

Sorry for not updating for long time. Today my daughter Varsshini had a home work about what number is divisible by what number. I just pushed that content here.

Divisibility by 2: If its units digit is any of 0,2,4,6,8.
Ex : 100 is divisible by 2 while 101 is not.

Divisibility by 3: If the sum of its digits is divisible by 3.
Ex: 309 is divisible by 3, since sum of its digits = (3+0+9) = 12 , which is divisible by 3.

Divisibility by 4: If the number formed by the last two digits is divisible by 4

Ex: 2648 is divisible by 4, since the number formed by the last two digits is 48 which is divisible by 4.

Divisibility by 5: If its units digit is either 0 or 5.
Ex: 20825 and 50545 are divisible by 5.

Divisibility by 6: If it is divisible by both 2 & 3.
Ex: 53256 is divisible by 6 because it is divisible by 2 as well as 3.

Divisibility by 7: If after subtraction of a number consisting of the last three digits from a number consisting of the rest of its digits the result is a number that can be divided by 7 evenly

Ex.: 414141 is divisible 7 as 414-141= 273 is divisible by 7

Many different ways to test divisibility by seven have been devised. Some are long and complex, a few involve rewriting the digits, and one even consists of a grid-like box. We have chosen one of the more simplistic versions even though in almost every case it is quicker to merely perform long division.

Divisibility by 8: If the last three digits of the number are divisible by 8.
Ex: 3652736 is divisible by 8 because last three digits (736) is divisible by 8.

Divisibility by 9: If the sum of its digit is divisible by 9.
Ex: 672381 is divisible by 9, since sum of digits = (6+7+2+3+8+1) = 27 is divisible by 9.

Divisibility by 10: If the digit at units place is 0 it is divisible by10.
Ex: 69410, 10840 is divisible by 10.

Divisibility by 11: If the difference of the sum of its digits at odd places and sum of its digits at even places, is either 0 or a number divisible by 11.
Ex: 4832718 is divisible by 11, since:
(Sum of digits at odd places) subtract (sum of digits at even places)
= (8+7+3+4)-(1+2+8) = 11

Divisibility by 12: A number is divisible by 12 if it is divisible by both 4 and 3.
Ex: 34632
(i) The number formed by last two digits is 32, which is divisible by 4
(ii) Sum of digits = (3+4+6+2) = 18, which is divisible by 3.

Divisibility by 13: Remove the last digit of a number. Multiply it by 4 and add it to the remaining truncated number. Â Continue doing these steps until you reach a 2 digit number. If the result is divisible by 13, then so was the first number.

Example: 113945-->11394+20=11414-->1141+16=1157-->115+28=143 (since this number is divisible by 13, you can say 113945 is also divisible by 13)

You can go a step forward

14 + 12 = 26 is 2*13, so 113945 is divisible by 13.

Divisibility by 14: If a number is divisible by 2 as well as 7.

Divisibility by 15: If a number is divisible by both 3 & 5.

Divisibility by 16: If the number formed by the last 4 digits is divisible by 16.
Ex: 7957536 is divisible by 16, since the number formed by the last four digits is 7536, which is divisible by 16.

Divisibility by 24: If a number is divisible by both 3 & 8.

Divisibility by 40: If it is divisible by both 5 & 8.

Divisibility by 80: If a number is divisible by both 5 & 16.


Thanks
Ramesh S Babu

Speed Maths Session 5

Dear Friends,

I was waiting for exam to get over . I'm back now :-)

MULTIPLYING NUMBERS ABOVE 100

Here we talk about multiply number above its base or reference number.

We will take 108 x 102

We will take 100 as its reference number like what we did in earlier sessions

For the session 3 we know what number to add to make the number 100 and now we will see what need to subtract to make it 100


So we take 108 and need 8 to minus to make it 100

108 - 8

And for 102, it is 2 to minus to make it 100

102 - 2

So we take like this, I put plus sign between the original number and its different

108 + 8

102 + 2


In session 3 we will subtract the different number in cross. Now we need to add in cross. E.g. add 8 to 102 or 2 to 108 so

108 + 2 = 110

102 + 8 = 110

So the left hand side answer is 110 and its 100 base so 11000(110 * 100)

Now second part of result is +2 x +8 = 16

So the answer is 11000 + 16 = 11016

I hope you understood, any clarification kindly revert back to me.


Practice
a) 112 × 105 =

b) 103 × 114 =

c) 112 × 102 =

d) 113 × 103 =

e) 112 × 104 =

f) 102 × 106 =

g) 104 × 114 =

h) 115 × 105 =

i) 112 × 108 =

j) 106 × 114 =

Thanks
Ramesh

Speed Maths Session 4

MULTIPLYING NUMBERS ABOVE 10

Here we talk about multiply number above its base or reference number.

We will take 13 x 14

We will take 10 as its reference number like what we did in session for any number above 5 and below 10

For the session 1 we know what number to add to make the number 10 and now we will see what need to subtract to make it 10

So we take 13 and need 3 to minus to make it 10

13 - 3

And for 14, it is 4 to minus to make it 10

14 - 4


So we take like this, I put plus sign between the original number and its different

13 + 3

14 + 4

In session 1 we will subtract the different number in cross. Now we need to add in cross. E.g. add 4 to 13 or 3 to 14 so

14 + 3 = 17

13 + 4 = 17

So the left hand side answer is 17 and its 10 base so 170

Now second part of result is +3 x +4 = 12

So the answer is 170 + 12 = 182

I hope you understood, any clarification kindly revert back to me.

Practice
a) 12 × 15 =

b) 13 × 14 =

c) 12 × 12 =

d) 13 × 13 =

e) 12 × 14 =

f) 12 × 16 =

g) 14 × 14 =

h) 15 × 15 =

i) 12 × 18 =

j) 16 × 14 =

Have nice fun with day to day math’s

Thanks

Ramesh

Speed Maths Session 3

Dear Friends,

THE SPEED MATHEMATICS METHOD

Today we will learn double multiplication. We will take 92 x 94

as per our earlier session we multiply 92x94


92

x 94



We now look at each number and ask how many more do we need to make 100?


We start with the 92. If we have 92, how many more do we need to make 100?

The answer is 8. 92 plus 8 equals 100. We write 8 next to the 92. Our equation now looks like this:



92 - 08

x 94



We now go to 94. How many more to make 100? The answer is 6.

We write 6 next to the 94.

This is how the problem looks now:

92 - 08

x 94 - 06



We now take away, or subtract, crossways or diagonally. We either


Subtract 6 from 92 or 8 from 94. It doesn’t matter which way we subtract—


The answer will be the same, so choose the calculation that looks easier. 6 from 92 is 86, or 8 from 94 is 86. Either way the answer is 86.


You only take away one time, since it is 100 base we multiply 86 with 100 so its 8600


Write 8600 below answer line.

92 - 08

x 94 - 06

-----------

8600



For the last part of the answer you multiply, the numbers next to actual multiplication number. What is 8 times 6? Again you have trouble remembering this multiplication, follow the session 1 math



Different of 8 to become 10 is 2 and 6 to become 10 is 4 so


92 - 08 -2

x 94 - 06 -4

-----------

8600



So we have two parts in last part. First one is 8 - 4 or 6 - 2 is 4 and it will be the 10 base so it is 4 * 10 = 40


92 - 08 -2

x 94 - 06 -4

-----------

8600 + 40

the second part is 4 x 2 is 8 so

92 - 08 -2

x 94 - 06 -4

-----------

8600 + 40 + 8 = 8648 is the answer.



I tried my best to explain this. If you still have any query, confusion or clarification. Kindly revert back to me. Nice week end.



Thanks,

-Ramesh

Speed Maths Session 2B

Dear Friends,


THE SPEED MATHEMATICS METHOD

I am now going to show you the speed mathematics way of working with two digit near to 100 number multiplication in this session


The problem now looks like this:

98

× 96


We now look at each number and ask, how many more do we need to make 100?


We start with the 98. If we have 98, how many more do we need to make 100?


The answer is 2. 98 plus 2 equals 100. We write 2 next to the 98. Our equation now looks like this:


98 - 02

× 96

We now go to 96. How many more to make 100? The answer is 4.


We write 4 next to the 96.


This is how the problem looks now:


98 - 02


× 96 - 04



We now take away, or subtract, crossways or diagonally. We either subtract 2 from 96 or 4 from 98. It doesn’t matter which way we subtract the answer will be the same, so choose the calculation that looks

easier. Two from 96 is 94, or 4 from 98 is 94. Either way the answer is 94.


You only take away one time.

since it is 100 base we multiply 94 with 100 so its 9400

Write 9400 below answer line.


98 - 02


x 96 - 04


-----------


94


For the last part of the answer, you “times,” or multiply, the numbers next to actual multiplication number. What is 2 times 4? Two times 4 means two fours added together. Two fours are 8. since the compliment as two digit add zero in front of 8 as 08. Write the 08 as the last part of the answer.


The answer is 9408.


98 - 02


× 96 - 04


------------ -


9408


Any clarification kindly revert back to me.


Practice: Try this out (Don't skip this since higher level need this practice)






a) 96 × 96 = e) 98 × 94 =
b) 97 × 95 = f) 97 × 94 =
c) 95 × 95 = g) 98 × 92 =
d) 98 × 95 = h) 97 × 93 =






More fun to follow.


Note: We can instead of asking how many more to make it 100, you can use the formula we learned in 2A. eg. 98 complement no. is "all by 9 and last by 10" the answer is 9-9 = 0 , 10-8 = 2, so the complement no. is 02 and for 96, 9-9 = 0 , 10-6 = 4 and 04 is the complement no.


Thanks,


-Ramesh

Speed Maths Session 2A

Dear Friends,


I hope I need to cover the complement number before I proceed further.


There are 10,100,1000,.... base numbers, for an example for 10 base 1's complement number is 9. that means the number added with its complement will give its base number.


so this is how it follow
number complement
1 9
2 8
3 7
4 6
5 5
6 4
4 6
3 7
2 8
1 9


For small number it is easy, When we go bigger number it will become difficult. Let we try 100 base few before we see a standard formula
number complement
10 90
20 80
.... so the number added with its complement number will give its base. So for the above number the base is 100. So now we need to remember a formula when we try a complement of big number.


Formulat: All from 9 and last from 10.


So we always use the number from left to right.
for example a complement of 1234 is all from 9 is subtract all number from 9 and the last digit(unit digit) from 10.
Note. The last digit should not be 0, if 0 then its earlier digit will be subtracted from 10.


So take 1234
so 9 - 1 = 8
9 - 2 = 7
9 - 3 = 6
10 - 4(last digit) = 6


so the complement number for 1234 is 8766


the number 5500 complement is
9 - 5 = 4
10 - 5 = 5 (the 5 in hundred position should be subtracted by 10 since remaining small digits are 0's.)


So the complement of 5500 is 4500


try the following
568945
365400
100000
265847
984565457
358479
8555457




Thanks,
Ramesh