CLASS 10TH DAY 7
INTRODUCTION
Vedic Math
The addition is essentially the most fundamental operation and adding number 1 to the earlier number generates all the numbers. The Sutra “By one more than the previous one describes the generation of numbers from unity.”
0 + 1 = 1 ,1 + 1 = 2 ,2 + 1 = 3, 3 + 1 = 4, 4 + 1 = 5, 5 + 1 = 6, 6 + 1 = 7, 7 + 1 = 8, 8 + 1 = 9, 9 + 1 = 10……
General Method: The conventional method in mathematics addition is to calculate from right towards the left. In Vedic mathematics we can do addition from left to right which is more, useful, easier and sometimes quicker.
Add from left to right: This type of method is simple enough to do mentally, we add the first column and increase this by 1 if there’s carry coming over from the second column. Then we tag the last figure of the second column onto this.
Pure Numbers
Single digit numbers i.e. 0, 1, 2, 3…9 are known as pure numbers.
Shudh/Pure method
In the Shudh method for addition we carry only the single digit forward and drop the 1 at the tens place.
- Start adding either from top or bottom, (once decided follow that pattern only)
- Add the digits mentally
- As soon as you come across a two digit number, put a dot in front of that number and carry only the single digit forward for further addition.
- Follow this to the end.
- In the end write down the single digit, that you have in the end.
- Now, to have the first digit, count the dots and write it in front of the single digit.
Two or three digit numbers list
Example: Add 234, 658, 818 and 46
Start from the bottom of the rightmost columns and get a single digit 6 on the unit place. There are two dots so we add two to the first number (4) of the second column and proceed as earlier. The one dot of this column is added to the subsequent and ultimately we simply put 1 down (for one dot) as the primary digit of the answer.
Number Splitting Method
Quick mental calculations could be carried out extra simply if the numbers are ‘split into more manageable parts’.
Tip: Think about the best place to keep the split line. It’s best to avoid the carry over the split up lines.
Subtraction: The Base Method
Numbers made up of only 1’s and 0’s like 10, 100, 1000, 1, .01….etc are known as a Base. The base method is used for subtracting numbers like 98, 898, 78999 etc that are close to base.
Subtracting from a BASE
Rule: All from 9 and the Last from 10
Example:1000 – 784 = 216
Solution: Just apply ‘All from 9 and the Last from 10’ to 784, difference of 7 from 9 is 2, 8 from 9 is 1, 4 from 10 is 6 so we get 216 after subtraction. When subtracting a number from a power of 10 subtract all digits from 9 and last from 10.
Subtracting from a Multiple of a Base
Sutra: ‘All from 9 and the last from 10’ And ‘One less than the one before’
Example: 600 – 98
Solution: Here we have 600 which is a multiple of base 100. So, 6 is reduced by one to 5. Now All from 9 and last from 10 is applied to 98 to give 02.
∴ 600 – 98 = 502
[Note : First subtract from 100 then add 500, as 500 + 03 = 502]
Example: 10000- 4250
Solution: Here the number to be subtracted ends in zero, so in this case, use the last non zero number.
Hence 10000 – 4250 = 5750
Adding Zeroes:
In all the above examples, the number of zeros in the first number is the same as the numbers of digits in the number being subtracted.
Example: Find 9000 – 5749
Solution: Carefully see that the 9 at thousands place will be reduced by 6, since a number more than 5000 is being subtracted.(So, thousands place will be 9-6=3) Apply ‘All from 9 and the last from 10’ to 749 to give 251. Therefore, 9000 – 5749 = 3251
Example: 7000 – 3876
Solution: Carefully see that the 7 at thousands place will be reduced by 4, since a number more than 3000 is being subtracted.(So, thousands place will be 7-4=3) Apply ‘All from 9 and the last from 10’ to 876 to give 124. So, 7000-3876= 3124
Remember:
1. If the number is less digits, then append zero the start :
2. When subtracting form a multiple of a power of 10, just decrement the first digit by 1, then subtract remaining digits :
3. When the number to be subtracted ends in zero, use the last non zero number.
Money: Money is a great application of “all from 9 and last from 10”. Change can be calculated by applying this sutra mentally for example :
This is helpful because most of our rupee notes are multiples of 10.
Subtracting Near a base: When subtracting a number close to a multiple of 10. Just subtract from the multiple of 10 and correct the answer accordingly.
Example : 53 – 39
Solution: 1. Observe 39 is close to 40, just 1 short.
2. Subtract 40 from 53 which gives 13.
3. Now, since 39 was 1 short of 40, so add 1 to the answer, i.e, 13+1=14
53 – 39 = 53 – 40 + 1 = 13 + 1 = 14
Subtracting number just below the base:
Example: 65 – 39
Solution: Step 1: 40 is the sub base close to 39, 39 is 1 below 40
Step 2: take 40 from 65 (to get 25)
Step 3: Since 39 was 1 short of 40, so add 1 back to 25 to get 26.
Answer=26
Example: 51 – 38
Solution: Since 38 is near to 40
40 – 38 = 2 =51-38 = 51 – 40+2 = 11+2 = 13
Example: 44 – 16
Solution: Since 16 + 4 = 20 (16 is 4 short of 20)
44 – 20 = 24
44 – 16 = 24 + 4 = 28
Example: 88 – 79
Solution: 79 is 1 short of 80, So, 88 – 80 = 08
Thus, 88 – 79 = 8 + 1 = 09
Example: 55 – 47
Solution: Since 47 is 3 short of 50.
55 – 50 = 07
Now since 47 was 3 short of 50, so 55 – 47 = 7+3=10
Number splitting Method: As you have use this method in addition the same can be done for subtraction also :
Note : The split allows on to add ’36 – 24′ and 42 – 39 both of which can be done mentally.
General Method of subtraction:
Subtraction from left to right: In this section we show a very easy method of subtracting numbers from left to right that we have probably not seen before. We start from the left, subtract, and write it down if the subtraction in the next column can be done. If it cannot be done you put down one less and carry 1, and then subtract in the second column.
Example:
Consider the subtraction of 83 and 37. We will be doing the subtraction from left to right. So, for the leftmost numbers, gives 8-3= 5. Now moving to the other column, where 3-7 cannot be done , so we will take 1 from the previous step, and so it becomes 13-7 which could be done and it gives 6. Now since we have taken 1 from the previous step, so there 5 will become 4. Hence the answer is 46.
Consider the subtraction of 76 and 56. We will be doing the subtraction from left to right. So, for the leftmost numbers, gives 7-5= 2. Now moving to the other column, where 38-6 could be done, and gives 2 as the result. Hence the answer is 22.
Here is a small quiz to test your understanding. Try to attempt all the questions and get the highest marks possible.👇 👇
How Sugary Drink affects our teeth?
Ever thought of why our elders always say “Beta jayda meetha mut khayo teeth kharab ho jayenge”, “Beta cold drinks mut piyo”. Today, we will explore how the sugary drinks affect our teeth and how brushing our teeth helps to improve the condition. So let’s get started with the activity.
Procedure:
1. Take a mug and fill the coke in the mug.
2. Now gently lower the egg in the mug filled with coke.
3. Let the egg inside the mug for about 24 hours/overnight.
4. After you left the mug for 24 hours, take out the egg from the mug.
5. Observe the texture of the egg after it is kept in coke for 24 hours.
6. Now, take a toothbrush and rub the surface of the egg with this toothbrush and observe what happens.
7. Now take out toothpaste and use it and toothbrush to clean the egg and rinse with water, just like we clean our teeth.
8. Observe how much of the stain can be removed from the egg and how much is left.
To access the video for this experiment follow the link.👇 👇
Reason:
Firstly, let us understand why we have taken eggs?
This is because the composition of egg shells is similar to our teeth.Both eggshells and teeth are made of calcium, a hard white substance that also makes up our bones. So , the outcomes of this activity would be the same as that when done on actual teeth.
Now let us understand why this happens?
The hard shell of an egg protects the delicate parts inside, similar to the hard enamel in your tooth protects the soft and tender pulp. Sugar and acids are very harmful to teeth. Acids actually dissolve the enamel, giving bacteria an inroad to start decaying it, and sugar promotes decay (cavities).
Note, you may observe that it takes a lot longer than you think to clear away the stain, and you will probably find that a lot of the stain is permanent.
GAME TIME
Gomoku, also called Five in a Row, is an abstract strategy board game. It is traditionally played with Go pieces (black and white stones) on a Go board. It can be played using the 15×15 board[1] or the 19×19 board[2]. Because pieces are typically not moved or removed from the board, Gomoku may also be played as a paper-and-pencil game. The game is known in several countries under different names. Players alternate turns placing a stone of their color on an empty intersection. The winner is the first player to form an unbroken chain of five stones horizontally, vertically, or diagonally.
To know more about the game👇 👇
