Mathematics my way

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Asss

http://mathematicsworld.blogspot.com/

Sample Paper Class IX

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http://www.cbse.nic.in/cce/qp/MATHS_SQP_1.pdf

Assorted Multiplication Tips

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Assorted Multiplication Rules

Multiply by 5: Multiply by 10 and divide by 2.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number.
Multiply by 16: Double four times, or multiply by 8 and then by 2.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 18: Multiply by 20 and subtract twice the original number.
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number.
Multiply by 45: Multiply by 50 and subtract 5 times the original number.
Multiply by 90: Multiply by 9 (as above) and put a zero on the right.
Multiply by 98: Multiply by 100 and subtract twice the original number.
Multiply by 99: Multiply by 100 and subtract the original number.

Try and verify your answers .

Tips on Percentage

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Percentages

Understand the word “Percent.”
The first part is PER , PER = FOR EACH.
The second part of the word is CENT, as in 100.
PERCENT = For Each 100.

Find 7 % of 300.

7% of the first hundred is 7.
7% of 2nd hundred is also 7
7% of the 3rd hundred is also 7.
So, 7 % of 300 = 7+7+7 = 21.

If 8 % of 100 is 8,
8% of 50 is half of 8 , or 4.

Break down every number that’s asked into questions of 100,
if the number is less then 100, then move the decimal point accordingly.

EXAMPLES:
8% of 200 = 8 + 8 = 16.
8% of 250 = 8 + 8 + 4 = 20.
8% of 25 = 2.0 (Moving the decimal back).

15%300 = 15+15+15 = 45.

15%350 = 15+15+15+7.5 = 52.5

More tips on multiplication

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Multiply by 5

Take any number, then divide it by 2 (in other words, halve the number).
If the result is whole, add a 0 at the end.
If it is not, ignore the remainder and add a 5 at the end.

Example:
2682 x 5
2682 / 2 = 1341 (whole number, so add 0)
So, 2682 x 5 = 13410

Another example :
5887 x 5
2943.5 (fractional number,ignore remainder, add 5)
So, 5887 x 5 = 29435

Multiply by 9

To multiple any number between 1 and 9 by 9 hold both hands in front of your face
- drop the finger that corresponds to the number you are multiplying (for example 9×3 - drop your third finger)
- count the fingers before the dropped finger (in the case of 9×3 it is 2)
- then count the numbers after (in this case 7)
- the answer is 27.

Subtraction from 1000

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Subtracting from 1,000

To subtract a large number from 1,000 you can use this basic rule:

Subtract all but the last number from 9,

then subtract the last number from 10

Example -
1000-648

step1: subtract 6 from 9 = 3

step2: subtract 4 from 9 = 5

step3: subtract 8 from 10 = 2

Answer: 352

Multiplication of large numbers

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Tough Multiplication

If you have a large number to multiply and one of the numbers is even,
you can easily subdivide to get to the answer:

32 x 125, is the same as
16 x 250 is the same as
8 x 500 is the same as
4 x 1000 = 4,000

Tips -Multiplication by 11

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The 11 Times Trick

Easy trick for multiplying a two digit number by 11

Take the original number and imagine a space between the two digits

Example: 52

5_2

Now add the two numbers together and put them in the middle:

5_(5+2)_2

That is it - you have the answer: 572.

If the numbers in the middle add up to a 2 digit number, just insert the second number and add 1 to the first:

9_(9+9)_9

(9+1)_8_9

10_8_9

1089

Easy tips of squaring numbers

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Quick Square

If you need to square a 2 digit number ending in 5,

Mulitply the first digit by itself + 1, and put 25 on the end.

252 = (2x(2+1)) 25

= (2 X 3)25

= 625

Try with other numbers ending in 5

Divisibility Tests

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2 - Even (units digit is 0, 2, 4, 6, or 8).
Eg - 4587216 is divisible by 2 as units digit is 6

3 - Sum of digits is divisible by 3.
Eg - 5684121 is divisible by 3 as sum of digits that is 27 is divisible by 3

4 - Number formed by the tens and ones digits is divisible by 4
Eg - 68452196 is divisible by 4 as 96 1s divisible by 4

5 - Units digit is 0 or 5.
Eg - 56487690 is divisible by 5 as units digit is 0

8 - Number formed by the hundreds,tens and units digits is divisible by 8.
Eg - 784580816 is divisible by 8 as 816 is divisible by 8

9 - Sum of digits is divisible by 9.
Eg - 59684121 is divisible by 9 as sum of digits that is 36 is divisible by 9

10 - Units digit is 0.
Eg - 58746210 is divisible by 10 as units digit is 0

11 - The difference between the sum of the odd numbered digits (1st, 3rd, 5th...)

and the sum of the even numbered digits ( 2nd ,4th ,6th …) Is divisible by 11

Example: 34871903

3+8+1+0=12

4+7+9+3=23

23-12=11

11 is divisible by 11

So,34871903 is divisible by 11

Divisibility tests by 7

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Divisibility by 7 ( First method)

Take the two left-most digits, multiply the left digit by 3 and add it to the second digit. Replace these two digits with the result. Then we can keep repeating, always dealing with only the two left-most digits, until we end up with a small number which is either divisible by 7 or not.

4712954379 4 x 3 +7 = 19
1912954379 1 x 3 +9 = 12 so on
1212954379
512954379
162954379
92954379
29954379
15954379
8954379
3354379
1254379
554379
204379
64379
22379
8379
2779
1379
679
259
119
49
49 is divisible by 7. Since 49 is divisible by 7, every number above it is also divisible by 7.

Test for divisibility by 7. ( second method )

Double the last digit and subtract it from the remaining number. If the result is divisible by 7, then so was the original number. Apply this rule over and over again as necessary.
Example: 826.
Twice 6 is 12.
So take 12 from 82.
Now 82-12=70.
This is divisible by 7, so 826 is divisible by 7 also.

Divisibility tests for some prime numbers

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Test for divisibility by 13.
Add four times the last digit to the remaining number. If the result is divisible by 13, then so was the first number. Apply this rule over and over again as necessary.
Example: 50661
5066+4=5070
507+0=507
50+28=78
78 is 6*13, so 50661 is divisible by 13.

Test for divisibility by 17.
Subtract five times the last digit from the remaining number. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary.
Example: 3978
397-5*8=357
35-5*7=0. So 3978 is divisible by 17.

Test for divisibility by 19.
Add two times the last digit to the remaining number. If the result is divisible by 19, then so was the first number. Apply this rule over and over again as necessary.
Example: 101156
10115+2*6=10127
1012+2*7=1026
102+2*6=114 and 114=6*19, so 101156 is divisible by 19.

Test for divisibility by 23.
Add seven times the last digit to the remaining number. If the result is divisible by 23, then so was the first number. Apply this rule over and over again as necessary.
Example: 17043
1704+7*3=1725
172+7*5=207
20+7*7=69 which is 3*23, so 17043 is also divisible by 23.

Test for divisibility by 29.
Add three times the last digit to the remaining number. If the result is divisible by 29, then so was the first number. Apply this rule over and over again as necessary.
Example: 15689
1568+3*9=1595
159+3*5=174
17+3*4=29, so 15689 is also divisible by 29.

Test for divisibility by 31.
Subtract three times the last digit from the remaining number. If the result is divisible by 31, then so was the first number. Apply this rule over and over again as necessary.
Example: 7998
799-3*8=775
77-3*5=62 which is twice 31, so 7998 is also divisible by 31.

Test for divisibility by 37.
Subtract eleven times the last digit from the remaining number. If the result is divisible by 37, then so was the first number. Apply this rule over and over again as necessary.
Example: 23384
2338-11*4=2294
229-11*4=185 which is five times 37, so 23384 is also divisible by 37.

Test for divisibility by 41.
Subtract four times the last digit from the remaining number. If the result is divisible by 41, then so was the first number. Apply this rule over and over again as necessary.
Example: 30873
3087-4*3=3075
307-4*5=287
28-4*7=0, remainder is zero and so 30873 is also divisible by 41.

Test for divisibility by 43.
Add thirteen times the last digit to the remaining leading number. If the result is divisible by 43, then so was the first number. Apply this rule over and over again as necessary.
Example: 3182
318+13*2=344
34+13*4=86 which is recognisably twice 43, and so 3182 is also divisible by 43.

Test for divisibility by 47.
Subtract fourteen times the last digit from the remaining leading truncated number. If the result is divisible by 47, then so was the first number. Apply this rule over and over again as necessary.
Example: 34827
3482-14*7=3384
338-14*4=282
28-14*2=0 , remainder is zero and so 34827 is divisible by 47.

ClustrMaps -Visitors from 20 /8 /2007 to 21/8/2008

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Visitors from 20 /8 /2007 to 21/8/2008 -- 1341

Taking a Mathematics Test

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Just as it is important to think about how you spend your study time , it is important to think about what strategies you will use when you take a test. Good test-taking strategy can make a big difference to your grade!

Taking a Test

First look over the entire test. You'll get a sense of its length. Try to identify those problems you definitely know how to do right away, and those you expect to have to think about.
Do the problems in the order that suits you! Start with the problems that you know for sure you can do. This builds confidence and means you don't miss any sure points just because you run out of time. Then try the problems you think you can figure out; then finally try the ones you are least sure about.

Time is of the essence - work as quickly and continuously as you can while still writing legibly and showing all your work. If you get stuck on a problem, move on to another one - you can come back later.

Work by the clock. On a 50 minute, 100 point test, you have about 5 minutes for a 10 point question. Starting with the easy questions will probably put you ahead of the clock. When you work on a harder problem, spend the allotted time (e.g., 5 minutes) on that question, and if you have not almost finished it, go on to another problem. Do not spend 20 minutes on a problem which will yield few or no points when there are other problems still to try.

Show all your work: make it as easy as possible for the Instructor to see how much you do know. Try to write a well-reasoned solution. If your answer is incorrect, the Instructor will assign partial credit based on the work you show.

Never waste time erasing! Just draw a line through the work you want ignored and move on. Not only does erasing waste precious time, but you may discover later that you erased something useful (and/or maybe worth partial credit if you cannot complete the problem). You are (usually) not required to fit your answer in the space provided - you can put your answer on another sheet to avoid needing to erase.

Make sure you read the questions carefully, and do all parts of each problem.

Verify your answers - does each answer make sense given the context of the problem?

If you finish early, check every problem (that means rework everything from scratch).

Studying Mathematics

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Studying Mathematics is Different from Studying Other Subjects

Mathematics is learned by doing problems. Do the homework. The problems help you learn the formulas and techniques you do need to know, as well as improve your problem-solving power.

A word of warning: Each class builds on the previous ones, all semester long. You must keep up with the Instructor: attend class, read the text and do homework every day. Falling a day behind puts you at a disadvantage. Falling a week behind puts you in deep trouble.

A word of encouragement: Each class builds on the previous ones, all semester long. You're always reviewing previous material as you do new material. Many of the ideas hang together. Identifying and learning the key concepts means you don't have to memorize as much.

The higher the math class, the more types of problems: in earlier classes, problems often required just one step to find a solution. Increasingly, you will tackle problems which require several steps to solve them. Break these problems down into smaller pieces and solve each piece - divide and conquer!

When you work problems on homework, write out complete solutions, as if you were taking a test. Don't just scratch out a few lines and check the answer in the back of the book. If your answer is not right, rework the problem; don't just do some mental gymnastics to convince yourself that you could get the correct answer. If you can't get the answer, get help.

The practice you get doing homework and reviewing will make test problems easier to tackle.

Solving an Applied Problem

First convert the problem into mathematics. This step is (usually) the most challenging part of an applied problem. If possible, start by drawing a picture. Label it with all the quantities mentioned in the problem. If a quantity in the problem is not a fixed number, name it by a variable. Identify the goal of the problem. Then complete the conversion of the problem into math, i.e., find equations which describe relationships among the variables, and describe the goal of the problem mathematically.

Solve the mathematics problem you have generated, using whatever skills and techniques you need .

As a final step, you should convert the answer of your mathematics problem back into words, so that you have now solved the original applied problem.

Some Great Indian Mathematicians

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Adding consecutive integers

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If you want to add consecutive integers , add first the first and last integers .Then multiply the result by half the number of integers.

E xample : 14+15+16+17+18+19 = (14+ 19) x 6/2
= 33 x 3
= 99

Quotation

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THE VALUE OF A HUMAN LIFE EQUALS TO THE FRACTION

ASSETS / DESIRES

The value cannot be increased so much by increasing the numerator. As desires decrease (tend to be zero ) the value of ones life becomes INFINITELY HIGH.

ROLE OF COMPUTER IN TEACHING OF MATHEMATICS

2008-06-03T18:58:00.001+05:30

Teaching Mathematics refers to the instruction of mathematical subjects. Addition, subtraction, multiplication and division are important concepts in teaching elementary mathematics. Algebra, Calculus, Geometry and Trigonometry are important subjects in teaching secondary mathematics. The four major approaches to teaching mathematics are the skills, conceptual, problem solving and investigative methods.
In the relatively near future, mathematics will be mandatory for all students because of the demands of our technological times. People in all walks of life will need a higher level of proficiency in mathematics. Mathematics is the key to the door of opportunity as students decide about careers, learn to make informed decisions, and function as self-motivated, lifelong learners. “Working smarter” is replacing “working harder” mathematically. In working smarter, individuals must be mentally fit. We are living in a time when technology is changing almost faster than we can adapt to. There is no magic formula for teaching mathematics. Using computers to practice basic skills, have benefits. Computer based exercises can raise student motivation levels. The computer’s most powerful uses are for making things visual. It can make visual abstract processes that are otherwise ineffable. If we truly want to promote excellence in mathematics education, we must consider adapting to change and using the best tools available to us. Technology plays a critical role in doing this. Using Computer Guided Learning (CGL) allows teachers to move in this direction, while being confident they have a resource correlated to the curriculum outcomes they are mandated to teach. Computer Guided Learning refers to high quality world class CD-ROM materials supported by print resources for teaching and learning. This will improve student performance and retention of expected mathematics outcome. The language of mathematics is reinforced throughout the lessons with features such as vocabulary checks, a built in glossary and such response models which incorporate phrases, symbols and maths vocabulary which allow students to explore and build their understanding of key mathematics concepts. CGL has the following advantages : § Students are able to click on a word or mathematics expression when they have forgotten what it means, and get a very specific explanation, with an example. § When students make an error, they immediately receive appropriate feed back to move them towards the correct response or solutions. § There are more than enough examples at all the levels with lots of problem solving. § Students are able to see full solutions to problems to compare with their own work. § Students can see alternate solutions or methods at the click of a button. § The computer can repeat things over and over and is infinitely patient. § It can be fun and easy to use. § The program provides more depth to the concepts (than a text book). It allows for an internalization of knowledge and greater understanding in the long run. § Most of the presentations have some animated effects that add to the effectiveness of the lesson. Computers are bringing turbulent changes to mathematics itself. With their capacity for crunching through vast numbers of equations, examining millions of possibilities, and the use of graphics to give new conceptual insights, mathematicians are coming to use computers as essential tools. “Mathematicians helped to establish computer science, but it is now bringing revolution to their own subject”

Riddles & Puzzles

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Use your mathematic skills to solve the following problems

1 .If there are three oranges and you take away two, how many will you have?

2. There are a mix of red, green and blue balls in a bag. The total number of balls is 60. There are four times as many red balls as green balls and 6 more blue balls than green balls. How many balls of each colour are there?

3. What's my number?
I am a three digit number.
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I?

4. How many times can you subtract the number 5 from 25?

Answers
1.2
2.Blue balls = 15
Red balls = 36
Green balls = 9
3. 194
4. Only once.
After the first calculation, you will be subtracting 5 from 20, then 5 from 15, and so on

More Kolam Designs

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Kolam Patterns

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Geometry in Kolam Designs

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Kolam is a decorative design drawn using rice powder by female members of the family in front of their home, especially near the threshold. It is widely practised by Hindus in South India. A Kolam is a sort of painted prayer -- a line drawing composed of curved loops, drawn around a grid pattern of dots. They are generally symmetric.

Kolams are thought to bestow prosperity to the homes. For special occasions limestone and red brick powder to contrast are also used. Though kolams are usually done with dry rice flour, for longevity, dilute rice paste or even paints are also used.

Every morning in southern India , before sunrise, the floor is cleaned with water, the universal purifier, and the muddy floor is swept well for an even surface. The kolams are generally drawn while the surface is still damp so that it is held better.

Decoration was not the sole purpose of a Kolam. In olden days, kolams used to be drawn in coarse rice flour, so that the ants don't have to work so hard for a meal. The rice powder is said to invite birds and other small critters to eat it, thus inviting other beings into one's home and everyday life: a daily tribute to harmonious co-existence. It is a sign of invitation to welcome all into the home, not the least of whom is Goddess Lakshmi, the Goddess of prosperity. The patterns range between geometric and mathematical line drawings around a matrix of dots to free form art work and closed shapes.

In some patterns ,
1. a stroke (Kambi, Sikku in Tamil) runs once around each dot (Pulli), and goes to the beginning point (endless/cycle), as a mostly geometrical figure.
2. a stroke runs around each dot not completely, but open.
3. strokes are connected between the dots. Sometimes it represents kinds of objects, flowers, or animals etc.
4. dots are set in a radial arrangement, called Lotus.

Geometry in Nature

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Geometry in Nature

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9 ,99 , 999 as multipliers

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Multiplying by 9, or 99, or 999

Multiplying by 9 is really multiplying by 10-1.
So, 9×9 = 9x(10-1)
= 9×10-9
= 90-9 or 81.
Similarly , 46×9 = 46×10-46
= 460-46
= 414.
In the same way , to multiply by 99, you multiply by 100-1.
So, 46×99 = 46x(100-1)
= 4600-46
= 4554.
Multiplying by 999 is similar to multiplying by 9 and by 99.
38×999 = 38x(1000-1)
= 38000-38
= 37962.

Fun with products

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To multiply 76 by 82
76 = 70 + 6
82 = 80 + 2
To multiply 76 by 82 we add all the products of

70 & 80 ,70 & 2 ,80 &6 ,6 & 2 ( 5600 + 140 + 480 + 12 )
Product of 76 & 82 = 6232

Try more products

Square's magic

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Difference of the squares of 2 cosecutive numbers is equal to the sum of the numbers.
Example:
Square of 5 - Square of 4
= 25 -16
= 9
Also 5+ 4 = 9
Square of 10 - Square of 9
= 100 - 81
= 19
Also 10 + 9 = 19

Test 4 fun

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Find the words that fit
Eg: 12 = M in an Y
You need to find what the M and Y stand for
Answer :
12 = Months in an Year

7 = D of a W
100 = K in a Q
1000 = K in a T
12 = D in a G
52 = W in an Y
180 = D in a S
366 = D in a L
60 = S in a M
3600 = S in an H
1000 = M in a M

Tricks in adition

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Adding consecutive numbers

If you want to add consecutive integers , add first the first and last integers .Then multiply the result by half the number of integers.

Example : 14+15+16+17+18+19 = (14+ 19) x 6/2

= 33 x 3

= 99

Tricks on multiplication

2007-09-17T17:39:00.000+05:30

Multiplying a number by 9999999……..

To multiply a number by 9999999…….. annex as many zeros as there are 9s in the multiplier and from the result subtract the number itself.

Example : 345 x 99 = 34500 – 345 = 34155

75 x 9 = 750 -75 = 675

Laugh with Jokes

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Teacher: "Who can tell me what 7 times 6 is?"
Student: "It's 42!"
Teacher: "Very good! - And who can tell me what 6 times 7 is?"
Same student: "It's 24!"

My life is all arithmetic", the young businesswoman explains. "I try to add to my income, subtract from my weight, divide my time, and avoid multiplying..."

Son : We are going to be rich very soon.
Father : How?
Son : Today our math teacher taught us how to change paise into rupees.

Juciy Problems

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1) A man was born in the year 50 BC. How old was he on his birthday in 50 A D ?

2 ) In a party ,those whose hands shook arrived at about 28 altogether.How many guests were checked in?

3) A monkey starts upping a tree 30 feet tall.Each hour ,it hops 3 feet and slips back 2 feet .How many days does it take to reach the top ?

4 ) 10 cats ate 10 rats in 10 seconds.How many seconds are required for 100 cats to gobble 100 rats ?

5) A boy celebrates his birthday only after every 4 years.What is his date of birth?

6) If a clock in a mirror tells 20 to 3, what time it was?

7) Which number appears same,if read either in the conventional manner or in the reverse order?

8) A bow and an arrow costs Rs.21.The bow costs Rs.20 more than the arrow. What shall be the price of each?

Answers : 1) 99years 2) 8 guests 3) 28 hours 4)10 seconds 5) 29th February

6) 20 past 9 7) 1961 8) Bow - Rs.20.50 , Arrow Rs.0.50

Googol & Googolplex

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Googol is one of the largest numbers that has ever been named.It has been defined as 1 followed by one hundred zeros.

Googol = 10 raised to the power of 100

Googolplex is defined as 1 followed by a googol of zeros.It is claimed that there would not even be room between the earth & the moon to write all the zeros in a googolplex!

DIVIDING A NUMBER BY 5 , 25 and 125

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Using rules of dividing a number by 10 ,100 and 1000, you can divide a number by 5, 25 and 125 quickly.

a) 425 ÷ 5 = 425 ÷ 10/2
= 850/10
= 85

b) 4257 ÷25 = 4257 ÷ 100/4
= 17028 / 100
= 170.28

c) 125762 ÷ 125 = 125762 ÷ 10000/8
= 1006096 / 1000
= 1006.096

MULTIPLICATION OF A NUMBER BY 5 , 25 , and 125

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Using the rules of multiplying a number by 10,100,and1000,you can multiply a number by 5, 25 and 125 quickly.

a) 86 X 5 = 86 X10/2
= 860/2
= 430

b) 126X 25 = 126 X 100/4
= 12600/4
= 3150

c) 3197 X 125 = 3197 X 1000/8
= 3197000/8
= 399625

MULTIPLING BY HALVING AND DOUBLING PROCESS

2007-09-05T17:46:00.000+05:30

Suppose we want to find the product of 27 and 196

Step 1: Mark 2 columns headed by 27 and 196

Step 2: Write numbers in the first column by halving (dividing by 2) the preceeding number and ignoring the remainder if any till the last number is 1

27 -------------- 196
13 -------------- 392
6 ------------- 784
3 ------------------- 1568
1 ------------------- 3136

Step 3: Write the numbers in the second column by doubling ( multiplying by 2) the preceeding number , till a number is written opposite to 1 of the first column

Step 4: Add together all those numbers in the second column which come on the right of an odd number in the first column

196 + 392 + 1568 + 3136 = 5292

The sum obtained is the product of 27 and 196

NUMBERS MAN

2007-09-02T17:47:00.000+05:30

Look here he comes the numbers man.
Draw him, yes, you easily can,
Take 1 and make a vertical line
Add 2 to make a nose so fine
His mouth with 3 you can design
Chin and neck with 4 define
Use 5 and 6 and a moustache fix
Then 7,a cap on his head affix
8 will form the trimming lace
Use 9 to put his ear in place
Last of all, his eye with 10
Oh, you’ve created a gentleman

Difference between Drawing and Construction

2007-09-01T21:28:00.000+05:30

Drawing is a representation on a plane with the use of suitable instruments such as a protractor, marked ruler , compass etc

Construction is an imaginary drawing in which required points on lines are determined by the use of just 2 idealized instruments – a straight edge and a compass.

WORLD NUMERALS

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In the early centuries of the Christian Era a system of expressing numbers by words was evolved. The numbers from 0 to 9 were related to physical realities. Several different words were used for expressing numbers.0 was derived from the emptiness of the sky or outer space vyoma.

1 - Surya - one Sun
2 - Two Netras -two Eyes
3 - Lok three lokas
4 - Vedas –Four Vedas
5 - Panchabhuta – five elements
6 - Ritu -Six elements
7 - Swasra – Seven notes of music
8 - Ashtabujadhari – Goddess Durga with eight powers
9 - Grahas – Nine planets

A HANDFUL OF GRAINS

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CHESS IS THE NATIONAL GAME OF RUSSIA.A CHESS BOARD CONSISTS OF 64 SQUARES WITHIN.IF YOU WANT TO ASK FOR SOMETHING FROM SOMEONE ASK FOR A HANDFUL OF GRAINS.GIVE HIM A CHESSBOARD AND TELL HIM TO PUT ONE GRAIN ON THE FIRST SQUARE, 2 ON THE SECOND,4 ON THIRD, 8 ON FOURTH,16 ON FIFTH AND SO ON. i.e THE GRAIN ON EACH SQUARE ONLY DOUBLE THE LAST.
DO YOU KNOW THE NUMBER WHICH ONE HAS TO PUT ON THE LAST SQUARE?
IT WOULD BE

18,446,744,099,486,767,615 GRAINS.

PICTURE STORY

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1 ) My name is ten.

2) I have 2 digits.

3) I am the number of fingers in my 2 hands.

4) My successor is 11

5) My predessor is 9

6) I come between 9 and 10

7) I am the smallest number of 2 digits.

8) I come in the multiplicaton table of 2,5,10

9) The sum of my digits is 1

10) The difference of my digits is also 1

Now draw the picture and write the story of the following numbers

a) 75 b) 100 c) 4528

know the following

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Know the following

Arithmetic- The study of numbers.
It is the oldest branch of Mathematics.

Geometry – Study of the properties of shapes in space.
The study of points, lines and other plain figures is called Plane Geometry

and the study of 3 dimensional figures is called Solid Geometry.

Natural numbers – The numbers we use for counting are called counting numbers or Natural numbers.1,2,3,4,……… are called the Natural numbers. There is no greatest Natural number as each natural number has a successor.

1 is the smallest natural number.

Whole Numbers

– Zero along with natural numbers are called Whole numbers.0,1,2,3,4,…….are the whole numbers. There is no greatest whole number as each whole number has a successor.0 is the smallest natural number.

Even numbers – Any number which is exactly divisible by 2 is called an even number.2,4,6,8…..are even numbers.

Odd numbers - Any number which is not divisible by 2 is called an odd number.1,3,5,7,9,….…..are odd numbers.

Fraction – Fractions express numbers which are part of a whole.A fraction has 2 parts.The number written above the dividing line is called the numerator and the number written below the dividing line is called the denominator.For example , 3/8 is a fraction.3 is the numerator and 8 is the denominator.

Proper fraction – When the numerator is less than the denominator ,the fraction is called a proper fraction .Example – ½, 5/9, 18/23

Improper fraction

– When the numerator is more than the denominator ,the fraction is called a proper fraction .Example –5/3 , 8/5 , 56/11

Mixed fraction - A combination of a whole number and a proper fraction is called a mixed fraction. Example - 3 ½ ,5 ⅓

FASCINATING MATH OPERATIONS(LOGIC)

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Multiplying any number by 5

To multiply a number by 5,annex 0 to the number & divide the result by 2

172 × 5 = 1720 ÷ 2 = 860

To multiply a number by 125,annex 000 to the number & divide the result by 8

89 × 125 = 89000 ÷ 8 = 11125

Multiplying any number by 11

To multiply 345 by 11

First write the units digit ,

Now add units and tens digit (5 +4 = 9) and

write it to the left of 5

Then add hundreds,tens & units digits & write it

to the left of 9

795

Finally write the hundreds digit namely 3

to the left of 7

3795

We get 345 × 11 = 3795

Few Conversions

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1 year =12 months
1 year = 365 days
1year = 52 weeks

1 leap year = 366 days
1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
1 hour = 3600 seconds

1 dozen = 12 units
1 score = 20 units
1 gross = 144 units
1gross = 12 dozens

1quintal = 100 kg
1 ton = 1000 kg
1kg = 1000 grams
1 litre = 1000 millilitres
1metre = 100 centimetres

1 decade = 10 years
1 century = 100 years

1 foot = 12 inches

1 inch = 2.5 cm

QUICK ADDITION

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Sum of first n

Natural numbers = ½ n × (n + 1)

Even numbers = n × (n + 1)

Odd numbers = n × n

Example:

Sum of first 20

a) natural numbers = ½ × (20 ×21) = 210

b) even Numbers = 20 × 21 = 420

c) odd numbers = 20 × 20 = 400

Now find the sum of first

a) 25 natural numbers
b) 42 even numbers
c) 100 odd numbers

24 hour day

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Prehistory

Why do clocks usually show just a division into 12 hours, when there are 24 hours in a day?

The origins of our 24 hour day can be traced back at least 4000 years, to ancient Egypt and Babylon. The Egyptians and Babylonians divided the parade of stars that appeared in the sky each night into 12 sections, marked by the various stars that rose and set that night. For example, the star Procyon might rise shortly after sunset one evening, followed about an hour later by Sirius. This defined a kind of heavenly clock, although different groups of 12 stars were used to cope with the slow shift of the night sky during the year. The daylight hours were divided into 12, to match. Two sets of 12 give 24, hence the number of hours in a day.

HAPPY NUMBER

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A happy number is one for which the sum of squares of its digits ends in one, after repeated squaring and adding

Example : consider 13
1² + 3² = 1 + 9 = 10
Now 1² + 0² = 1

Since after repeated squaring and adding of the digits of 13 we get 1, 13 is called a happy number.

44 - 4² + 4²= 16 + 16 = 32
32 - 3² + 2² = 9 + 4 = 13
13 - 1² + 3² = 1 + 9 = 10
10 - 1² + 0² = 1

So 44 is a happy number.

Find outwhether the following are happy numbers.
1. Your birth date
2. The date on which India got Independence
3. Childrens day

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Where was Zero invented?

The idea of zero was originally invented in India.Zero was used in 628 AD by well known Indian Mathematician Brahmagupta for carrying out 6 operations of Mathematics.The word ‘zero’ evolved from the Sanskrit word ‘shunya’meaning nothing.

Unique properties of Zero

When zero is placed to the right of 1 the number becomes 10. By continuing to put zeros to the right of 1,we make the value of 1 ten times great for every zero.
10 – ten
100 – one hundred

If zero is put to the left of 1 with a decimal point before it ,the value becomes one tenth.Two zeros make it one hundredth and so on.

0.1 – one tenth
0.01 – one hundredth

Addition or subtraction of zero does not alter the number.

7 + 0 = 7
7 – 0 = 7

The product of any number and zero is zero.

9 × 0 = 0

Zero divided by any number gives the quotient as zero.

0 ÷ 14 = 0

Division by zero is undefined.

15 ÷ 0 is undefined

HISTORY OF NUMERALS

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How did our ancestors count the things?

The people first used pebbles or knots or

marks of fingers for counting things.

Every morning as they let the sheep out ,they made marks on a tree – one mark for each sheep. In the evening ,when they bought the sheep back, they matched each sheep with the mark on the tree. In this way they could tell if there was any change in the number of sheep .

Several things were used for counting by the ancient man. Lion’s head was used to indicate one, wings of an eagle to indicate two, leaves of a clover to indicate three and so on.
The man created symbols as soon as he learned to write.

Number & Numeral

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A number is actually a way of thinking,an idea,that enables us to compare very different sets of objects.

A numeral is used to name a number, in other words a numeral is a symbol used to represent a number.
The numeral 4 is the name of number four.And again four is the idea that describes any collection of four objects.( 4 marbles,4 books etc)

what are digits?

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Digits are actually alphabets of numbers.Just like we use the twenty six alphabets to build words,we use the ten digits 0,1,2,3,4,5,6,7,8,& 9 to build numbers.
Example: Alphabets p,t,a are used to form the word pat or tap
Digits 2,5,4 Are used to form the numbers 254 or 524 etc

my first entry

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Today I have created this blog for enabling the children to know everything they wanted to know about numbers,having fun with numbers through puzzles, riddles, jokes etc.Practice the worksheets regularly because practice makes a man perfect.