Multiplying large numbers in your head

calculate a tip

Calculate a Tip

If you need to leave a 15% tip, here is the easy way to do it. Work out 10% (divide the number by 10) – then add that number to half its value and you have your answer:

15% of $25 = (10% of 25) + ((10% of 25) / 2)

$2.50 + $1.25 = $3.75

Easy Multiplication of Numbers

Multiply by 5: Multiply by 10 and divide by 2.
Multiply by 6: Sometimes multiplying by 3 and then 2 is easy.
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, as above.
Multiply by 16: You can double four times, if you want to. Or you can 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 (which is obvious from the first step).
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 (which is obvious from the first step).
Multiply by 45: Multiply by 50 and subtract 5 times the original number (which is obvious from the first step).
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.

Easy multiplication by 11

There are a number of simple techniques that can be used when multiplying by certain numbers. They are very useful in their own right but can be even more useful when combined with other techniques where they can facilitate the solution of more difficult problems.

Multiplying by 11

To multiply any number by 11 do the following:
Working from right to left

1. Write the rightmost digit of the starting number down.
2. Add each pair of digits and write the results down, (carrying digits where necessary right to left).
3. Finally write down the left most digit (adding any final carry if necessary).

It's as simple as that, e.g.

• Multiply 712x11

${\displaystyle {\begin{matrix}&7&&1&&2\\&\swarrow \searrow &+&\swarrow \searrow &+&\swarrow \searrow \\7&&8&&3&&2\end{matrix}}}$

712x11=7832

The reason for working from right to left instead of the more usual left to right is so any carries can be added in. e.g.

• Multiply 8738x11

${\displaystyle {\begin{matrix}&8&&7&&3&&8\\&\swarrow \searrow &+&\swarrow \searrow &+&\swarrow \searrow &+&\swarrow \searrow \\9&\leftarrow _{1}&6&\leftarrow _{1}&1&\leftarrow _{1}&1&&8\end{matrix}}}$

8738x11=96118

easy way to calculate percent value

Finding a fraction of whole no

The four lucky ones

The Four Lucky Ones

There are just four numbers (after 1) which are the sums of the cubes of their digits:

153 = 1^3 + 5^3 + 3^3

370 = 3^3 + 7^3 + 0^3

371 = 3^3 + 7^3 + 1^3

407 = 4^3 + 0^3 + 7^3  [ ^ means raised to power]

math in real world

Interesting facts about MAthematics

Trigonometry is the study of the relationship between the angles of triangles and their sides

 Abacus is considered the origin of the calculator

 Here is an interesting trick to check divisibility of any number by number 3.A number is divisible by three if the sum of its digits is divisible by three (3)

 Do you know the magic of no. nine (9)? Multiply any number with nine (9 ) and then sum all individual digits of the result (product) to make it single digit, the sum of all these individual digits would always be nine (9)

If you add up the numbers 1-100 consecutively (1+2+3+4+5...) the total is 5050

 A 'jiffy' is an actual unit of time for 1/100th of a second

Have you heard about a Palindrome Number? It is a number that reads the same backwards and forward, e.g. 12421

Have you heard about Fibonacci? It is the sequence of numbers wherein a number is the result of adding the two numbers before it! Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so 

famous mathematicians - 2

FAMOUS MATHEMATICIANS

• In 1642 French mathematician Blaise Pascal invented the mechanical calculator.
• Swiss mathematician Leonhard Euler was probably the most influential mathematician of the 18th century, making discoveries in graph theory and introducing many modern mathematical words and notations among other things.
• Born in 1777, German mathematician Carl Friedrich Gauss contributed brilliant work in geometry, statistics, number theories, algebra and much more.
  
• Bernhard Riemann was an influential German mathematician who contributed to differential geometry and analysis, paving the way for the development of general relativity by Albert Einstein.
  
• Born in 1882, Emmy Noether was a German mathematician who made important contributions to abstract algebra and theoretical physics, described by Einstein as the most important woman in the history of mathematics.
  
• Alan Turing was a British mathematician and computer scientist who cracked German ciphers (codes) in the Second World War, contributed to mathematical logic and played an important role in the development of algorithms, artificial intelligence and the modern computer.
• Born in 1953, British mathematician Andrew Wiles is most famous for proving Fermat’s Last Theorem. 

famous mathematicians

Famous Mathematicians

• Greek philosopher and mathematician Pythagoras lived around the year 500 BC and is known for his Pythagorean theorem relating to the three sides of a right angle triangle: a² + b² = c²
  
• Greek mathematician Euclid is often referred to as the ‘Father of Geometry’ for his revolutionary ideas and influential textbook called ‘Elements’ that he wrote around the year 300 BC.
  
• Archimedes of Syracuse lived around the year 250 BC and among other things, developed a method for determining the volume of objects with irregular shapes.
  
• Italian mathematician Leonardo of Pisa (better known as Fibonacci) lived between the years 1170 and 1250 and is best known today for Fibonacci numbers, the number sequence named after him. Fibonacci introduced the number sequence to Western Europe in his book ‘Liber Abaci’ after they had been described earlier by Indian mathematicians.
  
• The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ....
  
• In the 17th century Galileo Galilei and Johannes Kepler made important discoveries relating to planetary motion and orbits.
  
• German mathematician Gottfried Leibniz lived between 1646 and 1716, developing important calculus concepts and mathematical notation practices.
  
• Isaac Newton discovered the laws of physics and brought together many important concepts of infinitesimal calculus.
  
• Much of the work done by Leibniz and Newton is based on theories by French philosopher Rene Descartes. As well as his many contributions to philosophy, Descartes also had a huge impact on mathematics, creating analytical geometry, developing a system that describes geometry using algebra, contributing to optics and much more.
  
• Born in France, Pierre de Fermat was an amateur mathematician who is best known for Fermat’s Last Theorem.

The History of Mathematics

Enjoy learning about the history of mathematics with our historical math facts and information.

Read about Ancient Egyptian mathematics, Babylonian mathematics, Chinese mathematics, Greek mathematics and much more. Find out where the numerical digits we use today come from, who invented the equals sign and other interesting math timeline facts and trivia. Have fun improving your math knowledge with our brief history of mathematics.

• It is believed that Ancient Egyptians used complex mathematics such as algebra, arithmetic and geometry as far back as 3000 BC, such as equations to approximate the area of circles.
  
• Babylonians measured the circumference of a circle as approximately 3 times the diameter, which is fairly close to today’s measurement which uses the value of Pi (around 3.14).
  
• Chinese mathematics developed around the 11th century BC and included important concepts related to negative numbers, decimals, algebra and geometry.
  
• Greek mathematics developed from around the 7th century BC, producing many important theories thanks to great mathematicians such as Pythagoras, Euclid and Archimedes.
  
• The Hindu-Arabic numeral system began developing as early as the 1st century with a full system being established around the 9th century, forming the basis of 1, 2, 3, 4, 5, 6, 7, 8 and 9 that we use today.

• The symbols used for addition (+) and subtraction (-) have been around for thousands of years but it wasn't until the 16th century that most mathematical symbols were invented. Before this time math equations were written in words, making it very time consuming.
  
• The equals sign (=) was invented in 1557 by a Welsh mathematician named Robert Recorde.
  
• Mathematical developments increased rapidly around the time of the Italian Renaissance in the 16th century and continued through the scientific revolution of the 17th and 18th centuries, becoming increasingly abstract in the 19th and 20th centuries.
  
• The basic arithmetic operations used in mathematics are addition, subtraction, multiplication and division.
  
• Modern mathematics has advanced greatly thanks to the incredible computing power of today’s computers.
• These days mathematics is important in many different types of jobs, including those related to engineering, business, science, medicine and more.

Excercise 9 : video conferencing

Video conferencing is two-way interactive communication delivered using telephone or Internet technologies that allows people at different location to come together for a meeting. The video conference can be as simple as a conversation between two people in private offices (point-to-point) or involve several sites (multi-point) with more than one person in large rooms at different sites.

A basic video conference setup has a camera and a microphone. Video from the camera and audio from the microphone is converted into a digital format and transmitted to a receiving location using a coding and decoding device, often referred to as a "codec".

At that receiving location is another codec device that decodes the receiving digital stream into a form that can be seen and heard on monitors or televisions. At the same time, video and audio from cameras and microphones at the received location is sent back to the original location.

People use video conferencing when:

• a live conversation is needed;
• visual information is an important component of the conversation;
• the parties of the conversation can't physically come to the same location;
• the expense or time of travel is a consideration.

Excercise 6 : use of projector in classroom

Using a Projector in Classroom

PROJECTORS IN THE CLASSROOM
Many teachers find chalkboards to be almost a thing of the past with the advent of projectors in the classroom. Rather than writing notes across a board, teachers can make use of PowerPoint presentations, images and even film as teaching tools through the use of projectors. Consequently, teachers and students alike find projectors to be useful classroom devices.
Some Advantages of using Projector in classroom:

Easier Note Taking

• Projectors enable teachers to create bulleted PowerPoint presentations or other highly organized notes for the class. With the use of projectors in the classroom, students can take better notes with the ability to discern what information the teacher displays is most useful to them. Additionally, students can ask the teacher to repeat a slide if they missed information, or even ask that the teacher to email the presentation for further review.

Greater Teaching Versatility

• Projectors release teachers from being bound to chalk and dry-erase boards to present information to their students. With the use of projectors, teachers can now use films, slides, and images to teach students about a variety of subjects. Teachers will also find that the Internet is more useful since projectors can display web content to an entire class, rather than each student accessing information on individual computers, if they are available.

Better Use of Class Time

• Prior to the use of projectors in the classroom, teachers had to spend time writing notes on the board, as well as erasing information as the board filled up. Projectors require a simple click of a button or mouse, thus, freeing valuable class time. By using projectors, teachers can more easily prepare all notes prior to class for easy presentation. Teachers may also find that they spend less time repeating or rewriting information that is now accessible with a simple click.

Better Student Presentations

• Students will appreciate the use of projectors as they prepare class projects that they can now create in PowerPoint or other electronic mediums. Consequently, students will find that presentation creation will go faster with each person using their own computer to create their section of the presentation. Presentations on a projector, additionally, reduce the need to make copies of materials to pass out to classmates during presentations that can now be displayed for the entire class to view at once.

Education Implication 

I think using projector help us to give better teaching to the students. In order for a large classroom to see items clearly, the overhead projector needs to be at the perfect distance and angle. Panoramic views are very difficult to achieve and the inability to read slides can be distracting to observers. For this reason, using projector would provide better learning for the students. Using LCD projectors provides educators to reach students with multiple approaches. Students enjoy seeing, hearing and interacting with technology rather than simply reading a textbook or listening to a lecture. Students can participate in real-time, interactive activities. Problem-solving activities promote the development of critical thinking skills.

Excercise 7:Photo album on innovative and disabled schools

  visit to Innovative and special schools 

PPT on slum children

PPT on Kothari commission

Inclusive education

gender inequality

ppt on Buddhism

Excercise 4 : PPT on Marginalised children

INTERESTING FACTS ABOUT MATHEMATICS 1

INTERESTING FACTS ABOUT MATHEMATICS

1 )  111,111,111    x   111,111,111     = 12,345,678,987,654,321.       

2)    1089     x    9    =    9801.

3) If you have Pizza with radius Z and thickness A , its volume is = Pi *Z *Z * A

 

4) Ancient Babylonians did math in base 60 instead of base 10. That's why we have 60 seconds in a       minute and 360 degrees in a circle.

5) 2,520 is the smallest number that can be exactly divided by all the numbers 1 to 10.

6)  123 - 45 - 67 + 89 = 100.

     123 + 4 - 5 + 67 - 89 = 100.

     123 - 4 - 5 - 6 - 7 + 8 - 9 = 100.

     1 + 23 - 4 + 5 + 6 + 78 - 9 = 100.

7) In 1900, all the world's mathematical knowledge could be written in about 80 books; today it             would  fill more than 100,000 books.

8) The birthday paradox says that in a group of just 23 people, there's a 50% chance that at least           two will have the same birthday.

9) Multiplying 21978 by 4 reverses the order of the numbers: 87912.

10) 2200 years ago, Eratosthenes estimated the Earth's circumference using math, without ever l       leaving Egypt. He was remarkably accurate. Christopher Columbus later studied him.

11)Mathematician Paul Erdos could calculate in his head, given a person's age, how many seconds they had lived, when he was just 4 years old.

12)The largest prime number ever found is more than 22 million digits long.

13) Arabic numerals, like the ones we use today in English, were actually invented in India.

14) 2013 was the first year since 1432 that's a rearrangement of four consecutive numbers.

15)Philosopher René Descartes is most well known for the saying "I think, therefore I am," but he also developed the XY-coordinate system.

16)In many Israeli schools, algebra is taught without the use of the symbol "+" as it looks like a Christian cross. They use an inverted "T" instead.

17)The word ‘hundred' derives from ‘hundra' in Old Norse, which originally meant 120.

18)Newton invented/discovered calculus in about the same amount of time the average student learns it.