What is Mental Aritmetika and Why is it Important?
Mental aritmetika is the invaluable maths skill of doing calculations in your head, without the use of any tools, such as a calculator or pen and paper, or fingers. It can come in handy in countless everyday situations, from working out the best multi-buy deal in the supermarket, to calculating how long you will need to wait for the next train.
mental aritmetika
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The meaning and origin of mental aritmetika
The word "aritmetika" comes from the Greek word "arithmos", which means number or digit. Aritmetika is the science of numbers, or the art of calculation. Mental aritmetika is the ability to perform arithmetic operations mentally, using only your brain power.
Mental aritmetika has a long history, dating back to ancient times. Some of the earliest records of mental aritmetika are from India, China, Greece, and Egypt. These civilizations developed various methods and systems for mental aritmetika, such as the Vedic maths, the Chinese abacus, the Greek algorithm, and the Egyptian hieroglyphs.
The benefits of mental aritmetika for brain development, learning, and everyday life
Mental aritmetika is not only useful for solving maths problems, but also for enhancing your cognitive abilities, such as memory, concentration, creativity, logic, and reasoning. By practicing mental aritmetika regularly, you can stimulate both sides of your brain, the left hemisphere that is responsible for analytical thinking and language, and the right hemisphere that is responsible for spatial awareness and imagination.
How to improve your mental aritmetika skills
Benefits of mental aritmetika for children
Mental aritmetika courses and programs
Mental aritmetika exercises and games
Mental aritmetika techniques and tricks
Mental aritmetika competitions and challenges
Mental aritmetika apps and software
Mental aritmetika books and resources
Mental aritmetika vs calculator
Mental aritmetika and brain development
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Mental aritmetika can also improve your academic performance, especially in subjects that require numerical skills, such as maths, science, engineering, accounting, etc. By mastering mental aritmetika techniques, you can save time and avoid errors when doing calculations. You can also develop a deeper understanding of mathematical concepts and principles.
Moreover, mental aritmetika can help you in your daily life activities that involve numbers, such as budgeting, shopping, travelling, cooking, etc. You can quickly estimate costs, distances, quantities, proportions, etc., without relying on external tools. You can also impress your friends and family with your mental aritmetika skills.
How to learn and practice mental aritmetika
Learning and practicing mental aritmetika is not as hard as it may seem. You just need to have a positive attitude, a willingness to learn new things, and a consistent practice routine. Here are some steps to follow:
Start with the basics. Learn the basic arithmetic operations (addition, subtraction, multiplication, division) and their properties (commutative, associative, distributive). Review the place value system (units, tens, hundreds, etc.) and how to read and write numbers in different formats (decimal, fraction, percentage).
Learn some techniques and tips. There are many techniques and tips that can help you do mental aritmetika faster and easier. For example, you can use rounding up or down to simplify numbers, you can use patterns and relationships to recognize multiples or factors, you can use shortcuts or tricks to multiply or divide by certain numbers, you can use visual aids or mnemonics to remember formulas or rules.
Practice regularly. The best way to improve your mental aritmetika skills is to practice them as often as possible. You can use various sources of exercises, such as books, apps, websites, etc., to challenge yourself with different levels and types of problems. You can also create your own problems or use real-life situations to apply your mental aritmetika skills.
Monitor your progress and set goals. It is important to keep track of your progress and set realistic and achievable goals for yourself. You can use a journal, a spreadsheet, or an app to record your performance, such as the number of problems you solved, the time you spent, the errors you made, etc. You can also use feedback, tests, or quizzes to evaluate your strengths and weaknesses and identify areas for improvement.
Have fun and enjoy the process. Learning and practicing mental aritmetika should not be boring or stressful. You should have fun and enjoy the process of learning new things and challenging yourself. You can make mental aritmetika more fun and enjoyable by using games, puzzles, riddles, jokes, stories, etc., to stimulate your interest and curiosity. You can also join a community of learners or enthusiasts who share your passion for mental aritmetika.
Mental Aritmetika Techniques and Tips
In this section, we will share some of the most common and useful techniques and tips for mental aritmetika. These techniques and tips can help you do mental aritmetika faster and easier, as well as boost your confidence and accuracy.
Multiplying numbers by 10, 100, 1000 and their multiples
One of the easiest and most useful techniques for mental aritmetika is multiplying numbers by 10, 100, 1000 and their multiples (such as 20, 30, 40, etc.). The trick is to simply move the decimal point to the right by the number of zeros in the multiplier. For example:
7 x 10 = 70 (move the decimal point one place to the right)
7 x 100 = 700 (move the decimal point two places to the right)
7 x 1000 = 7000 (move the decimal point three places to the right)
7 x 20 = 140 (multiply by 10 first, then double the result)
7 x 30 = 210 (multiply by 10 first, then triple the result)
7 x 40 = 280 (multiply by 10 first, then quadruple the result)
Adding and subtracting numbers mentally
Another basic and essential technique for mental aritmetika is adding and subtracting numbers mentally. There are several methods and strategies for doing this, depending on the type and size of the numbers involved. Here are some examples:
Adding or subtracting numbers that end with zeros: Simply add or subtract the non-zero digits first, then append the zeros at the end. For example:
50 + 30 = 80 (add 5 + 3 first, then add two zeros)
50 - 30 = 20 (subtract 5 - 3 first, then add two zeros)
500 + 300 = 800 (add 5 + 3 first, then add three zeros)
500 - 300 = 200 (subtract 5 - 3 first, then add three zeros)
Adding or subtracting numbers that are close to multiples of 10: Use rounding up or down to make one of the numbers a multiple of 10, then adjust the result accordingly. For example:
9 + 6 = 15 (round up 9 to 10, then add 6 - 1)
9 - 6 = 3 (round up 9 to 10, then subtract 6 + 1)
11 + 7 = 18 (round up 11 to 10, then add 7 + 1)
11 - 7 = 4 (round up 11 to 10, then subtract 7 - 1)
Adding or subtracting numbers that have the same tens digit: Simply add or subtract the units digits first, then append the tens digit at the beginning. For example:
23 + 25 = 48 (add 3 + 5 first, then add 2 at the beginning)
23 - 25 = -2 (subtract 3 - 5 first, then add 2 at the beginning)
34 + 36 = 70 (add 4 + 6 first, then add 3 at the beginning)
34 - 36 = -2 (subtract 4 - 6 first, then add 3 at the beginning)
Adding or subtracting numbers that have different tens digits: Use a combination of the previous methods, such as rounding up or down, or splitting the numbers into tens and units. For example:
27 + 35 = 62 (round up 27 to 30, then add 35 - 3)
27 - 35 = -8 (round up 27 to 30, then subtract 35 + 3)
46 + 25 = 71 (split 46 into 40 and 6, then add 25 to each part separately)
46 - 25 = 21 (split 46 into 40 and 6, then subtract 25 from each part separately)
Using the abacus as a tool for mental aritmetika
The abacus is an ancient device that consists of a frame with rods and beads that can be moved to represent numbers and perform calculations. The abacus is still widely used in some countries, such as China and Japan, as a tool for teaching and practicing mental aritmetika.
The abacus can help you develop your mental aritmetika skills by enhancing your visual memory, concentration, and coordination. By using the abacus, you can learn how to manipulate numbers mentally, using the image of the abacus in your mind. You can also learn how to use different methods and systems for mental aritmetika, such as the Chinese soroban or the Japanese soroban.
To use the abacus for mental aritmetika, you need to learn how to read and write numbers on the abacus, how to perform basic arithmetic operations on the abacus, and how to transfer the abacus image to your mind. You can find many online tutorials and videos that can teach you how to use the abacus for mental aritmetika.
Other tricks and shortcuts for mental aritmetika
Besides the techniques and tips mentioned above, there are many other tricks and shortcuts that can help you do mental aritmetika faster and easier. Here are some examples:
Squaring numbers that end with 5: To square a number that ends with 5, simply multiply the first digit by the next higher digit, then append 25 at the end. For example:
15 x 15 = 225 (multiply 1 by 2, then add 25)
25 x 25 = 625 (multiply 2 by 3, then add 25)
35 x 35 = 1225 (multiply 3 by 4, then add 25)
Multiplying numbers that are close to 100: To multiply two numbers that are close to 100, simply subtract each number from 100, then add the differences together and subtract the result from 100. This will give you the first two digits of the answer. Then multiply the differences together and append the result to the first two digits. This will give you the final answer. For example:
98 x 97 = (100 - 98) + (100 - 97) = 2 + 3 = 5 (100 - 5) = 95 (first two digits) 2 x 3 = 6 (last two digits) 98 x 97 = 9506
102 x 104 = (100 - 102) + (100 - 104) = -2 + -4 = -6 (100 - (-6)) = 106 (first two digits) -2 x -4 = 8 (last two digits) 102 x 104 = 10608
Dividing numbers by 5: To divide a number by 5, simply multiply the number by 2, then move the decimal point one place to the left. For example:
20 / 5 = 20 x 2 = 40 (move the decimal point one place to the left) = 4
50 / 5 = 50 x 2 = 100 (move the decimal point one place to the left) = 10
75 / 5 = 75 x 2 = 150 (move the decimal point one place to the left) = 15
Finding the percentage of a number: To find the percentage of a number, simply multiply the number by the percentage, then move the decimal point two places to the left. For example:
25% of 80 = 80 x 25 = 2000 (move the decimal point two places to the left) = 20
10% of 50 = 50 x 10 = 500 (move the decimal point two places to the left) = 5
5% of 60 = 60 x 5 = 300 (move the decimal point two places to the left) = 3
Mental Aritmetika Courses and Resources
If you want to learn more about mental aritmetika and improve your skills, there are many courses and resources that you can use. Here are some of them:
Online courses and apps for mental aritmetika
There are many online courses and apps that can teach you mental aritmetika techniques and provide you with exercises and feedback. Some of them are:
: This is a comprehensive course that covers all aspects of mental aritmetika, from basic operations to advanced topics, such as fractions, decimals, percentages, roots, powers, etc. The course includes video lectures, quizzes, assignments, and a certificate of completion.
: This is an app that helps you practice mental aritmetika tricks and shortcuts, such as multiplying by 11, squaring numbers that end with 5, dividing by 5, etc. The app includes levels, challenges, achievements, and leaderboards.
: This is an app that offers fun and educational games for mental aritmetika and other cognitive skills, such as memory, attention, logic, etc. The app adapts to your level and provides feedback and reports.
Books and videos for mental aritmetika
There are also many books and videos that can teach you mental aritmetika techniques and provide you with examples and exercises. Some of them are:
: This is a book by Arthur Benjamin and Michael Shermer that reveals the secrets of mental aritmetika and shows you how to do amazing calculations in your head. The book covers topics such as addition, subtraction, multiplication, division, squaring, cubing, roots, fractions, decimals, percentages, etc.
: This is a video series by Scott Flansburg that teaches you how to do mental aritmetika using simple and easy methods. The video series covers topics such as counting, adding, subtracting, multiplying, dividing, estimating, etc.
: This is a book by Edward H. Julius that provides you with 30 easy-to-learn math shortcuts for doing mental aritmetika faster and more accurately. The book covers topics such as multiplying by 9, 99, 999, etc., dividing by 5, 25, 125, etc., finding the percentage of a number, finding the average of a group of numbers, etc.
Competitions and challenges for mental aritmetika
If you want to test your mental aritmetika skills and compete with others who share your passion for mental aritmetika, there are many competitions and challenges that you can join. Some of them are:
: This is an international competition that tests the mental calculation abilities of participants in various categories, such as addition, multiplication, square roots, calendar dates, etc. The competition is held every two years in different countries.
: This is an online competition that challenges participants to solve mental calculation problems in a limited time. The competition is open to anyone who wants to participate and has four rounds of increasing difficulty.
: This is an online challenge that offers daily mental aritmetika problems for different levels and ages. The challenge also provides tips and solutions for each problem.
Conclusion
Mental aritmetika is a valuable skill that can benefit your brain development, learning, and everyday life. By learning and practicing mental aritmetika techniques and tips, you can improve your numerical skills, speed, and accuracy, as well as your cognitive abilities, such as memory, concentration, creativity, logic, and reasoning. You can also have fun and enjoy the process of learning new things and challenging yourself. There are many courses and resources that can help you learn and practice mental aritmetika, such as online courses and apps, books and videos, competitions and challenges. We hope that this article has inspired you to start or continue your journey of mental aritmetika.
FAQs
Here are some frequently asked questions about mental aritmetika:
Q: How can I improve my mental aritmetika skills?A: You can improve your mental aritmetika skills by following these steps:
Start with the basics. Learn the basic arithmetic operations and their properties.
Learn some techniques and tips. There are many techniques and tips that can help you do mental aritmetika faster and easier.
Practice regularly. The best way to improve your mental aritmetika skills is to practice them as often as possible.
Monitor your progress and set goals. It is important to keep track of your progress and set realistic and achievable goals for yourself.
Have fun and enjoy the process. Learning and practicing mental aritmetika should not be boring or stressful. You should have fun and enjoy the process of learning new things and challenging yourself.
Q: What are some of the best books and videos for mental aritmetika?A: Some of the best books and videos for mental aritmetika are:
: This is a book by Arthur Benjamin and Michael Shermer that reveals the secrets of mental aritmetika and shows you how to do amazing calculations in your head.
: This is a video series by Scott Flansburg that teaches you how to do mental aritmetika using simple and easy methods.
: This is a book by Edward H. Julius that provides you with 30 easy-to-learn math shortcuts for doing mental aritmetika faster and more accurately.
Q: How can I use the abacus for mental aritmetika?A: You can use the abacus for mental aritmetika by following these steps:
Learn how to read and write numbers on the abacus. The abacus consists of a frame with rods and beads that can be moved to represent numbers. Each rod has a value of 10, 100, 1000, etc., depending on its position. Each bead has a value of 1 or 5, depending on its location.
Learn how to perform basic arithmetic operations on the abacus. You can use the abacus to perform addition, subtraction, multiplication, and division by moving the beads according to certain rules and methods.
Learn how to transfer the abacus image to your mind. You can use the abacus as a tool for mental aritmetika by visualizing the abacus in your mind and manipulating the beads mentally. This can help you improve your visual memory, concentration, and coordination.
Q: What are some of the best online courses and apps for mental aritmetika?A: Some of the best online courses and apps for mental aritmetika are:
: This is a comprehensive course that covers all aspects of mental aritmetika, from basic operations to advanced topics.
: This is an app that helps you practice mental aritmetika tricks and shortcuts.
: This is an app that offers fun and educational games for mental aritmetika and other cognitive skills.
Q: What are some of the best competitions and challenges for mental aritmetika?A: Some of the best competitions and challenges for mental aritmetika are:
: This is an international competition that tests the mental calculation abilities of participants in various categories.
: This is an online competition that challenges participants to solve mental calculation problems in a limited time.
: This is an online challenge that offers daily mental aritmetika problems for different levels and ages.
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