Mental aritmetika öyrənmək üçün abaküs lazımdır?

Mental Arithmetic: What Is It and How to Learn It?

Mental arithmetic is the ability to perform calculations using only the brain, without any tools or devices. It is a useful skill that can improve your number sense, logical thinking, memory, and concentration. It can also help you in various situations in your daily life, such as shopping, cooking, tipping, converting units, investing, scoring, comparing values, etc.

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In this article, you will learn about the history of mental arithmetic, the methods and techniques for doing different types of calculations in your head, the psychological benefits of mental arithmetic, and how to practice and improve your mental arithmetic skills.

Here are some examples of mental arithmetic problems that you might encounter:

• What is 25% of 80?

• What is the square root of 144?

• What is 7 x 8 x 9?

• What is 123 + 456?

• What is 9999 divided by 9?

Do you know how to solve these problems without using a calculator or paper? If not, don't worry. By the end of this article, you will have learned some tricks and techniques that will help you do these calculations faster and easier.

History of Mental Arithmetic

Mental arithmetic has a long and rich history that spans across different cultures and periods. The earliest evidence of mental arithmetic can be traced back to ancient civilizations such as Egypt, Babylon, China, India, Greece, and Rome. These civilizations developed various systems of numeration, notation, and calculation that enabled them to perform complex mathematical operations using only their minds.

Some famous mathematicians who exhibited extraordinary abilities in mental arithmetic include Archimedes (287-212 BC), who could calculate large numbers using his own method of exponentiation; Apollonius (262-190 BC), who could find the cube root of any number up to nine digits; Aryabhata (476-550 AD), who could solve quadratic equations mentally; Leonardo Fibonacci (1170-1250), who introduced the Hindu-Arabic numerals to Europe; John Napier (1550-1617), who invented logarithms; John Wallis (1616-1703), who could extract square roots mentally; Leonhard Euler (1707-1783), who could multiply large numbers mentally; Carl Friedrich Gauss (1777-1855), who could add up all the integers from 1 to 100 mentally; John von Neumann (1903-1957), who could memorize entire books verbatim; Alexander Aitken (1895-1967), who could multiply two nine-digit numbers 160 to get the exact answer. So 67 + 85 = 160 - 8 = 152.

Subtraction

Subtraction is another basic and frequent operation in mental arithmetic. To perform subtraction mentally, you can use the following techniques:

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• Subtract from left to right: Similar to addition, you can subtract from left to right by starting with the largest place value and moving to the smallest. For example, to subtract 456 - 123 mentally, you can start with 400 - 100 = 300, then subtract 50 - 20 = 30 to get 270, then subtract 6 - 3 = 3 to get 267.

• Subtract in groups: You can also group the numbers in a way that makes them easier to subtract mentally. For example, to subtract 48 - 37 mentally, you can group them as (40 - 30) - (8 - 7) = 10 - 1 = 9.

• Subtract by rounding: You can also round the numbers to the nearest multiple of 10 or 100 before subtracting them mentally. For example, to subtract 85 - 67 mentally, you can round them to 90 - 70 = 20. Then you can adjust the answer by adding the amount you rounded up or down. In this case, you rounded up by 5 for 85 and by 3 for 67. So you need to add (5 + 3) = 8 to 20 to get the exact answer. So 85 - 67 = 20 + 8 = 28.

Multiplication

Multiplication is a more complex and challenging operation in mental arithmetic. To perform multiplication mentally, you can use the following techniques:

• Use the distributive property: You can use the distributive property to multiply two numbers by splitting one of them into smaller parts and then adding the products. For example, to multiply 7 x 8 mentally, you can split 7 into 5 and 2, and then multiply each part by 8 and add the results. So 7 x 8 = (5 x 8) + (2 x 8) = 40 + 16 = 56.

• Use doubling and halving: You can also use doubling and halving to multiply two numbers by doubling one of them and halving the other until you get an easy product. For example, to multiply 6 x 7 mentally, you can double 6 and halve 7, then double 12 and halve 3.5, then multiply 24 by 1.75. So 6 x 7 = (12 x 3.5) = (24 x 1.75) = (24 x (1 + 0.5 + 0.25)) = (24 + 12 + 6) = 42.

• Use the multiplication table: You can also use the multiplication table to memorize and recall the products of single-digit numbers. For example, to multiply 9 x 8 mentally, you can recall that it is equal to 72 from the multiplication table.

Division

Division is another difficult and tricky operation in mental arithmetic. To perform division mentally, you can use the following techniques:

• Use the inverse of multiplication: You can use the inverse of multiplication to divide two numbers by finding the missing factor in a multiplication equation. For example, to divide 72 by 9 mentally, you can find the missing factor in the equation _ x 9 = 72. You can recall that it is equal to 8 from the multiplication table.

• Use repeated subtraction: You can also use repeated subtraction to divide two numbers by subtracting the divisor from the dividend repeatedly until you get zero or a remainder. For example, to divide 11 mentally, you can use the average of 10 and 12 as a reference. The average of 10 and 12 is 11. The difference between 10 and 12 is 2. So you need to add or subtract (2 / 2) x (2 / 2) = 1 from the average. So 11 x 11 = (11 + 1) x (11 - 1) = (12 x 10) = (120 - 1) = 119.

Roots

Roots are the inverse of powers. To find the root of a number mentally, you can use the following techniques:

• Use the nearest perfect square or cube: You can use the nearest perfect square or cube to find the root of a number by estimating the difference and adjusting the answer. For example, to find the square root of 50 mentally, you can use the nearest perfect square of 49 as a reference. The square root of 49 is 7. The difference between 50 and 49 is 1. So you need to add a small fraction to 7 to get the answer. So 50 = (49 + 1) (7 + 0.07) = 7.07.

• Use the prime factorization method: You can also use the prime factorization method to find the root of a number by finding the prime factors of the number and grouping them into pairs or triples. For example, to find the cube root of 216 mentally, you can use the prime factorization method. The prime factors of 216 are 2, 2, 2, 3, 3, and 3. You can group them into triples and find the cube root of each group. So 216 = (2 x 2 x 2) x (3 x 3 x 3) = (2 x 3) = 6.

Fractions

Fractions are numbers that represent parts of a whole. To work with fractions mentally, you can use the following techniques:

• Use equivalent fractions: You can use equivalent fractions to simplify or compare fractions by finding a common denominator or numerator. For example, to simplify 12/18 mentally, you can find a common factor of both the numerator and the denominator, such as 6. Then you can divide both by 6 to get an equivalent fraction. So 12/18 = (12 / 6) / (18 / 6) = 2/3.

• Use cross-multiplication: You can use cross-multiplication to multiply or divide fractions by multiplying the numerator of one fraction by the denominator of the other and vice versa. For example, to multiply 2/3 by 4/5 mentally, you can cross-multiply the numerators and denominators. So (2/3) x (4/5) = (2 x 5) / (3 x 4) = 10/12. Then you can simplify the result by using equivalent fractions.

• Use common fractions: You can also use common fractions to work with fractions mentally by memorizing and recalling some common fractions and their decimal or percentage equivalents. For example, to convert 3/4 to a decimal mentally, you can recall that 3/4 is equal to 0.75 or 75%. So 3/4 = 0.75 = 75%.

Decimals

Decimals are numbers that use a decimal point to separate the whole part from the fractional part. To work with decimals mentally, you can use the following techniques:

• Use the powers of 10: You can use the powers of 10 to move the decimal point to the left or right by multiplying or dividing by 10, 100, 1000, etc. For example, to move the decimal point two places to the left in 12.34, you can divide by 100. So 12.34 / 100 = 0.1234.

• Use the place value: You can also use the place value to identify and compare the value of each digit in a decimal number. For example, to compare 0.123 and 0.132 mentally, you can compare the value of each digit from left to right. The first digit is the same (0), the second digit is the same (1), but the third digit is different (2 and 3). Since 3 is greater than 2, 0.132 is greater than 0.123.

• Use fractions and percentages: You can also use fractions and percentages to work with decimals mentally by converting them into equivalent forms. For example, to add 0.25 and 0.75 mentally, you can convert them into fractions or percentages and then add them. So 0.25 + 0.75 = (1/4) + (3/4) = (4/4) = 1 = 100%.

Mental Arithmetic as a Psychological Skill

Mental arithmetic is not only a mathematical skill, but also a psychological skill. It involves various cognitive processes and brain regions that are responsible for numerical cognition, such as the parietal cortex, the prefrontal cortex, the hippocampus, and the cerebellum. Mental arithmetic can enhance various aspects of mental functioning, such as memory, attention, reasoning, creativity, etc.

Here are some of the psychological benefits of mental arithmetic:

• It improves memory: Mental arithmetic can improve both short-term and long-term memory by stimulating the hippocampus and other brain regions involved in memory formation and consolidation. It can also enhance working memory, which is the ability to hold and manipulate information in the mind for a short period of time.

• It increases attention: Mental arithmetic can increase attention by activating the prefrontal cortex and other brain regions involved in attention control and regulation. It can also improve selective attention, which is the ability to focus on relevant information and ignore distractions.

• It enhances reasoning: Mental arithmetic can enhance reasoning by stimulating the parietal cortex and other brain regions involved in logical thinking and problem-solving. It can also improve analytical reasoning, which is the ability to apply rules and principles to new situations and draw valid conclusions.

• It boosts creativity: Mental arithmetic can boost creativity by activating the cerebellum and other brain regions involved in divergent thinking and imagination. It can also improve lateral thinking, which is the ability to generate novel and original ideas and solutions.

To enjoy these psychological benefits of mental arithmetic, you need to practice and maintain your mental arithmetic skills regularly. Here are some tips and suggestions for doing so:

• Start with easy problems: Start with easy problems that you can solve confidently and accurately. Gradually increase the difficulty and complexity of the problems as you improve your skills.

• Use different methods: Use different methods and techniques for solving different types of problems. Experiment with different strategies and find out what works best for you.

• Challenge yourself: Challenge yourself by setting goals and deadlines for solving problems. Try to beat your own records or compete with others.

• Review your mistakes: Review your mistakes and learn from them. Identify your strengths and weaknesses and work on improving them.

• Have fun: Have fun with mental arithmetic by making it a game or a hobby. Find problems that interest you or relate to your life. Enjoy the process of learning and discovering new things.

Conclusion

Mental arithmetic is a valuable skill that can benefit you in many ways. It can improve your number sense, logical thinking, memory, and concentration. It can also help you in various situations in your daily life, such as shopping, cooking, tipping, converting units, investing, scoring, comparing values, etc.

In this article, you learned about the history of mental arithmetic, the methods and techniques for doing different types of calculations in your head, the psychological benefits of mental arithmetic, and how to practice and improve your mental arithmetic skills.

We hope you found this article helpful and enjoyable. We encourage you to continue learning and practicing mental arithmetic. You will be amazed by what you can do with your brain!

FAQs

Here are some frequently asked questions and answers about mental arithmetic:

• Q: How can I improve my mental arithmetic skills? - A: You can improve your mental arithmetic skills by practicing regularly, using different methods and techniques, challenging yourself, reviewing your mistakes, and having fun.

• Q: What are some of the benefits of mental arithmetic? - A: Some of the benefits of mental arithmetic are that it can improve your number sense, logical thinking, memory, and concentration. It can also help you in various situations in your daily life, such as shopping, cooking, tipping, converting units, investing, scoring, comparing values, etc.

• Q: What are some of the best resources for learning mental arithmetic? - A: Some of the best resources for learning mental arithmetic are books, courses, apps, and websites that teach and promote mental arithmetic to learners of all ages and levels. You can also find problems and exercises online or in magazines and newspapers.

• Q: How can I measure my mental arithmetic skills? - A: You can measure your mental arithmetic skills by taking tests or quizzes that assess your speed and accuracy in solving different types of problems. You can also compare your results with others or with your own previous records.

• Q: Is mental arithmetic a natural or learned skill? - A: Mental arithmetic is both a natural and a learned skill. Some people may have a natural aptitude or talent for mental arithmetic, but anyone can learn and improve their mental arithmetic skills with practice and training.

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