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How to Practice and Improve Your Mental Arithmetic Skills

Mental arithmetic is the skill of doing calculations in your head without using any tools or devices, such as a calculator, pen and paper, or abacus. It is a valuable skill that can help you in many everyday situations, such as shopping, cooking, traveling, and more. It can also improve your number sense, logical thinking, memory, and speed of computation.

But how do you practice and improve your mental arithmetic skills? What are some tips and techniques that can make it easier and faster? And what are some games and resources that can challenge you and make it fun? In this article, we will answer these questions and provide you with some useful information on how to become a master of mental math.

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Tips and Techniques for Mental Arithmetic

There are many tips and techniques that can help you perform mental arithmetic more efficiently and accurately. Here are some of the most common ones:

Break down the problems into parts

One of the easiest ways to simplify mental arithmetic problems is to break them down into smaller parts that are easier to handle. For example, if you need to add or subtract several numbers, you can group them by their place value (hundreds, tens, ones) and add or subtract them separately. For example:

712 + 281 = (700 + 200) + (10 + 80) + (2 + 1) = 900 + 90 + 3 = 993

815 - 521 = (800 - 500) + (10 - 20) + (5 - 1) = 300 - 10 + 4 = 294

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Use round numbers and adjust later

Another way to make mental arithmetic easier is to use round numbers that are close to the original ones and adjust the answer later by adding or subtracting the difference. For example:

596 + 380 = (600 + 380) - 4 = 980 - 4 = 976

38 x 3 = (40 x 3) - (2 x 3) = 120 - 6 = 114

Reorder the numbers to make convenient sums

Sometimes, you can reorder the numbers in an addition or subtraction problem to make convenient sums that are easy to remember or work with. For example, you can look for numbers that add up to a multiple of 10 or a power of 10. For example:

7 + 4 + 9 + 13 + 6 + 51 = (7 + 13) + (9 +51) + (6 +4) =20 +60+10=90


Multiply from left to right

Use square numbers and roots

Square numbers are the result of multiplying a number by itself, such as 4 4 = 16 or 9 9 = 81. Knowing some common square numbers can help you with mental arithmetic, especially when you need to multiply or divide large numbers. For example:

48 52 = (50 2) (50 + 2) = 50 2 = 2500 4 = 2496

Here, we used the identity (a b) (a + b) = a b to simplify the problem. We also used the fact that 50 = 2500, which is easy to remember.

Roots are the opposite of squares. The square root of a number is the number that, when multiplied by itself, gives that number. For example, the square root of 16 is 4, because 4 4 = 16. Finding square roots mentally can be tricky, but there are some methods that can help you estimate them or find them exactly. For example:

To estimate the square root of a number, find the two nearest square numbers and use them as a guide. For example, to estimate the square root of 75, we can use the fact that 64

To find the exact square root of a number, use the fact that the difference between two consecutive square numbers is equal to the sum of their square roots. For example, to find the square root of 169, we can use the fact that 169 144 = 25, and that the square roots of 169 and 144 are x and 12, respectively. Therefore, x + 12 = 25, and x = 13.

Estimate and approximate

Sometimes, you don't need to find the exact answer to a mental arithmetic problem, but only an estimate or an approximation. This can save you time and effort, and still give you a reasonable idea of the magnitude of the answer. Estimating and approximating can involve various techniques, such as rounding numbers, using benchmarks or reference points, using fractions or percentages, or using compatible numbers. For example:

To estimate how much money you will save by buying a shirt that is on sale for $24.99 instead of $29.99, you can round both prices to the nearest dollar and subtract them: $30 $25 = $5. This is not the exact answer, but it is close enough for most purposes.

To approximate how many hours are in a year, you can use the benchmark that one year is about 365 days, and multiply it by 24: 365 24 = (360 +5) 24=36024+524=8640+120=8760. This is not the exact answer either, because it does not account for leap years or fractional hours, but it is a good approximation.

Games and Resources for Mental Arithmetic

If you want to practice and improve your mental arithmetic skills further, there are many games and resources that you can use to challenge yourself and have fun. Here are some examples:

Math Trainer

Math Trainer is a free online tool that lets you practice mental arithmetic with different types of problems and difficulty levels. You can choose from addition, subtraction, multiplication, division, mixed operations, fractions, decimals, percentages, powers and roots. You can also set a time limit and track your progress and accuracy.

Mental Math Cards

Mental Math Cards is a free app for iOS and Android devices that helps you practice mental arithmetic with flashcards. You can customize your settings to choose from different operations, number ranges, decimal places and time limits. You can also view your statistics and achievements.

Arithmetic Game

Arithmetic Game is a free online game that tests your mental arithmetic skills with four basic operations: addition, subtraction, multiplication and division. You have to fill in the blanks with the correct numbers to complete the equations as fast as you can. You can choose from three difficulty levels: easy, normal and hard.