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:
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712 + 281 = (700 + 200) + (10 + 80) + (2 + 1) = 900 + 90 + 3 = 993
815 - 521 = (800 - 500) + (10 - 20) + (5 - 1) = 300 - 10 + 4 = 294
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
1000+20+1000+30+1000+40+1000+10=4000+100=4100
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.
Prodigy Game
Prodigy Game is a free online game that combines math skills with an adventure story. You have to create your own character and explore a fantasy world where you have to solve math problems to progress and unlock new features. You can choose from different topics and skills, such as mental arithmetic, fractions, geometry, algebra and more. You can also play with your friends and compete with other players. Prodigy Game is available for free on the web, or as an app for iOS and Android devices.
Mathnasium
Mathnasium is a learning center that offers personalized math tutoring and instruction for students of all ages and levels. Mathnasium uses a unique method that helps students develop their mental arithmetic skills, as well as their conceptual understanding, problem-solving abilities and confidence in math. Mathnasium has over 1,000 locations across the US and Canada, and you can find the nearest one to you on their website.
Conclusion
Mental arithmetic is a skill that can benefit you in many ways, both in school and in life. It can help you perform calculations faster and more accurately, improve your number sense and logical thinking, enhance your memory and concentration, and save you time and resources. By practicing some tips and techniques, such as breaking down problems, using round numbers, reordering numbers, multiplying from left to right, using square numbers and roots, and estimating and approximating, you can make mental arithmetic easier and more efficient. You can also use some games and resources, such as Math Trainer, Mental Math Cards, Arithmetic Game, Prodigy Game and Mathnasium, to challenge yourself and have fun while learning mental arithmetic.
FAQs
Here are some common questions and answers about mental arithmetic:
Q: How can I improve my mental arithmetic speed?
A: To improve your mental arithmetic speed, you need to practice regularly and consistently. You can use some of the games and resources mentioned above to practice different types of problems and difficulty levels. You can also set a time limit for yourself and try to beat your own records. The more you practice, the more familiar you will become with the numbers and the operations, and the faster you will be able to perform them.
Q: What are some benefits of mental arithmetic for children?
A: Mental arithmetic can help children develop their math skills from an early age. It can help them understand the meaning and relationships of numbers, operations, fractions, decimals, percentages and more. It can also help them improve their logical thinking, reasoning, creativity, memory and concentration. Mental arithmetic can also boost their confidence and motivation in math, as they can see their progress and achievements.
Q: What are some challenges of mental arithmetic?
A: Mental arithmetic can be challenging for some people because it requires a lot of attention, focus and mental effort. It can also be affected by factors such as stress, anxiety, fatigue or distraction. Some people may also have difficulties with certain types of problems or operations, such as division or fractions. To overcome these challenges, it is important to practice mental arithmetic in a relaxed and positive environment, start with simple problems and gradually increase the complexity, use some tips and techniques to simplify the problems, check your answers for accuracy, and seek help or feedback if needed.
Q: What are some applications of mental arithmetic in real life?
A: Mental arithmetic can be useful in many real-life situations, such as:
Shopping: You can use mental arithmetic to compare prices, calculate discounts, taxes or tips, or make a budget.
Cooking: You can use mental arithmetic to measure ingredients, convert units or temperatures, or adjust recipes.
Traveling: You can use mental arithmetic to plan your itinerary, convert currencies or distances, or estimate time or costs.
Gaming: You can use mental arithmetic to keep score, strategize or optimize your moves, or increase your chances of winning.
Learning: You can use mental arithmetic to reinforce your math skills, learn new concepts or topics, or prepare for exams or tests.
Q: How can I make mental arithmetic fun?
A: There are many ways to make mental arithmetic fun, such as:
Playing games: You can play some of the games mentioned above or create your own games with cards, dice, coins, or other objects. You can also play with your friends or family and make it a competition or a collaboration.
Using real-life scenarios: You can use mental arithmetic to solve problems or answer questions that relate to your interests, hobbies, or goals. For example, you can use mental arithmetic to calculate how much money you need to save for a trip, how many calories you burn in a workout, or how many books you can read in a year.
Setting goals and rewards: You can set goals for yourself to improve your mental arithmetic skills, such as solving a certain number of problems in a given time, reaching a certain level of difficulty, or learning a new technique or trick. You can also reward yourself for achieving your goals, such as buying yourself a treat, watching your favorite show, or doing something fun.
I hope you enjoyed this article and learned something new about mental arithmetic. If you have any questions or comments, feel free to leave them below. And don't forget to practice and have fun with mental arithmetic! 44f88ac181
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