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Learn how to Calculate Faster than a Calculator with our Maths Help

From Joseph, published on 26/05/2017 We Love Prof - UK > Academia > Maths > Mental Maths: How to Improve your calculating skills

From the second you start learning maths and taking maths tutorials, it requires a lot of concentration, persistence, and work, mental arithmetic. The works only gets harder by the time you do your SATs or GCSE maths revision at secondary school, A Levels at sixth form, and go on to university.

However, it’s also really useful to know how to do quick and effective mental arithmetic in our everyday lives, whether it’s for doing the shopping, DIY, sewing, etc.

Trick for getting better at mental maths. Improving your mental arithmetic requires concentration. (Source: Life Martini)

And while we all have a mobile phone, we don’t always have it to hand when we need it and, when we do, we waste a lot of time just looking for the “Calculator” app.

Going back over the basics of mental arithmetic can help you get out a lot of trouble during your exams. However, it’s not just for when you’re doing your A Levels. It can also help you make the most of other situations, such as during maths tutorials with a maths tutor.

How do you do it? How do you get better at maths? Are there exercises, techniques, or ways to improve your level?

Emma

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The Advantages of Mental Arithmetic

Whether your a student or not, mental arithmetic has a lot of considerable advantages in our daily lives, whether we’re a student or not.

It allows you to work out figures quickly in any situation and, even better, means you don’t need to get your calculator out.

Put simply, you can learn to count quickly!

For anyone who wants to improve their level in maths, mental arithmetic allows you to work better with numbers and familiarise yourself with certain operations and their properties.

Mental arithmetic is used all the time in various situations: it allows you to predict a calculation’s order of magnitude, which could come in handy when studying decimals or proportionality, for example.

What is the best way to learn my times tables? You’ll need to know your multiplication tables to do your shopping. (Source: This Is Money)

Finally, mental arithmetic can shape your brain, change your way of thinking, and improve your memory, your analytical, and rational thinking.

Though it mightn’t seem it, it can also be a lot of fun: If you like doing “Magic Squares” or playing “Countdown”, mental arithmetic can help you get your neurons firing at full speed all while having fun, as well as doing maths without really noticing.

Why Do Mental Arithmetic?

There are several reasons for doing mental arithmetic and developing your ability to carry out calculations in your head.

  • Once this becomes second nature, it’ll free up your mind to focus on rational thinking,
    You can save time and, in some cases, money (just ask either poker players or bankers!)
  • Travel light: you needn’t bring your heavy calculator with you. Fair enough, you’ve also got your smartphone but you won’t need to get it out to work out 8×7…
  • Impress: Thanks to your training, the multiplication tables up to 11 and 12 pose no problem,
  • You won’t get ripped off when it comes to money,
  • You’ll need fewer maths tutorials!

Good News! Mental Arithmetic Can Be Learnt

Now that you’ve got some good reasons to learn mental arithmetic, why are you hesitating?

Don’t worry!

Learning to manipulate numbers is just a learned habit. I can assure anyone that thinks mathematical ability is innate that this is far from the truth.

Can you learn mental arithmetic? Do you dream of being as good at maths as Dustin Hoffman was in Rain Man? (Source: Allocine)

If some people seem to have these abilities, it doesn’t mean that they were born with them. This is a skill they’ve learnt.

Some scientists have been able to determine that mental arithmetic activates areas of the brain related to spatial awareness. The representation of numbers can therefore be compared to spatial awareness. When we count, whether we add or subtract, it’s almost as if we move the numbers to one side or the other of a mental abacus to find the result. This is important to keep in mind when we find numeracy difficult.

It’s also useful to develop mental arithmetic skills, in children especially, so that you can tackle various pedagogic approaches. Games using numbers and counters in a physical space stimulate the area of the brain concerned.

So make sure you play Ludo with your children, it’ll help them!

Still not convinced?

Other researchers focused on Rüdiger Gamm, a mental athlete, to understand how he manages to carry out such complex calculations in his head.

It emerged that in this case the mental calculator activates the frontal temporal brain regions generally concerned with long-term memory. He has a plethora of information at his disposal which helps him to break records in mental arithmetic.

Don’t despair! He was drawn to arithmetic late on at the age 20 and it’s thanks to daily training that he managed to develop his skills to such a level!

At any rate, you should remember that memory is your best ally when it comes to becoming good at mental arithmetic!

Mental Arithmetic Training

In any case, mental arithmetic practice has to be regular, around 10 minutes per day should be enough: your brain needs to develop reflex actions for this, repeating the same formulae over and over, the same calculations until they become obvious and natural, like riding a bike or simply breathing.

What practice tests can I do to train myself in maths? Let’s try some easier maths exercises first! (Source: Freepik)

Mental arithmetic should be practised orally and written down, using exercise books, maths worksheets, a slate, cards, dice, computer programmes, etc.

It’s important to keep a record of your mental arithmetic progress so you can see your mental development. This will help you out with maths problems and help you become a good maths student.

Here are the basic tools to boost your mental arithmetic skills:

  • Addition and multiplication tables,
  • Knowledge of the complements of the number 10,
  • Knowledge of squares up to 15² (225) as well as the powers of 2,
  • Multiplying by powers of 10 with negative exponents (moving the decimal place to the left) and positive exponents (moving the decimal place to the right),
  • Dividing by a number is the same as multiplying by its reciprocal,
  • for example, divided by 0.25 is the same as multiplying by 4,
  • Learning the special products: (a+b) ² = a²+2ab+b², (a-b) ² = a²-2ab+b², (a+b) (a-b) = a²-b²,
  • Learning the rules of factorisation,
  • Knowledge of the orders of magnitude for Pi (3.14159), the Golden Ratio (1.618), etc.

What are the best ways to get better at maths? This is all you’ll need to improve your mental arithmetic! (Source: Polaris Smart)

Tips for Calculating like Einstein

Look at the last digit

Whatever the number, look at how it ends.

If it’s even (0, 2, 4, 6, 8) or 5, it’ll be divisible by 2, 5, or 10.

For example, 22 ends with an even number so it’s divisible by 2, while 45 ends with a 5 and is divisible by 5.

150 ends with a 0 so it’s therefore divisible by 10.

A number divisible by 3 or 9.

Add up the digits to find out if the number is divisible by 3 or 9.

In fact, a number is divisible by 3 if the sum of its digits is equal to a multiple of 3 (e.g.: 18 = 1 + 8 = 9, a multiple of 3).

A number is divisible by 9 if the sum of its digits is equal to a multiple of 9 (e.g.: 936, 9 + 3 + 6 = 18, which is 1 + 8 = 9, which is a multiple of 9).

It should be noted that if the sum of the digits is divisible by 3 and an even number, it’s divisible by 6, too.

For Addition

Deconstruct the numbers to make things simpler.

For example, 72 + 29 is (70 + 2) + (20 + 9) = (70 + 20) + (2 + 9) = 90 + 11 = 101.

Or even: 13 + 48 is 13 + (50 – 2) = 63 – 2 = 61.

For Subtraction

Learn to simplify numbers.

For example: 1958 – 1907. The number 1900 is included in both numbers so just subtract the tens and units, 58 – 7 = 51.

The Japanese Method of Multiplication

Are you not ready to do complicated multiplication in your head, yet?

With the visual Japanese multiplication technique, you’ll see these operations much more clearly. All you have to do is draw lines and the result appears as if by magic.

Easy, right?

Once you’ve learnt this technique, it’s much easier to carry out these operations in your head. In fact, by envisioning these lines in your head, you can visualise the result, without needing a sheet of paper to draw the lines.

Wisdom from the Land of the Rising Sun…

Butterfly Fractions

Not being able to solve fractions can give you a headache!

Adding or subtracting fractions requires a common denominator. To avoid this step, use the butterfly method. With a bit of training you can do this in your head.

For example: 3/4 + 2/5

First do some cross multiplication: 3 x 5 =15 and 4 x 2 = 8

Then add the two results to get the final numerator, 15 + 8 = 23

To find the denominator, multiply the two denominators: 4 x 5 =20

Therefore: 3/4 + 2/5 = 23/20

You can also use this technique to subtract fractions.

Maths quiz, how do you do butterfly fractions? Understand butterfly fractions yet? (Source: Inverse)

How Do You Multiply by 11?

It couldn’t be simpler.

To work out 32 x 11, all you have to do is multiply 32 x 10, then add 32, so 320 + 32 = 352.

Do you know the second technique? It’s really simple for doing in your head.

For the same problem, 32 x 11, all you have to do is add the 2 digits from the number being multiplied by 11 and place them between the two numbers.

Therefore, 3 + 2 =5, putting the resulting 5 between the 3 and 2 and we get: 352!

If the addition results in a number with two digits like multiplying 56 x 11, the solution is simple. 5 + 6 = 11, we place the second 1 between the 5 and 6 and we add the second 1 to the 5. We therefore get: 616.

Other advice for improving mental arithmetic

  • Wisely group numbers together before working anything out. For example, 1.2 / 1.8 = 12 / 18 = 120 / 180,
  • Put units that make 10 together in order to make your additions easier (1 + 9, 2 + 8, 3 + 7, etc.),
  • Adding or subtracting by 9, 19, or 29. Just add or subtract by 10, 20, or 30, before adding or subtracting 1,
  • Dividing by a number is the same as multiplying by its reciprocal,
  • To add 2 fractions, make sure they have the same denominator.

Follow these maths tips to the letter!

Online Resources for Working on Your Mental Arithmetic

To get better at maths and mental arithmetic, the internet is an excellent resource that complements your tutorials with a maths tutor.

There are plenty of websites that have quizzes, texts, and exercises. Here are a select few:

  • Khan Academy: This website features video lessons as well as practice questions to help you learn.
  • BBC Bitesize: The BBC provides resources for students of all ages. Great school-aged children.
  • TES: Resources for teachers in a variety of subject, including maths.

When you learn while having fun, you don’t even notice you’re learning.

We’ve realised that if you want to get good at maths, and mental arithmetic in particular, memorising is hugely important: remember that you have to learn the principles off by heart and know your addition and multiplication tables. Do this repeatedly, again and again.

Train your brain to remember, everything will become second nature, and your ability in mental arithmetic will increase tenfold.

You have to train, using different strategies, in order to make these things come naturally to you.

This, of course, requires time and a personal commitment but the result is worth the cost because you’ll have these reflexes for the rest of your life.

Using Games to Get Better at Mental Arithmetic

Struggling maths students at school are a common issue. A lack of mental arithmetic can negatively impact students’ futures. A study carried out in 2014 highlighted that 40% of students at primary school have problems with maths.

It was also shown that these problems at primary school included multiplication and division tables, decimals, and representing large numbers.

Given these findings, new programmes tend to have a focus on mental arithmetic. After learning subtraction, addition, and multiplication tables, mental arithmetic also includes:

  • Establishing reflexes,
  • Refining logical thinking,
  • Getting used to working with numbers,
  • Learning the properties of numbers.

To help children get better at mental arithmetic, you should ensure that this practice is fun. Let them learn while they’re having fun! This is a great way to encourage them to enjoy numeracy.

Learning has to be progressive. Games are a good way to learn to calculate without being subjected to the stricter aspects of tutorials with a maths tutor.

The Incredible Performances of the Mental Calculation World Cup Champions

Even if such mathematical genius is rare, I still have to tell you about some of the best performances from the Mental Calculation World Cup Champions…

These sorts of performances show to what extent humans can train their brain and improve their reasoning and memory. These talented mathematicians are living proof.

What have they got in common? A high IQ, of course, but mainly incredible mental arithmetic records!

Rüdiger Gamm

This talented calculator only became interested in maths at the age of 20. Even though he has a good memory for numbers, he wasn’t very good at maths in school. As soon as he became interested in mental arithmetic, he memorised figures and techniques for specific calculations. He can also raise 2-digit numbers to the power of 15, divide 2 prime numbers, and carry out operations with complex numbers in just a few seconds.

Gert Mittring

Another incredible example! In 2016, Gert Mittring worked out the 89,247th root of a number in 6 minutes 1.4 seconds. This resulted in over a million digits over 154 pages. Pretty impressive, right? You can see why this maths-mad German psychologist has already 11 world champion titles.

Alexis Lemaire

France also has its own mental athlete star. Alexis Lemaire. In 2007, he worked out the 13th root of a 200-digit number chosen randomly by a computer in 72 seconds. To get this you have to multiply this number by itself 13 times. With this taking just over a minute, it’s safe to say this isn’t something everyone can do!

The world of mental arithmetic is really fascinating! So, as you can see, the human brain is capable of incredible things. You’ve got no excuse for not learning those time tables!

Have fun, get training, use all the resources available online and in print, challenge yourself (or ask someone to challenge you), but always train and revise regularly. This is the price you have to pay if you want to get good at mental arithmetic.

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