Mental Math Trainer

Mathematics Runs the Universe

When math is omnipresent in our world then mastering it and being comfortable with numbers will make you a smarter person in all aspects of your life. This is not only true because you will be able to calculate the change you are supposed to receive in a split second when buying bread at the bakery. No, not at all. It is not limited to this. For instance, after a delicious dinner, you will also be able to determine the tip that you might want to give to the obliging waitress with ease and very comfortably.

Not to mention that other people will believe that you are a mental calculator. 'What an impressive person', they will be thinking while they wonder how you have acquired these great skills.

Already our ancestors most likely came up with the idea of counting things. They might have sat around a campfire and checked the number of people in order to figure out how many pieces of fruit they have to collect so that each one of them is satisfied and can enjoy his or her fruit.

You might also have come across enumeration this way in the very first months or years of your life. You have started computing the total of birds in the trees or you have calculated the sum of white cars crossing a bridge.

Mathematics is the language of science or differently stated the language of Nature is math. The famous Fibonacci1 sequence first appears in a book written by Fibonacci where it is used to calculate the growth of rabbit populations. In addition, there is a closed-form expression known as Binet’s formula which relates the magic arrangement of numbers to the golden ratio. This shows that calculus is also present in arts.

Wherever you look you can see the presence of algebra. Flowers have coiled appearances that line up with this chain of integers. To give another example, seashells form perfect mathematical curves (logarithmic spirals to be precise) originating from their chemical balance.

When it comes to calculation without pen and paper, did you know that both our numbers and our fingers are called digits. What a coincidence! The first and simple mental arithmetic tasks are performed with our fingers as aid. Later in (primary) school we used abacus to count to even higher totals.

What is Mental Math?

Have you ever wondered what it is about to do complex estimations solely in your head without writing down anything? Numerical data is needed, it is part of our lives every day, and we typically do not even notice how strongly they are omnipresent in our day-to-day life.

For example, to call a friend, you need an address that you can ring. The time you spent on the phone is measured in numbers of hours, minutes and seconds. Birthday dates are represented as digits as well. And when you want to prepare a dinner and you have invited some guests, you will have to compute the sum of people to prepare enough food for everyone. These examples are not exhaustive as there are a lot more but you probably get the point.

You can already see that being comfortable with decimals will make daily life easier and more satisfactory. In addition, being able to memorize them or doing simple arithmetic operations with them in your head will bring even more ease and will be even more gratifying in your regular routines.

This is not limited to your leisure or recreational time at all. You will also benefit in your professional environment. You can calculate estimates or exact results quickly in your head so you know that there is no typo when using a pocket calculator, spread sheet, or personal computer. You are working in a grocery store and you are comfortable determining the change easily mentally. Another example: You are a teacher or professor and you write some formula at the blackboard without any additional tools.

Example of someone doing mental arithmetic.
Illustrative example of someone doing mental math. The person thinks of a so-called two-by-two (2by2) and a three-by-one (3by1) multiplication problem. Besides, there is also one-by-one (1by1) exercises, among others (not shown in the figure).

All these reasons have hopefully convinced you that it is good to get better at doing complex analytics in your head, be it multiplication, addition, subtraction, or division. All are important, interesting and worth familiarizing with. You will learn, understand, and enhance the concepts with the help of this tool.

Your Private Online Math Tutor

If you have read so far, you have seen that mastering the computation of more or less difficult tasks in your head will have a crucial impact on your life.

On one hand, you will feel more comfortable solving daily problems on the spot such as figuring the tip for a waitress or estimating the change when buying something at the local grocery store.

On the other hand, if you become an expert in mental math, that is, you can add, subtract, multiply, and divide integers in your head faster than most people can do with a calculator. Or you can square two-digit, three-digit, or even four-digit numbers fast and without writing anything down on paper, it will make you an artist and you could perform and demonstrate your skills in front of various audiences. You would be a so-called mathemagician as it appears that you are doing some sort of magic.

In either case, this web application will help you to practice and improve your abilities in cerebral arithmetic. It does not matter whether you are a beginner or an advanced mathematician. The problems are tailor-made so that it is ensured you progress at your pace and level of skill.

Once you are signed up, which is absolutely free of any charge, you can track your improvement with detailed statistical analyses, graphs, and charts. It shows your daily activity as well as how you have improved over a longer time period. Not to mention that, in case you want to, you can also climb the leaderboard to show off your skills to others. This will be a worldwide competition as users are from all over the world. However, this can be toggled: You do not have to reveal your level of expertise and you also can of course stay anonymous.

You can see this website as a math teacher that can and will help you to become more comfortable with numbers and do mental calculations with ease. It basically will help you to benefit from knowing all about it in the modern world and you can see your progress at any point in time.

Since this application is designed as a web page it will always be available as soon as you have Internet. Furthermore, you do not have to download or update any software because as soon as there is an improvement it can be directly implemented. We will take care that everything runs smoothly and stays up to date. Whenever you will visit the site the next time you want to practice and/or compete it will be the newest version that is available. This kind of implementation makes it also easier to consider and put into effect users' suggestions for improvement which are highly appreciated!

How to Learn and Practice Mental Math?

Unfortunately, it is the truth that in order to get better and faster at it, one needs to do a lot of repetition. There are no shortcuts. Thus, exercising and training on a regular basis are indispensable and essential ingredients that cannot be omitted.

This is also encouraged and once you are signed up, your progress is tracked and everything will be retrievable, so you can see your activity and improvement. This will help also for your motivation.

However, just practicing without any proper plan might also not be the most time efficient way to get better. Therefore, here is a breakdown of how to understand the foundations as well as improve:

  1. Learn the basics of how to do arithmetic
  2. Repeat and practice the concepts with the help of a math trainer. This can be best done at
  3. Remember that is fun: It all (the whole process, that is a. and b. above) should be seen as a game and the process has to provide pleasure (not only the final destination)!

The basics of how to conduct it are actually not so complicated and can be broken down into the following steps:

  1. Memorizing mental math tricks

    For instance, multiplying a two-digit number with 11 is as simple as adding the digits of the two-digit number and writing it in between the first and second digit. Here is an example to test it. Let’s say the problem is 34 x 11. Therefore, the two digits of the two-digit number add up to 3 + 4 = 7. Writing it in between gives us 374 and voilà this is the result. Finally, we obtain 34 x 11 = 374 in a split second. This was very simple, wasn’t it?

  2. Calculating from left to right

    In (primary) school we usually learn it the other way around, but note that this is also done with pen and paper and therefore it is just fine! However, when it comes to problem solving skills in your head, it is most likely faster to do it the other way around. Another advantage is, that while you do the computation, you can already start saying out loud the beginning of the solution.

  3. Breaking the exercise into smaller, less complicated assignments

    An example will clarify what is meant. In the addition task 4 + 18, we break the 18 into 8 and 10. So it can be calculated as 4 + 8 which is 12, then adding the remaining 10, 12 + 10 which is 22. Finally, we obtain 4 + 18 = 22.

You can also consult resources on the Internet for further information and many different strategies. See references below 2–5. By following the steps above, being patient, disciplined, and ambitious, you will eventually get better at calculating in your brain. Remember that the learning curve is not always steep which means you will not see improvements every day. There are also plateaus. Do not let yourself be put off by this and keep thinking of your goals!

This means that despite practicing and training, you do not see immediate amelioration in your statistics and data. These times can range from a couple of days to a couple of weeks or even to a couple of months. Such experiences should not discourage you though.

Remember that it is normal and inherent to learning of human beings. In addition, what also helps is to find friends who also want to get better at mental math. This way you can share your experiences and motivate each other. Make it a competition if you feel like it but keep in mind that in the end it should be fun.

Finally, this website and web app should represent a math learning center for you. Or differently stated it is a teacher and tutor with which (or who) you can do your (daily) training wherever you are and whenever you want. So that in the end you are going to improve your feel for numbers and your capabilities in complex calculations solely in your head.

Will Mental Math Boost Your Memory?

One way of prioritizing your cognitive heath is by living a healthy lifestyle. This means that you eat well, exercise physically on a regular basis, socialize, reduce stress and get enough quality sleep. However, there is also the following experts’ opinion: By playing games that exercise parts of your brain which are responsible for doing abstract things such as storing and retrieving information you can increase your cognitive capabilities.

There are different types of memory: Amongst others, there are short-term and long-term memory regions in the brain. Each type of memory activates different parts of the human brain. Games that stimulate these different brain regions will improve your memory.

What is the relation to finding the solution of an addition problem solely in my head? There are many games which will be of interest in order to expand your mind. One quite old one is chess for example. It involves accurate planning and requires creativity. It also needs problem-solving as well as decision-making skills. Depending on the circumstances, sometimes those workouts have to be done under heavy time pressure. Furthermore, chess increases your spatial memory because you have to visualize the board and possible sequences of moves.

When you do arithmetic in your head, the situation is actually quite similar. These kind of math games fulfill all requirements mentioned above in order to advance your brain. On one hand, you have to remember some basics such as addition, subtraction, or multiplication tables. Retrieving the corresponding information when solving such a puzzle activates the long-term memory.

On the other hand, as described above, larger and more difficult problems have to be broken in smaller ones. The results of each smaller exercise have to be memorized and used to construct the final solution. This in turn invokes the usage of short-term memory capacities.

In addition, calculation assignments can oftentimes be solved in different ways as it somewhat depends on how a bigger task is broken in smaller ones. This creativity requirement further sharpens and activates the memory of your brain.


[1] Fibonacci was a famous Italian mathematician. You can find out more about him and other mathematicians here.

[2] How to Improve Mental Math Skills: wikiHow

[3] Fast Arithmetic Tips: cut-the-knot

[4] Amazing Mental Math Techniques and Tricks: reddit

[5] Mental Calculation: wikipedia