Do you think mathematics is only for the genius minds and those who have an IQ of 140+? Maybe not.
Mathematics has given us varied tool sets to solve some of the complex problems that world around us presents. From counting objects to calculating distance between extra terrestrial bodies, the applications are endless.
But mental math as a stream of mathematics has been ignored in the modern world due to the advent of calculators and computers which can carry out possibly any calculation you could imagine.
In business, you come across numbers everyday. Especially leaders have to make most of their key decisions by analyzing numbers to derive logical conclusions. While in a business negotiation, there could be multiple situations where you need to quickly estimate – if not find the accurate value – overall deal size, profitability or amount of resources required. Or maybe you are in a discussion with a firm to strike a potential partnership where you need to run some numbers in your head. And this is where mental math comes to your rescue. It is a collection of techniques or practices that help you do fast mental calculations without using any tools or gadgets.
Even with numbers being a critical part of our professional life, multiple studies show that a significant percentage of adults do not possess basic math skills.
In a YouGov poll of 2000 people commissioned by BAE Systems in the UK, 38 percent said that their job requires some knowledge of mathematics. The study also found that 13% needed a calculator to add numbers greater than 100. According to another study conducted by PIAAC (Programme for International Assessment of Adult Competencies) in 2012. US ranks even lower in terms of numeracy skills.
Let us put the stats aside for a while, and look at what science says.
According to a new brain-scanning study published by Duke University researchers, engaging a specific part of the brain during mental math exercises is connected with better emotional health. Also a study conducted by Ryuta Kawashima of Tohuku University concluded that mental arithmetic bulks up brain muscle far more than any quick-fingered exercise on a PlayStation.
With such a difference it could make, are we prepared with our mental math skills? This article is intended to get you started with some of the simplest techniques, and develop an interest in this area.
Two and three digit addition
The fundamental difference in the approach used in mental math and traditional way of doing arithmetic is that in the former we try to identify patterns and structure of numbers to simplify the problem rather than mugging up steps to arrive at the final solution.
For example, instead of just seeing 87 as a single number, identify that it is a combination of 10s and 1s.
This means 87 = (8×10) + (7×1)
Every number can be represented in such a simple format. This helps to visualize the number better, and hence will make mental addition easier and faster.
Let us first start with adding two 2 digit numbers 54 and 78. The traditional method is as shown below.
We have been taught to add numbers using the above method. This requires pen and paper, and is very difficult to visualize if you attempt to do it in your head.
Instead, as mentioned above, try to break down the two numbers into 10s and 1s.
Then 54 = (5×10) + (4×1)
And 78 = (7×10) + (8×1)
When you add the two numbers, group the 10s and 1s together.
This would give 54 + 78 = (5×10) + (7×10) + (4×1) + (8×1)
Now when you do the operation in your head, add the 10s and 1s separately.
There are 5 + 7 = 12 tens (120) and 12 ones (12)
The final answer would be 120 + 12 = 132.
Here, by breaking down the numbers into smaller units, we are helping our brain to think in a more structured way and reduce confusion. This method of feeding objects or information into the brain in a structured way is used by many memory experts. The Major System used to memorize numbers is an example for this approach.
If you find this too obvious, try to sum a series of two digit numbers in your mind using the traditional method, and then the shortcut.
Let us look at the following example:
38 + 74+82+57+49 = ?
Adding these numbers using the traditional method is a pain, and would definitely require paper and pen. Let us see how we can do this really fast using the shortcut.
While you do this, add two numbers at a time. So rather than trying to break down all the numbers, do it for only two numbers at a time.
For example, start by adding 38 and 74. This is how you would add this in your head
38 + 74 = (3×10) + (7×10) + (8×1) + (4×1) = 112
The sum of first two numbers is more than 100. So how would you break this down?
Write it as (11×10) + (2×1). And continue the addition the same way with the rest of the numbers. With a bit of practice, you will be able to master this, and do all of this in your head with ease.
Once you find yourself comfortable with two digit addition, you could try adding 3 digit numbers. We have already seen how to break down a 3 digit number.
Subtraction works the same way as addition. Using the break down method, you could convert any number into smaller components and carry out the operation. Let us just look at one example here
Take 47 + 54 – 72 -29 +61.
Here for ease of doing the problem, you can club together the numbers to be added and subtracted.
This would give us (47 + 54 + 61) – (72 + 29).
= 162 – 101
You can break down 162 as (16 x 10) + (2 x 1), and 101 as (10 x 10) + (1 x 1)
So the equation can be written as (16 x 10) – (10 x 10) + (2 x 1) – (1 x 1)
= (6 x 10) + (1 x 1) = 61
Practice subtraction yourself by taking more such examples.
Multiplication and percentages
Many of us see multiplication as a tough exercise. This perception needs to change. The fundamental concept of breaking down numbers into smaller units applies in the case of multiplication as well. In this section we will look at a universal technique you could apply to any multiplication problem. Then we would also look at how to use this method to easily calculate percentages that have more practical applications in a business setting.
To be able to do 2×2 multiplications (2 digit multiplied by a 2 digit) fast, you need to be comfortable with 2×1 multiplication (2 digit multiplied by 1 digit).
Let us look at such an example first. Take 87 x 8.
Apply the same concept of breaking down numbers.
87 x 8 = (80+7) x 8 = (80 x 8) + (7 x 8) = 696.
Practice a few more examples for 2×1 multiplication.
Let us now see how to multiply two 2 digit numbers fast. Take 37 x 67 as an example.
Break down the problem as 37 x 67 = 37 x (60 + 7) = (37 x 60) + (37 x 7).
If you have practiced your 2×1 multiplication enough, you would be able to carry out the above operation easily. See how it can be done below
37 x 60 = 37 x 6 x 10 = (30 + 7) x 6 x 10 = 2220
Similarly, 37 x 7 = 259
Which gives 37 x 67 = 2220 + 259
You could break down 2220 into (22 x 100) + (2×10), and 259 into (25 x 10) + (9 x 1)
The answer is 2479.
When you write it down, it looks like too many steps. But if you take one leap at a time by starting with addition, you would be able to move to multiplication after enough practice. Look at it like different grades. Only when you clear a particular grade/exam, you would be able to move to the next. Once you start having a good grab of it, you would love to do more due to the mere mental satisfaction you get while solving arithmetic that you otherwise thought was impossible.
Some of you might be thinking that multiplication does not have too much of application in a typical day of a business professional. But that will change if you start applying it to calculate percentages.
Be it to carry out profitability calculations, cost-benefit analyses, or ROI estimation, percentages are required in numerous transactional and strategic business activities. Deriving percentages is nothing but an extension of multiplication. Let us understand how.
Let us say you want to find out 17% of 64. The value would be (17/100) x 64
= (17 x 64)/100
Now apply the shortcut for multiplication.
17 x 64 = 17 x (60 + 4) = 1088
So 17% of 64 = 1088/100 = 10.88
Let us look at another example
54% of 72 = (54 x 72)/100
54 x 72 = 54 x (70 +2) = 3888
So 54% of 72 = 3888/100 = 38.88
Calculating percentages of 3 digit numbers requires us to be comfortable with either 3×2 multiplication or division. Please have a look at Mental math for business – part 02 – fast multiplication and division to learn how.
Do all these make a difference?
We have discussed so far some of the basic techniques used for addition, subtraction and multiplication. But is it really possible for you to do all these fast mental calculations?
If you believe that the ability of your brain is limited, you are wrong. According to Harvard health, brain can learn and grow as we age. This process is called brain plasticity. This means you can train it to do certain things through constant practice and attention.
Now, the extent to which each individual can train his/her brain depends on a lot of factors. Some might be able to do mental math faster than others. But the idea here is to create better versions of yourself, and enable you to make faster business decisions through better number crunching and analysis.
The techniques mentioned in this article will help you get started. What you could do with mental math is a never ending discussion. So expect more to come your way soon. Meanwhile please feel free to state your opinion and feedback in the comments section.