Mental math tricks in this post will teach you how do mental math with speed and ease that you previously thought was impossible. You will be able to do complex calculations without the aid of a calculator entirely in your head. With a little practice you will quickly get a hang of these mental math tricks to do speed math. You will find yourself extremely confident with numbers like you have never been before.
We will look into some of the easy but still impressive stuff first as an introduction. Then we will look into the mental math tricks to do addition and subtraction. We will cover Multiplication Tricks for Mental Math in the next post. These techniques require you to use nothing but your mind. You should stay away from a pen, paper or a calculator as you learn and apply the techniques.
Each mental math technique will have two examples. The first example is visible for everybody, but you will need to register/login to see the workings for the second example of each technique.
What is Multiplicand and Multiplier?
Before we get into mental math tricks to do speed math, let us quickly understand what a multiplicand and a multiplier is. Take for example, the multiplication problem 43 x 23. Here 43 is the multiplicand – the number being multiplied, and 23 is the multiplier – the number which is multiplying the first number.
Introduction to Multiplication Mental Math Tricks
Try multiplying 423 x 11. It might take you a while if you do not know the technique. Let us look at the mental math technique to multiply by 11:
- The first number of the multiplicand (number multiplied) is put down as the left-hand number of the answer.
- Each successive number of the multiplicand is added to its neighbor at the right.
- The last number of the multiplicand becomes the right hand number of the answer.
Now you try multiplying 534 x 11. The procedure to arrive at this answer is the same as before and you can find it below:
Carrying Over in Mental Math Tricks
Try multiplying 619 x 11. If you said, 67109 then you made a rookie mistake of not carrying over the number. Carrying over numbers is something common in speed math. The steps to multiply by 11 are the same as before but with one slight difference.
- The first number of the multiplicand (number multiplied) is put down as the left-hand number of the answer just like before.
- Each successive number of the multiplicand is added to its neighbor at the left, just like before. If the addition results in two figures, carry over the 1 (Note: Two figure number will not be more than 19), so you will always be carrying over 1.
- The last number of the multiplicand becomes the right hand number of the answer, just like before.
Now you try multiplying 348 x 11. The procedure to arrive at this answer is the same as the previous example and you can find it below:
Mental Math of Multiplication of Other Numbers
Now you must be asking what about multiplication of numbers other than 11. Before we get into that, it is very important to understand the mental math tricks for addition and subtraction, since it serves as a foundation for multiplication. We will look at Multiplication Tricks for Mental Math in the next post.
The Secret of Mental Math Tricks
Solving math from right to left is what makes mental math hard to do in your head. The secret of mental math is to solve from left to right, instead of the other way round. We are taught to solve from right to left in school because it is easier to solve math this way on paper. But when it comes to solving math in your head, the opposite holds true. When you solve from left to right, you will start calling out the answer, before you even complete the full calculation. It might feel weird at first but you will discover that this is the most natural way to do calculations in your head. With a little practice, you will get comfortable solving math left to right really fast.
Mental Math Tricks for Addition
Applying the Secret of Mental Math Tricks to Addition
Let us apply the secret of mental math tricks to add two numbers 9881 + 1234.
The rule is simple. Add from left to right. One digit at a time.
The reason why left to right addition is fast is because you have to remember lesser numbers in your head when you try to add from left to right. Also you will immediately start calling out the answer from the very first step of the process.
Now you give it a shot and add 5321 + 1234. The procedure to arrive at this answer is the same as the previous example and you can find it below:
Addition by Rounding Up
Sometimes the addition might result in a lot of numbers to be carried over. The hardest mental math addition problem you can ever get will be where you need to carry over numbers in all the steps. In that case, it is easier to add it by rounding up the number first and subtracting the amount rounded up. We will look at how to do this as we add 5492 + 8739.
- Round up the number
- Add from left to right
- Subtract the amount you rounded up
Now you give it a shot by adding the numbers 9881 + 1234. The procedure to arrive at this answer is the same as the previous example and you can find the working below:
Mental Math Tricks for Subtraction
Applying the Secret of Mental Math Tricks to Subtraction
The mental math technique for subtraction is no different from that of addition. You simply subtract left to right. Let us apply the secret of mental math tricks to subtract two numbers 8431 – 5741.
- The rule is simple. Subtract from left to right. One digit at a time. Borrow numbers where necessary.
Now you give it a shot and subtract 5389 – 1234. The procedure to arrive at this answer is the same as the previous example and you can find it below:
Subtraction by Rounding Up
Left to right subtraction is easy and straight forward when there is no borrowing. Sometimes the subtraction might result in a lot of numbers to be borrowed from its neighbor. In that case, it is easier to subtract by rounding up the number and adding the amount rounded up. Let us look at how to do this by subtracting 4530 – 3898
- Round up the number
- Subtract from left to right
- Add the amount you rounded up.
By rounding up you have an addition problem instead of a subtraction problem. In mental math it is slightly easier to do addition instead of subtraction.
You might have problem in figuring out how much you rounded up. There is an easy way to find out how much you rounded up. But before we get into that, you give subtracting the numbers 7520 – 4998 a shot. The procedure to arrive at this answer is the same as the previous example and you can find the working below:
Finding Out How Much You Rounded Up
When we subtracted 4530 – 3898, we rounded up 3898 to 4000. You rounded up 102. It can be difficult to figure out how much you rounded up in this case 102. You will need this to add in the end (Step 3 of our earlier example).
To find how much you rounded up when you rounded 3898 to 4000, you need to use compliments. 102 to is the compliment of 898 (the last three digits of 3898).
So how do you find the compliment of a number? It is quite simple. Take for example 898. The compliment of this number will also have three digits. The number (898) should add up with its compliment (102) to give 1000. The first two digits will add to 9 and the last digit will add to 10.
If you notice:
- The first digit of the number (8) and the first digit of its compliment (1), add up to 9.
- Similarly the second digit of the number (9) and the second digit of its compliment (0) add up to 9.
- The last digit of the number (8) and its compliment (2) add up to 10.
So the last digit of a number should add up with the last digit of its compliment to give 10. All the other digits should add up with the corresponding digit in the compliment to give 9.
Okay keeping the above in mind, quickly find the compliment of:
47, 351, 4352
The compliments are 53, 649, 5648.
All the numbers will add up to its compliment to give 9 except for the last digit will add to give 10. Use compliments to find how much you rounded up when you do your subtraction. To practice rounding up using compliments, there are more subtraction exercises in the practice workbook.
Practice Workbooks for Mental Math Tricks
You can download some of the practise workbooks for the techniques covered in this post below.
How To Become A Human Calculator
If you want to take your math skills to the next level, you can really learn a lot from my personal journey. I wasn’t always good at math. I used to hate it and was terrible at it. I made a video to share my personal journey and the secret I learned that changed the way I did math forever. Click here to watch the video now.
If you have any questions or clarifications on this post, post it in the comments sections below. You might have understood the technique, but it will take practise before the technique becomes second nature to you. Initially you will usually find it hard to remember all the number in your head, as you work through the problem. But your memory will improve with practice. When you find yourself reaching out to a calculator in your daily life, calculate from left to right first before double checking your answer with a calculator. With practise your speed and your ability to do mental math will improve.
Next Multiplication Tricks for Mental Math
This post serves as a foundation for other advanced mental math tricks. Once you have practiced and mastered the mental math tricks covered here, you can move on to the next post which covers Multiplication Tricks for Mental Math.