The mental multiplication tricks and tips in this post will let you do mental math faster than a calculator entirely in your head. There are many mental strategies for multiplication, but the mental multiplication strategies covered here can be applied to multiply any set of numbers. Learning the mental multiplication tips in this post will be like learning to ride a bicycle. Once you learn it, it is really very hard to forget it.
Prerequisite For These Multiplication Tricks
Before we proceed, you must have mastered single-digit multiplication. It is a prerequisite that you know your single-digit multiplication tables from 1 x 1 to 9 x 9 before you do mental multiplication of large numbers. If you are a little rusty, bookmark this post now and make sure you memorize your single digit multiplication tables first. If you are strong in your single digit multiplication, you can read on.
This post is the second part of a Mental Math Tricks series. It is highly advised you read the first post of this series – Mental Math Tricks for Speed Math, before you proceed with learning how to do mental math in multiplication.
The Secret of Mental Multiplication Tricks
In the first part of Mental Math Tricks, we learnt that mental math becomes harder to do when you calculate from right to left. Therefore, the secret of mental math is to do the opposite and calculate from left to right instead. By solving from left to right, you will start calling out the answer, before you finish the full calculation. Calculating from left to right might feel a bit weird at first, but it will feel natural with a little practice. In this post, we will see how to apply this to mental multiplication.
What is a Multiplicand and a Multiplier?
Before we get into multiplication tricks to do mental math, let us quickly define what a multiplicand and a multiplier is. Take for example, the multiplication problem 43 x 23. Here the number 43 is the multiplicand – the number being multiplied. The number 23 is the multiplier – the number which is multiplying the first number.
There are several multiplication tricks for mental math in this post. Each mental multiplication method will have two examples. The first example, visible to everybody, will introduce you to the multiplication trick. The second example, visible only to logged-in users, will have variations not covered in the first example. So log in or sign up for free to access the entire content.
Multiplication Tricks for 1 Digit Number
General Mental Multiplication for 1 Digit Multiplier
The general mental multiplication method is to multiply from left to right. Though the general method can be applied for any number, it works best when the numbers don’t end with 7, 8 and 9. We have a separate technique for numbers ending with 7, 8 and 9. For now, let us apply the mental multiplication method to multiply 5321 x 4.
The rule is simple. Multiply from left to right. One digit at a time.
Left to right multiplication is faster because you have to remember fewer numbers to recall and use later. You will immediately start calling out the answer from the very first step of the calculation.
Now try multiplying 7142 x 6. The procedure is the same as before and you can find it below:
Mental Multiplication With Rounding Up for 1 Digit Multiplier
Using mental multiplication tricks after rounding up is useful when the numbers end in 7, 8 or 9. It greatly simplifies the multiplication. Let us see how to apply this with an example. Multiply 68 x 3.
1. Round up the number
2. Multiply from left to right
3. Multiply the amount you rounded up
4. Subtract the numbers from the previous two steps
If you try doing this the way you normally do it on paper, you will realize that it takes more time than what it takes you now to do it in your head. If you don’t have the speed yet, don’t worry. It will come with practice. There are mental multiplication practice exercises and worksheets at the end that you can download and practice.
Now you try multiplying 96 x 7. The procedure is the same as before and you can find it below:
Mental Multiplication of 2 Digit Numbers
General Multiplication Tricks
Let us now look at how to do mental multiplication for 2 digit numbers now. The multiplication tricks we saw earlier needs to be slightly modified. Let us see how to do that with an example. Multiply 36 x 32.
1. Break the multiplicand
2. Multiply from left to right
3. Add the individual answers together to get the final answer
You can solve the same problem by breaking the multiplier instead of the multiplicand. Your choice will depend on which gives you the simpler addition process in Step 3. Try to select the number that has the smaller one’s digit because that will usually result in you adding smaller numbers, in most cases.
Now you try multiplying 26 x 23. The procedure is the same as before and you can find it below:
Rounding Up for 2 Digit Multiplier
Just like with one digit multipliers, rounding up and multiplying is useful when the numbers end in 7, 8 or 9. Let us look at how to do it with an example. Multiply 87 x 99:
1. Round up a number
2. Multiply the rounded-up value and the amount rounded up from left to right
3. Subtract the two numbers
Now you try multiplying 41 x 57. The procedure is the same as before and you can find it below:
Mental Multiplication Using Factors
Like rounding up, one of the multiplication tricks is to factor the number before multiplying it. Let us look at how to do that by trying to multiply 45 x 22.
1. Factor the number
2. Multiply the number with the first factor (left to right)
4. Multiply the product with the second factor (left to right)
In the multiplication tricks we saw earlier, you will have to remember the product of the first digit to add/subtract with the product of the second digit. However, in mental multiplication using factors you just multiply the second factor with the first product, so you don’t have to remember so many numbers as you calculate.
Now you try multiplying 21 x 63 using the factor method. The procedure is the same as before and you can find it below:
Mental Multiplication Tricks Practice Worksheets
Below you can download the PDF mental multiplication practise worksheets to apply the multiplication tricks covered.
Becoming A Human Calculator
You have learnt the basic multiplication tricks. But We have only scratched the surface and there is so much more to cover. If you really want to become a human calculator and take your mental math skills to the next level, then watch this video. In the video I will share the story of how I actually struggled with math and how I got to where I am today. You will learn the secret that will shorten your learning curve and speed up your journey to mental math mastery. To watch the video click here.
Post your questions, clarifications and feedback in the comments. It will take practice before applying the multiplication tricks becomes easy and effortless. You will find it hard initially to remember all the number in your head as you calculate. But practice will help you improve your short term memory for numbers. Force yourself to do mental calculation from left to right for your everyday calculation, and use a calculator only to double-check your numbers. Your speed and ability will improve the more you practice.
15 thoughts on “Mental Multiplication Tricks & Tips To Do Mental Math Faster In Your Head”
Your animations for the last two examples are in the wrong order.
Thanks for letting me know. Fixed it.
In the example you have shown 68 x 3 but initially you hv mentioned 68 x 2.
It was good to read all
Thanks for the comment fixed it.
Thanks. Fixed the Typo
Can you do a similar post for 3 digit number multiplication to 3 digit number?
Yes will do that.
Wow! This has really helped me
Glad it helped.
it helped but still need to learn it
i realy need the same thing as sashank
Practice, learning and thinking again about the steps are great idea for mathematic prectice. Thanks for this informative article on this, and subscribed your blog.
Is there an existing tool in assessing if the learner mastered multiplying two digits mentally
Yes. You can use the website mathtrainer.org to practice
Wow I enjoyed it ,it was so interesting (I love mathematics)