Multiplication Tricks For Mental Math

Multiplication Tricks For Mental Math

Multiplication tricks for mental math in this post will let you do multiplication faster than a calculator. There are many multiplication tricks to do mental math, but the ones covered here can be applied to multiply any set of numbers. Learning the techniques in this post will be like learning to ride a bi-cycle. Once you learnt it, it is really very hard to forget.

What You Need To Know

Before you proceed, you must be adept with single digit multiplication. It is a prerequisite that you know single digit multiplication tables from 1 x 1 to 9 x 9. If you are a little rusty, book mark this post now and make sure you memorize your single digit multiplication tables. If you are strong in your single digit multiplication, you can read on.

This post is the second part of a two part series. It is highly advised you read the first post of this series – Mental Math Tricks for Speed Math, before you proceed with reading this post.

The Secret of Mental Multiplication Tricks

In the earlier post on Mental Math Tricks, we saw solving math from right to left is what makes mental math hard. The secret of mental math is to however to do the reverse and solve from left to right. By solving left to right, you will start calling out the answer, before you do the full calculation. This might feel weird at first but will become natural with a little practice. The same technique can be applied to do multiplication.

What is Multiplicand and 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 43 is the multiplicand - the number being multiplied, and 23 is the multiplier - the number which is multiplying the first number.

There are several multiplication tricks for mental math in this post. Each technique will have two examples. The first example is visible to everybody, but you will need to register/login to see the workings for the second example of each technique.

Multiplication Tricks for One Digit Multiplier

General Method

The general method is nothing but the application of secret of multiplication tricks for mental math we saw earlier – 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 secret of multiplication tricks for mental math to multiply 5321 x 4.

The rule is simple. Multiply from left to right. One digit at a time.

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The reason why left to right multiplication is fast is because you have to remember lesser numbers in your head when you try to multiply from left to right. Also you will immediately start calling out the answer from the very first step of the process.

Now you try multiplying 7142 x 6. The procedure to arrive at this answer is the same as before and you can find it below:

Rounding Up for 1 Digit Multiplier

Rounding up and then using the multiplication tricks is especially useful when the numbers end in 7, 8 or 9. It greatly simplifies the multiplication problem. Let us see how to apply this with an example. Multiply 68 x 2.

1. Round up the number

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2. Multiply from left to right

Mental Math Tricks To Do Speed Math - 6 - 4

3. Multiply the amount you rounded up

Mental Math Tricks To Do Speed Math - 6 - 5

4. Subtract the numbers from the previous two steps

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If you try doing these same calculations on paper, the way you normally do, you will see 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 workbooks at the end of this post that will give you tons of practice.

Now you try multiplying 96 x 7. The procedure to arrive at this answer is the same as before and you can find it below:

Multiplication Tricks for 2 Digit Multiplication

General Method

We looked a multiplication using a 1 digit multiplier. Let us look at a 2 digit multiplier now. The multiplication tricks we saw earlier can be applied here. Let us look at how to apply the multiplication tricks with an example. Multiply 36 x 32.

1. Break the multiplicand

Mental Math Tricks To Do Speed Math - 6 - 11

2. Multiply from left to right

Mental Math Tricks To Do Speed Math - 6 - 12 - 1

 

3. Add the individual answers together to get the final answer

Mental Math Tricks To Do Speed Math - 6 - 14

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 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 to arrive at this answer 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

Mental Math Tricks To Do Speed Math - 6 - 18

2. Multiply the rounded up value and the amount rounded up from left to right

Mental Math Tricks To Do Speed Math - 6 - 19

3. Subtract the two numbers

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Now you try multiplying 41 x 57. The procedure to arrive at this answer is the same as before and you can find it below:

Factoring Method

Like rounding up, another technique to use before you apply the secret of multiplication tricks, is to factor the number before multiplying it. Let us look at how to do that by trying to multiply 21 x 63.

1. Factor the number

Mental Math Tricks To Do Speed Math - 6 - 24

2. Multiply the number with the first factor (left to right)

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3. Multiply the product with the second factor (left to right)

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Using the factoring method will not require you to store too many numbers in memory, which is the advantage this method has over others. 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. In factoring method however, you just multiply the second factor with the first product.

Now you try multiplying 45 x 22 using the factor method. The procedure to arrive at this answer is the same as before and you can find it below:

Practice Workbooks for Mental Multiplication Tricks

You can download the practice workbooks to apply the techniques covered in this post below.

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.

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