Are you ready to twist a little bit more your brain?

As always, the goal is to strengthen your brain. Additionally, this post complements a previous one on how to add and subtract mentally. If you master this post too, you will be ready to perform mentally most of your daily life calculations.

The exercises of this post are going to strengthen your brain in several points:

First, your working memory will be challenged. A lot!

will be challenged. A lot! Second, if you want, you can train at the same time the memory techniques that are a base of the memory techniques (as explained in this post).

that are a base of the memory techniques (as explained in this post). Third, you will have to focus specially for the large multiplications.

The Technique

The techniques explained below build on a previous post explaining the techniques to add and subtract two numbers. If you haven’t performed the training explained in that post, go there and do it before continuing.

First I will describe how to multiply a number of any number of digits times another number of a single digit (for example 345 times 6). Then I will show you how to multiply two numbers of any number of digits (for example 345 times 69).

Multiplication

1. Multiplying a number of more than one digits by another of only one digit

The method is similar to addition:

Let’s assume we want to multiply 345 times 6.

First step, is to decompose the big number into its units, that is units, tens, hundreds,…

345 = 300 + 40 + 5

Then we multiply each unit number by the smaller number, and memorize the results. Optional: you can use the memory technique explained here to memorize the results.

300 * 6 = 1800 (optional: memorize as dove-sow) 40 * 6 = 240 (optional: memorize as nero-sow) 5 * 6 = 30 (optional: memorize as mule)

Then we add each of those numbers in one step each. At each step we add the superior one with the next number. Always start by the largest. Use the mental addition technique to perform the additions

1800 + 240 = 2040 2040 + 30 = 2070 Final result: 2070

2. Multiplying two numbers of any number of digits

When the numbers to multiply are both greater than 10 then a different method is required. Basically consists of decomposing the whole multiplication into a series of simpler multiplications with additions, writting the remaining into the result. Let me explain it with an example.

Let’s say we have to multiply 56 times 92

First, multiply 2 times 6. The result is 12, so I write in the answer 2 and keep 1 for the next operation

2 x 6 = 12 (say two, and remeber one to carry)

Then we multiply 2 times 5 plus the 1 I kept from previous operation. This is 11.

2 x 5 + 1 = 11

Then we multiply 9 times 6 and add the previous 11. This makes 65, so I write 5 and keep 6 for the next operation.

9 x 6 + 11 = 65 ( say five two, and carry six)

Finally we multiply 9 times 5 and add the previous 6. This makes 51, so I write this as the final part of the answer.

9 x 5 + 6 = 51 (say five one five two) Final result: 5152

Division

The division technique is a little different. In this post I am going to explain how to perform divisions of a number with any number of digits by another of a single digit.

Lets assume we are going to divide 163 by 7

First, we should figure out how many digits will have the result. For that, we take the single digit number (7) and multiply it by 10, 100, 1000, etc until we find the number that multiplied by the single digit is greater than the number with more digits (163). Once reached that result, we will know for sure that the result will have as many digits as zeroes has the las multiplication.

7 x 10 = 70 which is smaller than 163 7 x 100 = 700 which is larger than 163 The result will have then two digits (because 100 has two zeroes)

Determine the largest multiple of 10 that when multiplied by the one digit number (7), the answer is below the number with more digits (163). Hence, the answer should be in the range of that multiple.

7 x 20 = 140 (is below 163) 7 x 30 = 210 (is above 163) Hence, the solution will be twenty something (2x)

Next, we extract the multiple obtained at the last step (120) to the number with more digits (163). The result of the subtraction (which we will call the remainder) will be used to calculate the units of the solution

163 – 140 = 23

Now to calculate the units of the solution, just use the remainder of the previous operation to divide it by the single digit number (7)

23 / 7 = 3 with a remainder of 2

The previous result ( 3 ) is the units of the answer. Hence to complete the answer, just concatenate them

2x and 3 –> result is 23 with a remainder of 2

The Workout

Preparation: download a program for your mobile phone or computer that generates random numbers. You can find a list of programs at the end of this posts.

Do the following workouts every day from Monday to Friday for five minutes each day. It will only take you 10 minutes per day. Repeat the training for two weeks and the technique will be yours.

Workout 1 : MULTIPLICATION Start the random numbers generator and use it to generate 10 numbers between 0 and 99999. Write them down on a paper, one beneath another. Then generate 5 numbers between 1 and 9. Write them at the right hand side of the first 5 numbers of the previous list. Then generate 5 numbers between 10 and 99. Write them at the right hand side of the last 5 numbers of the previous list. Start a timer to count the time it takes you to perform the 10 multiplications. Multiply the numbers of the first column by the numbers of the second using the technique explained above. Write down on your Training Workbook the time it took you perform the calculations. Next day, try to beat that time

Workout 2: DIVISION S tart the random numbers generator and use it to generate 10 numbers between 0 and 999. Write them down on a paper, one beneath another. Then generate 10 numbers between 2 and 9 . Write them at the right hand side of the numbers of the previous list. Start a timer to count the time it takes you to perform the 10 divisions. Divide the numbers of the first column by the numbers of the second using the technique explained above. Write down on your Training Workbook the time it took you perform the calculations. Next day, try to beat that time.

Now, you are in your way to be a mental calculator. In next posts you will learn how to do different types of squares and increase your depth in division.

List of random generator programs

For Android

For iPhone

For Web (any operating system)

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