you will be able to perform many calculations faster than someone using a calculator. But in this chapter, my goal is to teach you some easy yet impressive calculations you can learn to do immediately. We’ll save some of the more serious stuff for later.
INSTANT MULTIPLICATION
Let’s begin with one of my favorite feats of mental math—how to multiply, in your head, any two-digit number by eleven. It’s very easy once you know the secret. Consider the problem: 32 x 11To solve this problem, simply add the digits, 3 + 2 = 5, put the 5 between the 3 and the 2, and there is your answer: 352
What could be easier? Now you try:
53 x 11
Since 5 + 3 = 8, your answer is simply 583.
One more. Without looking at the answer or writing anything
down, what is 81 x 11?
Did you get 891? Congratulations! Now before you get too excited, I have shown you only half of what you need to know. Suppose the problem is 85 x 11
Although 8 + 5 = 13, the answer is NOT 8135! As before, the 3 goes in between the numbers, but the 1 needs to be added to the 8 to get the correct answer: 935
Think of the problem this way:
1
835
What could be easier? Now you try:
53 x 11
Since 5 + 3 = 8, your answer is simply 583.
One more. Without looking at the answer or writing anything
down, what is 81 x 11?
Did you get 891? Congratulations! Now before you get too excited, I have shown you only half of what you need to know. Suppose the problem is 85 x 11
Although 8 + 5 = 13, the answer is NOT 8135! As before, the 3 goes in between the numbers, but the 1 needs to be added to the 8 to get the correct answer: 935
Think of the problem this way:
1
835
--------
935
Here is another example. Try 57 x 11.
Since 5 + 7 = 12, the answer is
935
Here is another example. Try 57 x 11.
Since 5 + 7 = 12, the answer is
1
527
527
-------
627
627
Okay, now it’s your turn. As fast as you can, what is 77 x 11? If you got the answer 847, then give yourself a pat on the back. You are on your way to becoming a mathemagician.
Now, I know from experience that if you tell a friend or teacher that you can multiply, in your head, any two-digit number by eleven, it won’t be long before they ask you to do
Now, I know from experience that if you tell a friend or teacher that you can multiply, in your head, any two-digit number by eleven, it won’t be long before they ask you to do
99 x 11. Let’s do that one now, so we are ready for it.
Since 9 + 9 = 18, the answer is:
Since 9 + 9 = 18, the answer is:
1
989
989
-------
1089
Okay, take a moment to practice your new skill a few times, then start showing off. You will be amazed at the reaction you get. (Whether or not you decide to reveal the secret is up to you!) Welcome back. At this point, you probably have a few questions,
such as:
“Can we use this method for multiplying three-digit numbers (or larger) by eleven?”
1
989
1089
Okay, take a moment to practice your new skill a few times, then start showing off. You will be amazed at the reaction you get. (Whether or not you decide to reveal the secret is up to you!) Welcome back. At this point, you probably have a few questions,
such as:
“Can we use this method for multiplying three-digit numbers (or larger) by eleven?”
1
989
-------
1089
1089
___________
1
527
1
527
------
627
For instance, for the problem 314 x 11, the answer still begins with 3 and ends with 4. Since 3 + 1 = 4, and 1 + 4 = 5, the answer is 3454. But we’ll save larger problems like this for later. More practically, you are probably saying to yourself, “Well, this is fine for multiplying by elevens, but what about larger numbers? How do I multiply numbers by twelve, or thirteen, or thirty-six?”
627
For instance, for the problem 314 x 11, the answer still begins with 3 and ends with 4. Since 3 + 1 = 4, and 1 + 4 = 5, the answer is 3454. But we’ll save larger problems like this for later. More practically, you are probably saying to yourself, “Well, this is fine for multiplying by elevens, but what about larger numbers? How do I multiply numbers by twelve, or thirteen, or thirty-six?”
My answer to that is, Patience! That’s what the rest of the posts are all about.
SQUARING AND MORE :
Here is another quick trick. As you probably know, the square of a number is a number
multiplied by itself. For example, the square of 7 is 7 x 7 = 49. Later, I will teach you a simple method that will enable you to easily calculate the square of any two-digit or three-digit (or higher) number. That method is especially simple when the number ends in 5, so let’s do that trick now. To square a two-digit number that ends in 5,
You need to remember only two things.
1. The answer begins by multiplying the first digit by the next higher digit.
2. The answer ends in 25.
For example, to square the number 35, we simply multiply the first digit (3) by the next higher digit (4), then attach 25. Since 3 x 4 = 12, the answer is 1225. Therefore, 35 x 35 = 1225. Our steps can be illustrated this way: How about the square of 85? Since 8 x 9 = 72, we immediately get 85 x 85 = 7225.
We can use a similar trick when multiplying two-digit numbers with the same first digit, and second digits that sum to 10. The answer begins the same way that it did before (the first digit multiplied by the next higher digit), followed by the product of the second digits. For example, let’s try 83 x 87. (Both numbers begin with 8, and the last digits sum to 3 + 7 = 10.)
Since 8 x 9 = 72, and 3 x 7 = 21, the answer is 7221.
83
x 87
------------
8 x 9 = 72
3 x 7 = 21
------------
Answer: 7221
___________________________
85
x 85
------------
8 x 9 = 72
5 x 5 = 25
Answer: 7225
__________________________
35
x 35
-----------
3 x 4 = 12
5 x 5 = 25
Answer:1225
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