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Wednesday, October 8, 2014
Saturday, July 26, 2014
Puzzle quiz 1
- Puzzle Quiz 1
- Puzzle Quiz 2
- Puzzle Quiz 3
- Puzzle Quiz 4
- Puzzle Quiz 5
- Puzzle Quiz 6
- Puzzle Quiz 7
- Puzzle Quiz 8
- Puzzle Quiz 9
- Puzzle Quiz 10
- Puzzle Quiz 12
- Puzzle Quiz 13
- Puzzle Quiz 14
Sunday, June 1, 2014
Two-Digit Addition
Two-Digit Addition
Our assumption is that you know how to add and subtract
one-digit numbers. We will begin with two-digit addition, something I suspect
you can already do fairly well in your head. The following exercises are good
practice, however, because the two-digit addition skills that you acquire here
will be needed for larger addition problems, as well as virtually all multiplication
problems in later lessons. This is the key to virtually every method you will learn
in this blog. To paraphrase an old saying, there are three components to
success—simplify, simplify, simplify.
The easiest two-digit addition problems are those that do not
require you to carry any numbers, when the first digits sum to 9 or below and
the last digits sum to 9 or below. For example:
47
+32(30+2)
To solve 47 +32, first add 30, then add 2. After adding 30, you
have the simpler problem 77 +2, which equals 79. We illustrate this as follows:
47 +32 = 77 +2 = 79
(first add 30) (then add 2)
The above diagram is simply a way of representing the mental
processes involved in arriving at an answer using our method. While you need to
be able to read and understand such diagrams as you work your way through this
book, our method does not require you to write down anything yourself.
Now let’s try a calculation that requires you to carry a
number:
28
+36(30+6)
Adding from left to right, you can simplify the problem by Adding 28+30=58; then 58+6=64.
28 +36 = 58 +6 =
64
(first add 30)
(then add 2)
Was that easier? If you would like to
try your hand at more two-digit addition problems, check out the set of
exercises below.
1. 44 + 67 =
2. 56 + 87 =
3. 76 + 43 =
4. 98 + 32 =
5. 78 + 83 =
Three-Digit Addition
Three-Digit Addition
The strategy for adding three-digit numbers is the same as
for adding two-digit numbers: you add from left to right. After each step, you
arrive at a new (and simpler) addition problem. Let’s try the following:
473
+326(300+20+6)
Starting with 473, we add 300, then
add 20, then add 6. After adding 300 (473 +300=773), the problem becomes 773+26.
After adding 20 (773+20=793), the problem simplifies to 793+6=799. This thought
process can be diagrammed as follows:
473 + 326 = 773 + 26 = 793 + 6 = 799
+300 +20 +6
Let’s try
another one for practice:
568
+496(400+40+6)
Then,
568 + 496 = 968 + 96 = 1058 + 6 = 1064
568 + 496 = 968 + 96 = 1058 + 6 = 1064
+400 +90 +6
This
addition problem is a little more difficult than the last one since it requires
you to carry numbers in all three steps. However, with this particular problem
you have the option of using an alternative method. I am sure you will agree
that it is a lot easier to add 500 to 759 than it is to add 496, so try adding
500 and then subtracting the difference:
568
+496(500-6)
Then
568 + 496 =
1068 - 4 = 1064
(
First add +500) ( then subtract -6
)
Practice the
following three-digit addition exercises,
1. 345 + 451 =
2. 673 + 496 =
. 3. 786 + 429 =
4. 369 + 345 =
5. 281 + 496 =
Thursday, May 29, 2014
INSTANT MULTIPLICATION BY ELVEN
INSTANT MULTIPLICATION BY ELVEN
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 *11
To 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 *11
Since 5 +3 =8, your answer is simply
583
One more. Without looking at the
answer or writing anything down, what is
81 =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
92*11
Although
9+2=11
1
9 1 2
1012
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?”
Absolutely. For instance, for the
problem 314 *11, the answer still begins with 3 and ends with 4. Since 3 +1 =4,
and
1+4=5, the answer is 3454
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