ich kann auch leichter rechnen

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This page will be expanded later to include fractions.

Example 1 (near 100)
95 x 82 = ?
1. Step: 100 - 95 = 5 and 100 - 82 = 18
2. Step: 95 - 18 = 77 or 82 - 5 = 77 (1. Partial result, this one moves forward)
3. Step: 5 x 18 = 90 (2. Partial result (i.e., the differences are multiplied) this goes to the end, so the 90.
4. Step: the solution of 95 x 82 = 7790
Was easy, or?

Example 2 (near 1000))
998 x 899 = ?
1. Step: 1000 - 998 = 2 1000 - 899 = 101
2. Step: 998 - 101 = 897 oder 899 - 2 = 897 (1. Partial result, this one moves forward)
3. Step: 2 x 101 = 202 (2nd partial result, this goes at the end)
4. Step: the solution of 998 x 899 = 897202

Now an example with carryover
 95 x 74 = ?
1. Step: 100 - 95 = 5 und 100 - 74 = 26
2. Step: 95 - 26 = 69 oder 74 - 5 = 69 (1. Partial result, this one moves forward)
3. Step: 5 x 26 = 130 (2nd partial result, this goes at the end)
4. Step: with carryover: 69 + 1 = 70 The carry-over from 130, because only the last two digits remain at the end.
Lösung: 95 x 74 = 7030

Here too, as with my memory exercises, you have to repeat it at least five times, then it will stick.

JNow an example where the numbers are above the power of ten.
 106 x 110 = ?
Step 1: 106 - 100 = 6 and 108 - 100 = (+8) Step 2: 110 + 6 = 116 oder 106 + 10 = 116 (1st partial result, this one goes first)
Step 3: 6 x 10 = 60x (2. Partial result, this goes at the end) Step 4: the solution von 106 x 110 = 11660. Now an example where one number is above the power of ten and one is below. 89 x 108 = ? Step 1: 100 - 89 = (-11) and 108 - 100 = (+8)
Step 2: 89 + 8 = 97 or 108 - 11 = 97 (1st partial result, this goes to the front)

It works from 10 to base infinity. Only when the numbers are too large or too far from the base is it difficult to do mentally; then you'll need a piece of paper. Now practice diligently and see how far you can do it mentally.
Now the rule is: all out of nine, the last out of ten The important thing is calculating the change. For example, you went shopping and spent €7.86 and paid with €10.00. Then the rule is:
All of the 9, the last of the 10. Seven to 9 = 2, then 8 to 9 = 1 and 6 to 102. Partial result, this goes at the end) = 4, so you get 2.14 back. It's simple, isn't it? Here's another example, but this time starting with €20 instead of €10. You still have to pay €7.86, and now you can simply select numbers 1 through 9; you'll just get €10 back more. Because 20 has one more ten at the beginning than €10, the difference is added. So, again, 8 to 9 = 1, then 4 to 9 = 5, and then 6 to 10 = 4, so you get 12.14 back.
Let's say you paid with a 50 note. Then, instead of just adding the ten, there are four tens between 10 and 50. So, the 4 must be at the beginning, and then it continues normally: 8 to 9 are 1, and 6 to 10 are the 4. So, you'll get 42.14 back.

Next, the rule: Perpendicular and Crosswise

example1:
x 36
x 64
Step 1: Multiply the last digits and write down only the last one. 4 x 6 = 24, so write the 4 at the end, remember the 2, or write it very small above it.
Step 2: Now multiply crosswise and then add the results + carry-over. So we have 3 x 4 = 12 + 6 x 6 = 36, which adds up to 48 + the 2 from the carry-over makes 50. Here we again only write the 0 to the left of the 4 and we remember the 5, or write it in small print above it.
Step 3: Now, back to the front, write down 3 x 6 = 18 + the carry-over 5 = 23 to the left of the 5, and then it will say:
Step 4: Result 2304
Here's another example if you'd like:

I always write the numbers one below the other for better clarity, e.g., like in example 1
Example 2:
x 34
x 42
Step 1: Back row 4 x 2 = 8, since there is no carry-over because it's less than 10
Step 2: Now multiply crosswise and then add them together (3 x 2 = 6) + (4 x 4 = 16) equals 22, so write the 2 to the left of the 8 and keep 2 in mind.
Step 3: Now, back to the front, vertically, the 3 x 4 = 12 + 2 = 14 go in front of it now.
Step 4: Result 1428. Did it work? Then try another problem yourself. As I said, if you've practiced at least five, it will get easier.
Important! Always remember to carry over. That's why I prefer to write them in small print above the problem, and once I've added them, I cross them off.

Next, if you like, try a two-digit and a three-digit number. That works too, it just involves a bit more cross-calculation, but otherwise it's exactly the same as with two three-digit numbers.
Since the tens and ones places come first, following the vertical lines, I usually just write "Carry" (Ü). Then crosswise from top left to bottom right and bottom left to top right, then vertically the middle, and then crosswise the hundreds and tens.
And finally, on the left, the hundreds again vertically. But that's a little later. For two-digit numbers, you simply replace the hundreds digit with a zero, e.g., 34 x 125 would then be 034 x 125. If you'd like to try it out on your own, don't worry, just give it a go. So, as always, start by vertically multiplying the units digit on the right. Then, treat it as if you were dealing with two two-digit numbers, and only now does it begin to change. You still proceed in a crisscross pattern, but from the top left to the bottom right.
Then, from the top right to the bottom left, it's best to use an example:
x 023
x 153
So, 3 x 3 (right vertical line), then (2 x 3) + (3 x 5). Since 23 is only a two-digit number, we put a 0 in front of it. But you know, zero always results in 0, so I'll leave that out and write it down immediately. So, on the right, a 9, in front of it the 1 from 21, noting the 2. Now, since 0 x 3 equals zero, directly (1 x 3) + (2 x 5) (middle vertical line). From that, 13 + carry 2 = 15, so write the 5 in front of the 1, and
now the left cross. For example:
x 355
x 344
So, 2 x 1 + carry = 3. Result: 3519. This works the same way with two full three-digit numbers, except that we don't have a zero there, but have to subtract everything. For example:
x 355
x 344
Step 1: Right vertically 4 x 5 = 20, the 0 to the far right and the 2 small as a Ü above it, then the
Step 2: the right cross (4 x 5) + 4 x 5) + Ü = 42, so the 2 in front of the 0 and the 4 as Ü.
Step 3: The outer cross + the vertical center (3 x 4) + (3 x 5) + (4 x 5) + exercise results in 12 + 15 + 20 + 4 = 51. The 1 is moved in front of the 2 and the 5 exercise. Now it says 120.
Step 4: The left cross (3 x 4) + (3 x 5) + 5 Ü = 12+15+5 = 32, so write down 2, 3 in the Ü 2120
Step 5: Vertically on the left (3 x 3) + 3 subtractions = 12, these come before so that the result should now be 122 120.
If you practice often enough, you won't forget a single step. I often forgot the carry-over at the beginning, but since I got into the habit of crossing it off, it works better.
Another numerical example for you to practice with!
x 436
x 553

If you have an 8 at the end and a 2 at the beginning, then the 6-digit result should be correct.

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Here's another page with tips that don't necessarily have anything to do with memorizing. clik here

If you need many more examples, I can only recommend my course. sieh hier.