Use the formula ALL FROM 9 AND THE LAST FROM 10 to perform instant subtractions.
For example 1000 - 357 = 643
We simply take each figure in 357 from 9 and the last figure from 10. So the answer is 1000 - 357 = 643
And thats all there is to it!
This always works for subtractions from numbers consisting of a 1 followed by noughts: 100; 1000; 10,000 etc.
Similarly 10,000 - 1049 = 8951
For 1000 - 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 83 is 083.
So 1000 - 83 becomes 1000 - 083 = 917
Top of Form
Try some yourself:
1) 1000 - 777 = 2) 1000 - 283 = 3) 1000 - 505 = 4) 10,000 - 2345 = 5) 10000 - 9876 = 6) 10,000 - 1101 = 7) 100 - 57 = 8) 1000 - 57 = 9) 10,000 - 321 = 10) 10,000 - 38 = Total Correct = Bottom of Form
Return to Index
Tutorial 2
Using VERTICALLY AND CROSSWISE you do not need to the multiplication tables beyond 5 X 5.
Suppose you need 8 x 7
8 is 2 below 10 and 7 is 3 below 10. Think of it like this: The answer is 56. The diagram below shows how you get it. You subtract crosswise 8-3 or 7 - 2 to get 5, the first figure of the answer. And you multiply vertically: 2 x 3 to get 6, the last figure of the answer.
That's all you do:
See how far the numbers are below 10, subtract one number's deficiency from the other number, and multiply the deficiencies together.
7 x 6 = 42 Here there is a carry: the 1 in the 12 goes over to make 3 into 4.
Top of Form
Multply These:
1) 8 8 x 2) 9 7 x 3) 8 9 x 4) 7 7 x 5) 9 9 x 6) 6 6 x Total Correct = Bottom of Form
Here's how to use VERTICALLY AND CROSSWISE for multiplying numbers close to 100.
Suppose you want to multiply 88 by 98.
Not easy,you might think. But with VERTICALLY AND CROSSWISE you can give the answer immediately, using the same method as above.
Both 88 and 98 are close to 100. 88 is 12 below 100 and 98 is 2 below 100.
You can imagine the sum set out like this:
As before the 86 comes from subtracting crosswise: 88 - 2 = 86 (or 98 - 12 = 86: you can subtract either way, you will always get the same answer). And the 24 in the answer is just 12 x 2: you multiply vertically. So 88 x 98 = 8624
This is so easy it is just mental arithmetic.
Top of Form
Try some:
1) 87 98 x 2) 88 97 x 3) 77 98 x 4) 93 96 x 5) 94 92 x 6) 64 99 7) 98 97 x Total Correct = Bottom of Form
Multiplying numbers just over 100.
103 x 104 = 10712
The answer is in two parts: 107 and 12, 107 is just 103 + 4 (or 104 + 3), and 12 is just 3 x 4.
Similarly 107 x 106 = 11342
107 + 6 = 113 and 7 x 6 = 42
Again, just for mental arithmetic
Top of Form
Try a few:
1) 102 x 107 = 1) 106 x 103 = 1) 104 x 104 = 4) 109 x 108 = 5) 101 x123 = 6) 103 x102 = Total Correct = Bottom of Form
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Tutorial 3
The easy way to add and subtract fractions.
Use VERTICALLY AND CROSSWISE to write the answer straight down!
Multiply crosswise and add to get the top of the answer: 2 x 5 = 10 and 1 x 3 = 3. Then 10 + 3 = 13. The bottom of the fraction is just 3 x 5 = 15. You multiply the bottom number together.
So:
Subtracting is just as easy: multiply crosswise as before, but the subtract:
Top of Form
Try a few:
Total Correct = Bottom of Form
Return to Index
Tutorial 4
A quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE.
752 = 5625
752 means 75 x 75. The answer is in two parts: 56 and 25. The last part is always 25. The first part is the first number, 7, multiplied by the number "one more", which is 8: so 7 x 8 = 56
Similarly 852 = 7225 because 8 x 9 = 72.
Top of Form
Try these:
1) 452 = 2) 652 = 3) 952 = 4) 352 = 5) 152 = Total Correct = Bottom of Form
Method for multiplying numbers where the first figures are the same and the last figures add up to 10.
32 x 38 = 1216
Both numbers here start with 3 and the last figures (2 and 8) add up to 10.
So we just multiply 3 by 4 (the next number up) to get 12 for the first part of the answer.
And we multiply the last figures: 2 x 8 = 16 to get the last part of the answer.
Diagrammatically:
And 81 x 89 = 7209
We put 09 since we need two figures as in all the other examples.
Top of Form
Practise some:
1) 43 x 47 = 2) 24 x 26 = 3) 62 x 68 = 4) 17 x 13 = 5) 59 x 51 = 6) 77 x 73 = Total Correct = Bottom of Form
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Tutorial 5
An elegant way of multiplying numbers using a simple pattern.
21 x 23 = 483
This is normally called long multiplication but actually the answer can be written straight down using the VERTICALLY AND CROSSWISE formula.
We first put, or imagine, 23 below 21:
There are 3 steps:
a) Multiply vertically on the left: 2 x 2 = 4. This gives the first figure of the answer. b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8 This gives the middle figure. c) Multiply vertically on the right: 1 x 3 = 3 This gives the last figure of the answer.
And thats all there is to it.
Similarly 61 x 31 = 1891
6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1
Top of Form
Try these, just write down the answer:
1) 14 21 x 2) 22 31 x 3) 21 31 x 4) 21 22 x 5) 32 21 x Total Correct = Bottom of Form
Multiply any 2-figure numbers together by mere mental arithmetic!
If you want 21 stamps at 26 pence each you can easily find the total price in your head.
There were no carries in the method given above. However, there only involve one small extra step.
21 x 26 = 546
The method is the same as above except that we get a 2-figure number, 14, in the middle step, so the 1 is carried over to the left (4 becomes 5).
So 21 stamps cost £5.46.
Top of Form
Practise a few:
1) 21 47 x 2) 23 43 x 3) 32 53 x 4) 42 32 x 5) 71 72 x Total Correct = Bottom of Form
33 x 44 = 1452
There may be more than one carry in a sum:
Vertically on the left we get 12. Crosswise gives us 24, so we carry 2 to the left and mentally get 144.
Then vertically on the right we get 12 and the 1 here is carried over to the 144 to make 1452.
Top of Form
6) 32 56 x 7) 32 54 x 8) 31 72 x 9) 44 53 x 10) 54 64 x Total Correct = Bottom of Form
Any two numbers, no matter how big, can be multiplied in one line by this method.
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Tutorial 6
Multiplying a number by 11.
To multiply any 2-figure number by 11 we just put the total of the two figures between the 2 figures.
26 x 11 = 286
Notice that the outer figures in 286 are the 26 being multiplied.
And the middle figure is just 2 and 6 added up.
So 72 x 11 = 792
Top of Form
Multiply by 11:
1) 43 = 2) 81 = 3) 15 = 4) 44 = 5) 11 = Total Correct = Bottom of Form
77 x 11 = 847
This involves a carry figure because 7 + 7 = 14 we get 77 x 11 = 7147 = 847.
Top of Form
Multiply by 11:
1) 88 = 2) 84 = 3) 48 = 4) 73 = 5) 56 = Total Correct = Bottom of Form
234 x 11 = 2574
We put the 2 and the 4 at the ends. We add the first pair 2 + 3 = 5. and we add the last pair: 3 + 4 = 7.
Top of Form
Multiply by 11:
1) 151 = 2) 527 = 3) 333 = 4) 714 = 5) 909 = Total Correct = Bottom of Form
Return to Index
Tutorial 7
Method for diving by 9.
23 / 9 = 2 remainder 5
The first figure of 23 is 2, and this is the answer. The remainder is just 2 and 3 added up!
43 / 9 = 4 remainder 7
The first figure 4 is the answer and 4 + 3 = 7 is the remainder - could it be easier?
Top of Form
Divide by 9:
1) 61 = remainder 2) 33 = remainder 3) 44 = remainder 4) 53 = remainder 5) 80 = remainder Total Correct = Bottom of Form
134 / 9 = 14 remainder 8
The answer consists of 1,4 and 8. 1 is just the first figure of 134. 4 is the total of the first two figures 1+ 3 = 4, and 8 is the total of all three figures 1+ 3 + 4 = 8.
Top of Form
Divide by 9:
6) 232 = remainder 7) 151 = remainder 8) 303 = remainder 9) 212 = remainder 10) 2121 = remainder Total Correct = Bottom of Form
842 / 9 = 812 remainder 14 = 92 remainder 14
Actually a remainder of 9 or more is not usually permitted because we are trying to find how many 9's there are in 842.
Since the remainder, 14 has one more 9 with 5 left over the final answer will be 93 remainder 5
Top of Form
Divide these by 9:
1) 771 = remainder 2) 942 = remainder 3) 565 = remainder 4) 555 = remainder 5) 777 = remainder 6) 2382 = remainder 7) 7070 = remainder Total Correct = Bottom of Form
Return to Index
Is it divisible by four?
This little math trick will show you whether a number is divisible by four or not.
So, this is how it works.
Let's look at 1234
Does 4 divide evenly into 1234?
For 4 to divide into any number we have to make sure that the last number is even
If it is an odd number, there is no way it will go in evenly. So, for example, 4 will not go evenly into 1233 or 1235
Now we know that for 4 to divide evenly into any number the number has to end with an even number.
Back to the question...
4 into 1234, the solution:
Take the last number and add it to 2 times the second last number
If 4 goes evenly into this number then you know that 4 will go evenly into the whole number.
So 4 + (2 X 3) = 10 4 goes into 10 two times with a remainder of 2 so it does not go in evenly.
Therefore 4 into 1234 does not go in completely.
Let’s try 4 into 3436546
So, from our example, take the last number, 6 and add it to two times the penultimate number, 4
6 + (2 X 4) = 14 4 goes into 14 three times with two remainder. So it doesn't go in evenly.
Let's try one more.
4 into 212334436
6 + (2 X 3) = 12 4 goes into 12 three times with 0 remainder.
Therefore 4 goes into 234436 evenly.
So what use is this trick to you? Well if you have learnt the tutorial at Memorymentor.com about telling the day in any year, then you can use it in working out whether the year you are calculating is a leap year or not.
Multiplying by 12 - shortcut
So how does the 12's shortcut work? Let's take a look.
12 X 7
The first thing is to always multiply the 1 of the twelve by the number we are multiplying by, in this case 7. So 1 X 7 = 7.
Multiply this 7 by 10 giving 70. (Why? We are working with BASES here. Bases are the fundamentals to easy calculations for all multiplication tables. To find out more check out our Vedic Maths ebook at
Now multiply the 7 by the 2 of twelve giving 14. Add this to 70 giving 84.
Therefore 7 X 12 = 84
Let's try another:
17 X 12
Remember, multiply the 17 by the 1 in 12 and multiply by 10 (Just add a zero to the end)
1 X 17 = 17, multiplied by 10 giving 170.
Multiply 17 by 2 giving 34.
Add 34 to 170 giving 204.
So 17 X 12 = 204
lets go one more
24 X 12
Multiply 24 X 1 = 24. Multiply by 10 giving 240. Multiply 24 by 2 = 48. Add to 240 giving us 288
24 X 12 = 288 (these are Seriously Simple Sums to do aren’t they?!)