Tutorial 1

• 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

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	=

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Tutorial 2

• 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.

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 =

• 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

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 =

• 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

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 =

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Tutorial 3

• 
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:
• 

Try a few:

Total Correct =

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Tutorial 4

• 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.

Try these:

1) 452 =

2) 652 =

3) 952 =

4) 352 =

5) 152 =

Total Correct =

• 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.

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 =

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Tutorial 5

• 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.

• Similarly 61 x 31 = 1891
  



• 6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1

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 =

• 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).

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 =

• 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.

6) 32     56 x	7) 32     54 x	8) 31     72 x	9) 44     53 x	10) 54       64 x
Total Correct =

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Tutorial 6

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

Multiply by 11:

1) 43 =

2) 81 =

3) 15 =

4) 44 =

5) 11 =

Total Correct =

• 77 x 11 = 847
  This involves a carry figure because 7 + 7 = 14
  we get 77 x 11 = 7₁47 = 847.

Multiply by 11:

1) 88 =

2) 84 =

3) 48 =

4) 73 =

5) 56 =

Total Correct =

• 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.

Multiply by 11:

1) 151 =

2) 527 =

3) 333 =

4) 714 =

5) 909 =

Total Correct =

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Tutorial 7

• 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?

Divide by 9:

1) 61 = remainder

2) 33 = remainder

3) 44 = remainder

4) 53 = remainder

5) 80 = remainder

Total Correct =

• 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.

Divide by 9:

6) 232 = remainder

7) 151 = remainder

8) 303 = remainder

9) 212 = remainder

10) 2121 = remainder

Total Correct =

• 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

1) 771 = remainder

2) 942 = remainder

3) 565 = remainder

4) 555 = remainder

5) 777 = remainder

6) 2382 = remainder

7) 7070 = remainder

Total Correct =