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Multiplication

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Multiplying a 2 digit number by a 2 digit number can be done as mental maths. Mnemonics are one way to approach it.

For example, 37 x 84 = 3108 ; and that involves:

1. Knowing that the right side 7 times the right side 4 helps to get the rightmost digit of the answer: 7 x 4 = 28 ; and so the 8 is the right side digit of the answer:

...8

The left side digit of that 7 x 4 calculation needs to be remembered temporarily: the 'carrier'.

Then the 3 of 37 x 84 and the 4 of 37 x 84 need a calculation; and

the 7 of 37 x 84 and the 8 of 37 x 84 need a calculation; and again,

the right side of each answer is what matters (and will be added to the carrier that was 2).

So, 3 x 4 = 12 but we just want to note the 2; and

7 x 8 = 56 but we just want the 6; then

that 2 plus that 6 equal 8; and add to that the carrier (from the early on 7 x 4 = 28) of 2 to get 10.

Write the 0 as the second digit of the answer; and note the 1 (right side of 10) as a carrier.

Now, we look at the two recent calculations but take an interest in their left side result rather than their right digit result:

The 3 x 4 = 12 has the 1 noted; and

the 7 x 8 = 56 has the 5 noted; and then they are summed and the carrier of 1 is also added:

1 + 5 + 1 = 7 ; but we see above that the actual answer is 3108; and

the missing part is that the 3 and 8 of 37 x 84 need calculating:

3 x 8 = 24 (and the 4 needs adding to that total we were just looking at): 7 + 4 = 11.

Write the right side 1 as the third digit of the answer; and use the left side 1 as a carrier.

Add that 1 to the 2 of '3 x 8 = 24' to get the 3 that is the fourth digit of the answer:

We now have 3108 .

The effort to learn the results of some common calculations would speed up the process of doing these maths steps.

The initial question is: 37 x 84 = ?

What if the left side digits (3 and 8) are expressed as consonants; and the right side digits (7 and 4) are expressed as vowels, according to the following table:

Digit Syllable Vowel
0 L o
1 J a
2 B u
3 N oo
4 D oh
5 F ay
6 S ee
7 G ie
8 H e
9 W i

So 37 x 84 becomes NieHoh; and then memorised results tables can help with some of the maths we were looking at earlier.

The 7 x 4 = 28 early on in those steps is basic maths that people learn at school; and the 3 x 8 near the end of the steps to work towards the left side digit of the answer 3108 is also quite basic.

The part in the middle is trickier: taking the right side or taking the left side of different calculations.

The NieHoh word could be mentally rearranged into NohHie so that Noh is like '3 x 4' and Hie is like '7 x 8' which occur in the steps we looked at earlier.

If you have a table where Noh is written next to NohB, and you memorised that table then, any multiplication challenge involving 3 x 4 can remind you of the 'B' which is the 'right side' 2 sub result needed in the calculation.

Also in the table, next to Noh you would find aNoh where the 'a' is the 'left side' 1 carrier that you would want in this type of calculation.

Furthermore, NH (the consonants of the word) could be wrote learned to give the answer 24 (the 3 x 8 calculation near the end). In this way, there is less thinking to do while the calculation is going on in your head.

Left_Carrier X_Consonant Y_Vowel Right_Carrier x y Result
o L o L 0 0 00
o L a L 0 1 00
o L u L 0 2 00
o L oo L 0 3 00
o L oh L 0 4 00
o L ay L 0 5 00
o L ee L 0 6 00
o L ie L 0 7 00
o L e L 0 8 00
o L i L 0 9 00
o J o L 1 0 00
o J a J 1 1 01
o J u B 1 2 02
o J oo N 1 3 03
o J oh D 1 4 04
o J ay F 1 5 05
o J ee S 1 6 06
o J ie G 1 7 07
o J e H 1 8 08
o J i W 1 9 09
o B o L 2 0 00
o B a B 2 1 02
o B u D 2 2 04
o B oo S 2 3 06
o B oh H 2 4 08
a B ay L 2 5 10
a B ee B 2 6 12
a B ie D 2 7 14
a B e S 2 8 16
a B i H 2 9 18
o N o L 3 0 00
o N a N 3 1 03
o N u S 3 2 06
o N oo W 3 3 09
a N oh B 3 4 12
a N ay F 3 5 15
a N ee H 3 6 18
u N ie J 3 7 21
u N e D 3 8 24
u N i G 3 9 27
o D o L 4 0 00
o D a D 4 1 04
o D u H 4 2 08
a D oo B 4 3 12
a D oh S 4 4 16
u D ay L 4 5 20
u D ee D 4 6 24
u D ie H 4 7 28
oo D e B 4 8 32
oo D i S 4 9 36
o F o L 5 0 00
o F a F 5 1 05
a F u L 5 2 10
a F oo F 5 3 15
u F oh L 5 4 20
u F ay F 5 5 25
oo F ee L 5 6 30
oo F ie F 5 7 35
oh F e L 5 8 40
oh F i F 5 9 45
o S o L 6 0 00
o S a S 6 1 06
a S u B 6 2 12
a S oo H 6 3 18
u S oh D 6 4 24
oo S ay L 6 5 30
oo S ee S 6 6 36
oh S ie B 6 7 42
oh S e H 6 8 48
ay S i D 6 9 54
o G o L 7 0 00
o G a G 7 1 07
a G u D 7 2 14
u G oo J 7 3 21
u G oh H 7 4 28
oo G ay F 7 5 35
oh G ee B 7 6 42
oh G ie W 7 7 49
ay G e S 7 8 56
ee G i N 7 9 63
o H o L 8 0 00
o H a H 8 1 08
a H u S 8 2 16
u H oo D 8 3 24
oo H oh B 8 4 32
oh H ay L 8 5 40
oh H ee H 8 6 48
ay H ie S 8 7 56
ee H e D 8 8 64
ie H i B 8 9 72
o W o L 9 0 00
o W a W 9 1 09
a W u H 9 2 18
u W oo G 9 3 27
oo W oh S 9 4 36
oh W ay F 9 5 45
ay W ee D 9 6 54
ee W ie N 9 7 63
ie W e B 9 8 72
e W i J 9 9 81