# Multiplication

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