### How much is 8 x 6?

*"If you can't solve the given problem, solve first a simpler problem."*

- How much is 8 x 6?

- I don't know, but I know that 2 x 6 = 12.

- So?

- Eight sixes is two sixes less than ten sixes, so 8 x 6 = 60 - 12 = 48.

- How much is 8 x 6?

- I don't know, but I know that 8 x 5 = 40.

- So?

- Six eights is 8 more than five eights, so 8 x 6 = 40 + 8 = 48.

- Six eights? The question was eight sixes!

- Same thing!

- Ah, yes!

- How much is 8 x 6?

- More than 5 x 5 = 25.

- How much more?

- If a chocolate bar is made of 8 rows and 6 columns, I would say 3 rows and 1 column.

- So?

- 3 rows is 18, 1 column is 8, so 8 x 6 = 25 + 18 + 8 = 51.

- Not entirely correct!

- That's true.

- So?

- I'll fix the method after dinner.

In 1492, the year the Arawaks discovered Columbus, a method called 'the ancient rule' was published in a book in Europe. It went like this.

- How much is 8 x 6?

- Make a 2 x 2 table and fill it in like this:

8 6

2 4

- Where did 2 and 4 come from?

- They are what is needed to make 8 and 6 reach 10.

- OK.

- Cross subtract: 8 - 4 = 4 and 6 - 2 = 4.

- What on earth!?

- Multiply the two lower numbers: 2 x 4 = 8.

- And?

- So 8 x 6 = 48. 4 from the cross subtraction and 8 from the bottom multiplication.

- Holy mackerel!

- One can never eat too much fish.

- I don't think this method always works!

- OK.

- Let me try 7 x 7.

7 7

3 3

- Cross subtraction gives 4 and 3 x 3 is 9, so the answer is 49. It worked!

- When you don't have paper available you can use your fingers for a similar method.

- Really?

- Let's try 8 x 6 again.

- OK.

- Hold your hands in front of you with the palms facing you.

- What for?

- Let the left middle finger touch the right little finger.

- Like this?

- Correct.

- And?

- Imagine a line just above the two touching fingers.

- OK.

- How many fingers do you have below the line?

- 3 on the left hand and 1 on the right.

- Add them up.

- 4.

- How many fingers do you have above the line?

- 2 on the left and 4 on the right.

- Multiply them.

- 8.

- There is your answer to 8 x 6.

- 4 and 8, 48. Neat!

- I agree.

- Does it always work?

- Why don't you find out?

- Let me try 7 x 7.

- OK.

- Which fingers should touch?

- Label your fingers from thumb to little finger with 10 to 6.

- So the ring fingers should touch?

- Right!

- I have 4 fingers below the line and 3 and 3 above, so 7 x 7 is 49 since 3 x 3 = 9.

- Great!

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