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!