Originally Posted by

**birdeen's call**
I'm not sure if I follow you.

That's OK.

Would you say it's correct to say,

a) 40 is 5 times bigger than 8. ** No.** Five times bigger than what? Do you mean that 40 is 5 times 8 bigger than 8 is? That means 40 is 5*8 (= 40) bigger than 8. Therefore, 40 = 48.

b) 40 is 5 times as big as 8. **Yes.** 40 = 5 * 8

c) 8 is 5 times smaller than 40. **No.** 8 is 5 times **what** smaller than 40? If you mean 8 is 5 times itself (8) smaller than 40, then again 8 is 40 less than 40, so 8 = 0.

d) 8 is 5 times as small as 40. **No.** 8 is a fifth the size of 40.

Here's how a mathematician (or any logical person, really) would see it:

e. Q. How many times 8 is 8 smaller than 40? (from d).

e. A. 8 is 32 smaller than 40. 32/8 = 4. So 8 is **4** times itself (8) smaller than 40. (Not 5 times)

f. Q. 40 is how many times bigger than 8 [ie. 40 is how many times 8 bigger than 8]. (as in a)

f. A. 40 is 32 bigger than 8. 32/8 = 4. So, 40 is **4** times 8 bigger than 8. (Not 5 times).

To my Polish ear, they're all fine except d) (which could be used in some particular contexts only) and a) means the same as b).

a can't mean b.

Let's say my wage is $150/hr and yours is $50/hr.

My wage is 3 times yours. (Since 3 times 50 is 150)

It is also twice bigger than yours. (= 2*50 bigger = $100/hr bigger than yours = 50 + 100 = $150/hr

If you claim that "2 times as big" means "2 times bigger", then "1 time as big" (the same size) must mean 1 time bigger (twice as big).

Similarly, you'd have to say that something which is 50% bigger than A is actually smaller than A, because "50% bigger" would mean "50% as big" (= 1/2 the size of A)!

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