Question

If two positive fractions are less than 1, why is their product also less than 1?

Answer 1

When you multiply something (x) by a proper fraction ( less than 1 ), you always get something less than x, or the original number, because you're taking part of x and a part can't be larger than the whole.

Here's an example :
5 * 1/5 = 1
1<5

When you start with something that's less than 1 ( and positive), and you multiply it by a fraction, you get part of that positive fraction, so it will never be greater than 1.

Hope this helps!
I'm sorry if this is confusing ... it's too late for my brain to work at max level.

Answer 2

The product of two positive fractions are also less than one because you are multiplying a number which is already less than 1.

For example.

1/ 2 = is 50% of a whole.

When you multiply 1/2 by 1/2 you do not get the 100% of the whole because you are only getting 50% of the 50% of the whole, which in turn is equivalent to 25% of the whole.

1/2 * 1/2 = 1/4 of the whole.

The only time you can get a result of 1 and above where two fractions are less than 1 is when you perform addition of these fractions.

1/2 + 1/2 = 1 - ALL CREDITS GO TO @TASKMASTERS!