O GREAT MATHEMATICIANS HELP Me !!!!?

Question

When we square or cube a number it becomes bigger
example: (2) cube = 8
but why is it that when I square or cube such fractions such as 1/2 or 1/4 or 1/8, it becomes smaller ?
example: 1/4 < 1/2 but when I square half then it becomes one fourth which is actually smaller !!!

Answer 1

You are still making it bigger in a sense. When you take the square or cube of a fraction you really are taking the square or cube of both the numerator and denominator. (1/2)^2 = (1^2)/(2^2) Thus individually both numbers are getting bigger. However, since for fractions less than one, the numerator is smaller than the denominator it is going to be comparatively an even smaller number when it is raised to a power. Thus overall you will get a smaller number.

Answer 2

That's because you are squaring the whole fraction.
1/2 is like 1 square/ 2 square. 1 square is 1 and 2 square is 4, So it makes sense to get 1/4. That's how all fractions work. It seems wierd, but it makes sense when you look at it this way.

Answer 3

I guess I don't understand the question. By this point in your education you have to have learned how to multiply fractions in general. So you should have already noticed that when multiply fractions, you get an answer smaller than either multiplier. So it can't be a surprise that squaring or cubing a fraction follows the same rules. The same theory holds true: multiply numerators and then multiply denominators and reduce/simplify as necessary.

Answer 4

The reason is if we take square of a number >1 we are multiplying by >1 so it becomes greater. But if the number < 1 when we take square then we multiply by a number <1 then it becomes smaller. But if we take square of 1 we multiply by 1 and it does not change

Answer 5

You may have heard of simplification where there is a term "of" which is used as a form of multiplication.
e.g. 2/3 of 6 which would be 4.
if you consider your problem in light of this , then 1/2^3 can be written as 1/2 of 1/2 of 1/2 or half of a half of a half which would have to be smaller.

Answer 6

Because you are dividing by 1 and not by a bigger number than the cube itself.

Answer 7

Would it do if I helped youy instead of the GREAT MATHEmATICIANS
When we raise fractions to any power the numerator 1 remains 1
But by raising the denominator we are increasing it So the numerator 1 gets divided by higher no and thus the value decreases

Answer 8

Because multiplying by a fraction is in effect dividing.