why do you have to multiply a fraction by the form of 1 in order for the 2 fractions to be equivalent?

Question

this is my sons math question! and he has to explain whyyou have to... and then give an example! He has to know this for the morning!

Answer 1

What he said. What you have to understand is that it's not changing the value at all, because any number times 1 is itself. The "multiplying it by 1" is just so you can see it a little better, in the sections that are convenient for you. Manipulating numbers so you can understand how they work is what math is all about. The reason you have to do it is so you can add fractions more easily, here's an example:
1/2 + 1/6= (1/2)x(3/3) + 1/6 = 3/6 + 1/6 = 4/6

Then you can divide by 1, too. That's what simplification of fractions really is.
(4/6)/(2/2)=2/3
If it helps you to see it that way. If it just confuses you, ignore it.

Answer 2

Actually if a fraction times a form of one is equivelent to another fraction, then the original fractions ARE equivilant.

5/10=1/2
When you might want to multiply by a form of one is when you want to solve a problem that requires a different denominator.
1/3 + 11/18 = ?
to solve this you would multiply 1/3 by a form of 1. What form of 1 should you multiply by?
3*6=18 so the form would be 6/6
1*6= 6 for the numerator and 3*6=18 for the denominator
6/18+11/18=17/18

Answer 3

Well, I think you are asking about changing fractions so you can add or subtract them easily. (Actually, you cannot make two fractions that are not equivalent to start with equivalent by multiplying them both by the same thing or one of them by some form of 1.) For instance, adding ½ and ¾. You multiply "½" by "2/2" (=1) to get "2/4" which, since now both fractions are some number of fourths, makes the adding easier because you just add the 2 and the 3 getting 5 fourths.

The thing you manage to do there is to make it easier to do and to end up with a useful answer, not to make anything equivalent. As far as easier goes, you could multiply the "¾" by "½ / ½" (=1) to end up adding the 1 and the 1½ getting 2½ halves. But that's incredibly not useful! So, though valid, you would never really do it because it isn't very useful and there is an alternative that IS very useful (as well as being pretty clear and understandable).

It's all about being useful, not about making anything equivalent. But a teacher might babble about finding equivalent this and that lending a great deal of confusion to your day.

Answer 4

You just want to change the form of the fraction without changing its value. You can do this by multiplying by 1 .

Ex.

1/2 = 3/6 because
(1/2)*(3/3) = 3/6 , see, the 3/3 is 1 and doesn't change the value of the fraction just it representation.