2007-03-17 01:42:07 · 6 answers · asked by Jos 1 in Science & Mathematics ➔ Mathematics
A fraction (i.e. a rational number of the form a/b where a and b are integers) is really a collection of equivalent fractions that represent the same number (i.e. it represents an equivalence class). For example: 1/2, 4/8, 160/320, 2506/5012 etc are all equivalent under simplification, and all of them represent the same rational number, namely 1/2 which is irreducible.
Thus if N is a positive non-zero integer, the fraction a/b where a and b are relatively prime (don't have a common divisor, i.e. the fraction is irreducible) is equivalent to the collection of all fractions of the form (N x a)/(N x b). Once could say that this collection can all be generated from a/b by multiplying numerator and denominator in a/b by a suitable N. In this sense a/b can be viewed as the "name" for the collection of all of its equivalent fractions.
When you simplify a fraction, you reduce it to the base fraction that represents the equivalence class it belongs to.
Why is this good? First, it gives a canonic representation for a collection of equivalent fractions (namely the simplest irreducible fraction that can be obtained by simplification). Second, as many have already answered, it is the simplest possible way to represent that class.
Simplicity in representation makes mathematical and logical thinking much easier.
2007-03-17 02:27:12 · answer #1 · answered by Bazz 4 · 0⤊ 0⤋
Fractions don't HAVE to be simplified, but they are usually. THe only reason you need to simplify them is so they are easier to work with. It's easier to understand and use 1/4 then 16/64. That's why math teachers say to simplify fractions. It's also easier to multiply and divide.
2007-03-17 09:05:17 · answer #2 · answered by Drew J 2 · 0⤊ 0⤋
simplifying fractions make your equations much easier to answer. 45/90 +60/120=1 or 1/2 +1/2=1 see!
2007-03-17 08:52:02 · answer #3 · answered by Crystal B 4 · 0⤊ 0⤋
Because it's a great deal easier to figure out how to cut a board in 1/2 instead of figuring out how to cut it into 689/1378. Or even in knowing that the two are the same thing.
2007-03-17 08:46:04 · answer #4 · answered by charmedchiclet 5 · 0⤊ 0⤋
To make it simple, or easy to read and understand. It is better to write 1/2 than 12/24
2007-03-17 08:50:14 · answer #5 · answered by detektibgapo 5 · 0⤊ 0⤋
when you work with lots of fractions and lots of numbers it is a lot easier when your fraction is in its simplest form.
2007-03-17 08:44:44 · answer #6 · answered by Anonymous · 0⤊ 0⤋