One difference between fractions and whole numbers is this. If
two whole numbers look different, then you can be sure
they are different. With fractions, though, it's more
complicated; the fraction 14 ⁄ 21 is just
another way of saying 2 ⁄ 3. Reducing a
fraction means finding the simplest way to write it.
The basic idea is to look for common factors of the numerator
(the first number) and the denominator (the second number). In the
case of 14 ⁄ 21, say, 7 goes evenly into both
14 and 21. So, we can divide both 14 and 21 by 7, which gives us
2 ⁄ 3. Remember that you always divide the
numerator and the denominator by the same number.
Here are some things to keep in mind:
- The number 1 goes evenly into everything. So we can always
divide both the numerator and denominator by 1. That won't
change anything, though, so why bother?
- You know you're done when the only number that goes
evenly into both the numerator and denominator is 1. So, if
your teacher asks you to reduce 2 ⁄ 3, you
don't have to do any work; the answer is just
2 ⁄ 3 again.
- A whole number is the same thing as a fraction whose
denominator is 1. So, if you have to reduce
9 ⁄ 3, you divide the numerator and
denominator each by 3, getting 3 ⁄ 1,
which you then write as 3. Similarly, if you're asked
to reduce 3, just write 3.
- If there's a negative sign in front of a fraction you're
asked to reduce, just leave it there.