Fractions have their own special vocabulary and a few important properties that are worth knowing right from the start. When you know them, you find working with fractions a lot easier.
Telling the numerator from the denominator
The top number in a fraction is called the numerator, and the bottom number is called the denominator. For example, look at the following fraction:
In this example, the number 3 is the numerator, and the number 4 is the denominator. Similarly, look at this fraction:
The number 55 is the numerator, and the number 89 is the denominator.
Flipping for reciprocals
When you flip over a fraction, you get its reciprocal. For example, the following numbers are reciprocals:
19/19 is its own reciprocal.
Using ones and zeros
When the denominator (bottom number) of a fraction is 1, the fraction is equal to the numerator by itself. Conversely, you can turn any whole number into a fraction by drawing a line and placing the number 1 under it. For example,
When the numerator and denominator match, the fraction equals 1. After all, if you cut a cake into eight pieces and you keep all eight of them, you have the entire cake. Here are some fractions that equal 1:
When the numerator of a fraction is 0, the fraction is equal to 0. For example,
The denominator of a fraction can never be 0. Fractions with 0 in the denominator are undefined — that is, they have no mathematical meaning.
Remember that placing a number in the denominator is similar to cutting a cake into that number of pieces. You can cut a cake into two, or ten, or even a million pieces. You can even cut it into one piece (that is, don't cut it at all). But you can't cut a cake into zero pieces.
For this reason, putting 0 in the denominator — much like lighting an entire book of matches on fire — is something you should never, never do.
Mixing things up
A mixed number is a combination of a whole number and a proper fraction added together. Here are some examples:
A mixed number is always equal to the whole number plus the fraction attached to it. So
