How to Convert a Mixed Number to an Improper Fraction
How to Work with Ratios and Proportions
How to Find the Sum of Fractions with the Same Denominator

Fraction Vocabulary You Should Know

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

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