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Fractions - What are they?

Fractions are another way of writing a number. More than this, they can also convey parts of a number (numbers less than 1.) Also interesting
about fractions is that they are actually a division problem that doesn't need to be done!

Let's show an example to better express what we mean:

Example 1:
½

This fraction is "one over two," or "one-half" or just "half." How do we know that it's half? Because the numerator (number on top) is half
of the denominator (number on the bottom.)

What else makes it half?

Because it is a division statement, it's "one divided by 2;" that is, how many times does 2 go into 1?" Since you can only fit "half" of 2 inside of
1, it's still a half!

There are other kinds of fractions called compound fractions. These contain not only a portion of a number, but also a whole number along with it.

Example 2: Compound Fractions

This is "five and one quarter." Another way to write this, called an improper fraction, is "21/4."

How did we get there from here? Simple!

Multiply the whole number (5) by the denominator (4) to get 20, and then add the numerator. 5x4 = 20 + 1 = 21. See the Compound and Improper Fraction tutorial for a more detailed example!

But in the end, no matter how it's written, it still represents the same number, and most often a fraction contains less-than-whole numbers. (This means that while we may have 5 in the 5¼ fraction, the value itself is less than the whole number of 6 - but still more than the next lower
whole number, 5.)

Another point to remember - Once you know fractions (or decimals), you'll be able to understand both quite easily. (And then from there, a lot more topics become much easier! For example, you could say that 1/3 is 33%.) That will become clearer as you become more familiar with using pieces of numbers (fractions and decimals) rather than only whole numbers.


Find another math lesson at the Math Lesson and Tutorial Center!

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