What are fractions, and what do they mean?
What is a fraction, and what do the individual pieces mean?
A fraction may look like a completely different kind of number, but the way we need to think about it is just as “part of a whole”.
A fraction always has two numbers: the top number, which is called the “numerator,” and the bottom number, which is called the “denominator.”
A fraction looks like this:
???\frac23???
where ???2??? is the numerator and ???3??? is the denominator. A fraction also represents the division of the numerator by the denominator. Since in math we can’t divide by ???0???, this means that the denominator of a fraction can’t ever be ???0???. So we can say that ???2/3??? is “???2??? divided by ???3???” or “???2??? over ???3???.”
Let’s use an example with pizza. Let’s say I have a whole pizza that I want to split with my friend. We’re going to split the pizza evenly, and I want to use a fraction to express how much of the pizza I get to eat.
Let’s just say up front that the denominator of the fraction will be the number of pieces I cut the pizza into, and the numerator of the fraction will be the number of pieces I personally get to eat.
So if I want to split the pizza equally with my friend, I’ll cut the whole pizza into two pieces. Because I’m cutting it into two pieces, I put a ???2??? in the denominator of the fraction:
???\frac{}{2\text{ pieces total}}???
After I cut it into two pieces, I give her one of the pieces, and I personally get to keep the other piece. Since I get to keep one piece, I put a ???1??? in the numerator of the fraction:
???\frac{1\text{ piece for me}}{2\text{ pieces total}}???
So I get to eat ???1??? of the ???2??? pieces, and “???1??? of ???2???” or “???1??? out of ???2???” is the fraction
???\frac12???
If we write a fraction on its own, we write it like we just did, with the numerator above the denominator. But if we write a fraction within a line of text, we write it with a slash as ???1/2???.
How to build and understand the meaning of a fraction
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Expressing real-life values in terms of fractions
Example
If a store is ???4??? miles from my home and I’ve already walked ???3??? miles, express my progress as a fraction.
Since I have to walk a total of ???4??? miles, I put a ???4??? in the denominator of the fraction.
???\frac{}{4\text{ miles total}}???
Since I’ve already walked ???3??? of those miles, I put a ???3??? in the numerator of the fraction.
???\frac{3\text{ miles I've walked}}{4\text{ miles total}}???
So the portion of the walk that I’ve completed is ???3/4???.
Here’s a table that summarizes how to describe some simple fractions.
Percent
When you hear the word “percent”, think “divided by ???100???” in order to turn the percent value into a fraction. So ???50\%???, expressed as a fraction is ???50/100???, and ???76\%??? is the same as ???76/100???.