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.”

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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 $3/4$.

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A fraction always has two numbers: the top number, which is called the “numerator,” and the bottom number, which is called the “denominator.”

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 $76/100$.

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