  ## The Basics of Fractions

### Are fractions integers?

Nah. Integers are whole numbers like 0 or 957 or negative numbers like -7. Think of a fraction like a piece of an integer, but not an integer itself.

But wait! You might have a fraction that simplifies into a whole number, like this:

$\frac{4}{2} = 2$

Since 2 is an integer, and 2 is equal to $\frac{4}{2}$, $\frac{4}{2}$ is also an integer. This is why it's helpful to always use the simplest form of the fraction.

### What fractions are equivalent to each other?

Let's say you're asked what fractions are equivalent to $\frac{1}{2}$.

To answer this, we should remember that multiplying the top and bottom of a fraction by the same number doesn't change the value of the fraction. So,

$\frac{1}{2}= \frac{1 \times \colorbox{yellow}{3}}{2 \times \colorbox{yellow}{3}} = \frac{3}{6}$

This makes sense logically, because 3 is exactly half of 6, so $\frac{3}{6} = \frac{1}{2}$.

That means there's an infinite number of fractions equal to any fraction you choose, because there's an infinite number of numbers we can multiply the top and bottom by!

### Can fractions be negative?

Yes! Just like -1 and 1 are both 1 away from 0 in opposite directions:

### 4

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Fractions have a negative version on the other side of the number line, too. Try dragging one hand to see how the other matches up.

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### How do I know if two fractions are equivalent? Or which fraction is bigger?

Let's say you have these two fractions and you're trying to figure out if they're equal or if one is bigger than the other:

$\frac{1}{2}$
$\frac{2}{5}$

Right now, it's hard to compare, because the first fraction is out of halves and the second is out of fifths, like below.

What we need is for the total number of pieces to be the same for both, so that we can figure out which one is bigger or smaller. To do this, we multiply the top and bottom of each fraction by the denominator of the other fraction:

$\frac{\colorbox{yellow}{5}}{\colorbox{yellow}{5}}\times\frac{1}{2}$
$\frac{2}{5}\times \frac{\colorbox{yellow}{2}}{\colorbox{yellow}{2}}$
$\frac{5}{10}$
$\frac{4}{10}$

Now, because the first fraction is 5 out of 10 pieces and the second is 4 out of 10 pieces, we can clearly see the first fraction is bigger!

$\frac{5}{10}>\frac{4}{10}$

So, in our original fractions:

$\frac{1}{2}>\frac{2}{5}$

There you go! So, remember, when comparing fractions, first make sure the denominators are the same, so the size of the pieces on each side are the same.