To compare two fractions and figure out which one is bigger, there are a few easy methods you can use. Here’s a simple breakdown of the most common ways:

1. Common Denominator Method:

   • First, find a common denominator for both fractions. This means you'll change the fractions so they have the same bottom number (denominator). Once that's done, it's easier to see which fraction is larger.
   • For example, let’s compare $\frac{1}{3}$ and $\frac{1}{4}$. The common denominator here is 12.
     • Change $\frac{1}{3}$ to $\frac{4}{12}$.
     • Change $\frac{1}{4}$ to $\frac{3}{12}$.
   • Now we can see that $\frac{4}{12} > \frac{3}{12}$. So, that means $\frac{1}{3} > \frac{1}{4}$.

2. Cross Multiplication Method:

   • Another fast way to compare fractions is by cross multiplying. For two fractions, like $\frac{a}{b}$ and $\frac{c}{d}$, you multiply across: $a$ times $d$ and $b$ times $c$.
   • Let’s say we want to compare $\frac{2}{5}$ and $\frac{3}{7}$.
     • Cross multiply: $2 \cdot 7 = 14$ and $5 \cdot 3 = 15$.
     • Since $14 < 15$, this means $\frac{2}{5} < \frac{3}{7}$.

3. Decimal Conversion:

   • You can also turn fractions into decimals to compare them. Just divide the top number (numerator) by the bottom number (denominator).
   • For example:
     • For $\frac{1}{3}$, divide $1$ by $3$ to get about $0.33$.
     • For $\frac{3}{8}$, divide $3$ by $8$ to get $0.375$.
   • Since $0.33 < 0.375$, it shows that $\frac{1}{3} < \frac{3}{8}$.

In summary, using the common denominator, cross multiplication, or converting to decimals are all great ways to compare fractions and see which one is bigger or smaller.