Comparing and Ordering Fractions

When we compare fractions, we are looking at two things: how many pieces we have (the numerator) and how big those pieces are (the denominator). If the denominators are the same, it's easy! $\frac{5}{8}$ is bigger than $\frac{3}{8}$ because 5 pieces are more than 3 pieces of the same size. But what if the denominators are different? That's like comparing big slices of watermelon to tiny slices of an apple. To compare them fairly, we often try to find a common denominator, which means making the slices the same size so we can just count the pieces.

Sometimes you don't need to do any hard math to compare fractions. You can use a benchmark, like $\frac{1}{2}$. A benchmark is a familiar number used as a point of reference. To see if a fraction is bigger or smaller than $\frac{1}{2}$, look at the denominator and ask: 'What is half of this number?' If the numerator is more than half, the fraction is greater than $\frac{1}{2}$. If it's less, the fraction is smaller than $\frac{1}{2}$. This is a fast way to compare two fractions that are on opposite sides of the middle!

When you have three or more fractions to put in order, you combine your skills. First, check if any are smaller than $\frac{1}{2}$ and if any are larger. This helps you group them. If two fractions are both larger than $\frac{1}{2}$, you might need to find a common denominator to see which one wins. To find a common denominator, you find a number that both denominators can multiply into. Once they look the same on the bottom, you can line them up from least to greatest easily.