Comparing Fractions Using Benchmarks

1. What are Benchmarks?

   • Benchmarks are common numbers we can use to help compare fractions.
   • Some easy benchmarks are $0$, $\frac{1}{2}$ (which is half), and $1$.
   • These benchmarks act like reference points for comparing different fractions.

2. How to Compare Fractions:

   • First, pick the fractions you want to compare. For example, let's compare $\frac{3}{4}$ and $\frac{2}{3}$.
   • Now, see how each fraction measures up to the benchmark of $\frac{1}{2}$:
     • $\frac{3}{4}$ is greater than $\frac{1}{2}$.
     • $\frac{2}{3}$ is also greater than $\frac{1}{2}$.
   • Another way to look at it is by thinking about percentages.
     • $\frac{3}{4}$ is the same as $75\%$, which is bigger than $66.67\%$, the percentage for $\frac{2}{3}$.

3. In Summary:

   • Using benchmarks helps us compare fractions easily and accurately.
   • This makes it simpler to order different fractions, especially in Year 7 math.