How to Use Benchmark to Compare Fractions?

A Step-by-step guide to using benchmarks to compare fractions

Definition of a Benchmark fraction: A common fraction utilized for comparing other fractions is called a benchmark fraction

These are simple common fractions everyone is accustomed to and allow seeing complicated fractions much simpler.

It’s possible to divide any object you want to measure easily or to compare it into two equal parts. So, the most common place benchmark fraction instance is (one-half).

You can also write in different formats or equivalent fractions, like, etc. Currently, one can do a comparison of the other fractions having different denominators to one half.

Using Benchmark to Compare Fractions-Example:

Compare each fraction to the benchmark. \(\frac{4}{8}\:\left(\right)\:1\), \(\frac{4}{3}\:\left(\right)\:1\). Then, use this information to compare the two fractions. \(\frac{4}{8}\:\left(\right)\:\frac{4}{3}\)

Solution: First, compare each fraction to the benchmark.

\(\frac{4}{8}\:\left(<\right)\:1\)

\(\frac{4}{3}\:\left(>\right)\:1\)

Now, use this information to compare the two fractions.

\(\frac{4}{8}\:\left(<\right)\:\frac{4}{3}\)

Exercises for Using Benchmark to Compare Fractions

Compare each fraction to the benchmark. Then compare the two fractions.

1. \(\color{blue}{\frac{5}{4}\:\left(\right)\:1,}\) \(\color{blue}{\frac{5}{9}\:\left(\right)\:1, \frac{5}{9}\:\left(\right)\:\frac{5}{4}}\)
2. \(\color{blue}{\frac{2}{3}\:\left(\right)\:\frac{1}{2}, \frac{7}{15}\:\left(\right)\:\frac{1}{2}, \frac{2}{3}\:\left(\right)\:\frac{7}{15}}\)

1. \(\color{blue}{\frac{5}{4}\:\left(>\right)\:1,\frac{5}{9}\:\left(<\right)\:1,\frac{5}{4}\:\left(>\right)\:\frac{5}{9}}\)
2. \(\color{blue}{\frac{2}{3}\:\left(>\right)\:\frac{1}{2},\frac{7}{15}\:\left(<\right)\:\frac{1}{2}, \frac{2}{3}\:\left(>\right)\:\frac{7}{15}}\)