Use benchmark fractions

Benchmark fractions—especially 0, 1/2, and 1—serve as reference points for interpreting a fraction’s size on a number line and for estimating or comparing fractions, including fractions with different denominators. The reasoning depends on recognizing whether a fraction is less than, near, or greater than a benchmark rather than judging its size from the numerator or denominator alone; more generalized benchmark strategies and complex fractional quantities are beyond this scope.

Detailed Explanation: Use benchmark fractions

A benchmark fraction is a familiar fraction you use to judge the size of another fraction. The most useful benchmarks are $0$ , $\frac{1}{2}$ , and $1$ .

To compare a fraction with $\frac{1}{2}$ :

Find half of the denominator.
Compare the numerator with that number.
If the numerator is smaller, the fraction is less than $\frac{1}{2}$ .
If the numerator is larger, the fraction is greater than $\frac{1}{2}$ .

Example

Which fraction is greater: $\frac{5}{8}$ or $\frac{3}{7}$ ?

Step 1: Compare $\frac{5}{8}$ with $\frac{1}{2}$ .

Half of $8$ is $4$ . Since $5>4$ ,

\frac{5}{8}>\frac{1}{2}.

So, $\frac{5}{8}$ is to the right of $\frac{1}{2}$ on a number line.

Step 2: Compare $\frac{3}{7}$ with $\frac{1}{2}$ .

Half of $7$ is $3.5$ . Since $3<3.5$ ,

\frac{3}{7}<\frac{1}{2}.

So, $\frac{3}{7}$ is to the left of $\frac{1}{2}$ on a number line.

Step 3: Compare the fractions using the benchmark.

Since $\frac{5}{8}$ is greater than $\frac{1}{2}$ and $\frac{3}{7}$ is less than $\frac{1}{2}$ ,

\boxed{\frac{5}{8}>\frac{3}{7}}.

Using $\frac{1}{2}$ as a benchmark helps you compare fractions without judging them only by their numerators or denominators.

Learn by doing: Use benchmark fractions

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Fraction Dominoes Compare - Above vs Below 1

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