Skill: Recognize benchmark fractions

Benchmark fractions are familiar fractions that help you understand where another fraction belongs. The most useful benchmarks are $0$, $\frac12$, and $1$. You can also use $\frac14$ and $\frac34$.

Example: Locate $\frac78$ on a number line and decide which benchmark it is closest to.

1. Choose helpful benchmarks.

   Use $\frac12$ and $1$:

$$\frac12=\frac48 \qquad\text{and}\qquad 1=\frac88$$

2. Compare $\frac78$ with the benchmarks.

   Since

$$\frac48<\frac78<\frac88,$$

$\frac78$ is between $\frac12$ and $1$.

3. Decide where it belongs.

   $\frac78$ is only $\frac18$ less than $1$, so it is very close to $1$. On a number line, place it just before $1$:

$$0 \qquad\qquad \frac12=\frac48 \qquad\qquad \frac78 \qquad 1=\frac88$$

Remember that the numerator or denominator alone does not tell you the fraction’s value. Compare the fraction with familiar benchmarks instead.