Compare simple fractions using benchmarks

Fractions are compared as numbers representing parts of the same whole, using benchmarks such as 0, 1/2, and 1 and locating fractions on a number line or interpreting them in equal-part models. The reasoning includes determining whether a fraction is less than, equal to, or greater than a benchmark—for example, recognizing that 3/8 is less than 1/2 and 5/6 is greater than 1/2—rather than assuming a larger denominator means a larger fraction; general procedures such as cross-multiplication are not included.

Detailed Explanation: Compare simple fractions using benchmarks

To compare fractions, think about where each one belongs compared with a benchmark such as $0$ , $\frac{1}{2}$ , or $1$ .

Example: Compare $\frac{3}{8}$ and $\frac{5}{6}$

Step 1: Compare $\frac{3}{8}$ with $\frac{1}{2}$ .

One-half of 8 equal parts is 4 parts:

\frac{1}{2}=\frac{4}{8}

Since 3 parts is less than 4 parts,

\frac{3}{8}<\frac{1}{2}

Step 2: Compare $\frac{5}{6}$ with $\frac{1}{2}$ .

One-half of 6 equal parts is 3 parts:

\frac{1}{2}=\frac{3}{6}

Since 5 parts is more than 3 parts,

\frac{5}{6}>\frac{1}{2}

Step 3: Compare the fractions.

$\frac{3}{8}$ is less than $\frac{1}{2}$ , while $\frac{5}{6}$ is greater than $\frac{1}{2}$ . Therefore,

\boxed{\frac{3}{8}<\frac{5}{6}}

The denominator tells how many equal parts make the whole, so a larger denominator does not automatically mean a larger fraction. Use benchmarks to decide where each fraction is located.

Learn by doing: Compare simple fractions using benchmarks

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Fraction Strips - Two Strips to Inequality

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