# 2. Compare Fractions with Half and One

Compare fractions to benchmark fractions (1/2 and 1). To compare a given fraction to a 1/2, one can think of a fraction equivalent to 1/2 with the same denominator as the given fraction. For example, to compare 2/6 with 1/2, the following reasoning can be used:

1/2 is equivalent to 3/6

and 2/6 < 3/6 (smaller numerator).

Therefore, 2/6 < 1/2.

To compare a fraction to 1, students can follow a similar logic. For example, to compare 4/7 with 1, the following reasoning can be used:

1 is equivalent to 7/7

and 4/7 < 1.

Therefore, 4/7 < 1.

As a shortcut, if the numerator is smaller than the denominator, the fraction is smaller than 1.

### Common Core Alignment

**4.NF.2**Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.