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.2Compare 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.