Compare fractions by reasoning about the size and number of their parts. Compare fractions with a shared denominator or numerator, work with different denominators, or use one half as a benchmark.
Fill each blank with the symbol for less than, greater than, or equal to. Assume both fractions refer to the same whole. Explain a comparison with a sketch, equivalent fractions, or a familiar benchmark.
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When denominators match, the parts have the same size. Three eighths is less than five eighths because it contains fewer of those parts, so \(\frac{3}{8}\lt\frac{5}{8}\).
When numerators match, compare the size of each part. Two thirds is greater than two sixths because a third of the same whole is larger than a sixth. This gives \(\frac{2}{3}\gt\frac{2}{6}\).
To compare \(\frac{3}{4}\) and \(\frac{5}{8}\), split each fourth into two eighths. Three fourths becomes six eighths, so \(\frac{3}{4}=\frac{6}{8}\gt\frac{5}{8}\). The same method shows why differently written fractions can be equal.
Three eighths is below one half because half of eight equal parts is four parts. Four sixths is above one half because half of six equal parts is three parts. Since \(\frac{3}{8}\lt\frac{1}{2}\lt\frac{4}{6}\), three eighths is less than four sixths. If both fractions are on the same side of one half, use another method to compare them.
Shared numerators and denominators provide a third-grade starting point. In fourth grade, use equivalent fractions or a benchmark to compare fractions with different numerators and denominators. Try a short set in the Compare Fractions Worksheet Generator and ask the learner to explain one answer before checking the key.