Choose the correct sign to compare the two fractions. Use the models to help.

Question

Two models. One model is labeled one-third and has 1 shaded section and 2 unshaded sections. The second model is labeled StartFraction 5 Over 6 EndFraction and has 5 shaded sections and 1 unshaded section. A question mark is between the 2 models.
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Answer 1

To compare the two fractions, one-third \(\left(\frac{1}{3}\right)\) and \(\frac{5}{6}\):

1. Convert to a common denominator: The denominators are 3 and 6. The least common denominator (LCD) is 6.

   • To convert \(\frac{1}{3}\) to a fraction with a denominator of 6, we multiply both the numerator and the denominator by 2: \[ \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \]

2. Now compare \(\frac{2}{6}\) and \(\frac{5}{6}\):

   • Since \(\frac{2}{6}\) represents a smaller quantity than \(\frac{5}{6}\), we have: \[ \frac{2}{6} < \frac{5}{6} \]

Therefore, the correct sign to use is:

\[ \frac{1}{3} < \frac{5}{6} \]