The first model is divided into two equal parts, and one part is shaded.
So, the first model shows $\frac{1}{2}$.

The second model is divided into three equal parts, and two parts are shaded.
So, the second model shows $\frac{2}{3}$.

To compare the fractions, it helps to divide the models into the same number of equal pieces. This is called finding a common denominator.

The least common denominator is the least common multiple of 2 and 3, which is 6. Divide both models into six parts.

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The model with more parts shaded represents the greater fraction.
So, $\frac{1}{2}<\frac{2}{3}$.

One way to compare fractions is to find a common denominator.
The least common denominator is the least common multiple of 6 and 4, which is 12.
Multiply both fractions by a fraction equivalent to 1 so that both fractions have 12 as their denominator.

First, since 6 × 2 = 12, multiply $\frac{1}{6}$ by $\frac{2}{2}$ to find a fraction equivalent to $\frac{1}{6}$ with a denominator of 12.

Next, since 4 × 3 = 12, multiply $\frac{3}{4}$ by $\frac{3}{3}$ to find a fraction equivalent to $\frac{3}{4}$ with a denominator of 12.

Then, compare the numerators. 9 > 2, so $\frac{9}{12}>\frac{2}{12}$.

Since $\frac{3}{4}$ is equivalent to $\frac{9}{12}$, and $\frac{1}{6}$ is equivalent to $\frac{2}{12}$, $\frac{3}{4}>\frac{1}{6}$.

One way to compare fractions is to find a common numerator.

In this case, the least common numerator is the least common multiple of 1 and 2, which is 2.
Multiply $\frac{1}{5}$ by a fraction equivalent to 1 so that both fractions have 2 as their numerator.

Since 1 × 2 = 2, multiply $\frac{1}{5}$ by $\frac{2}{2}$ to find a fraction equivalent to $\frac{1}{5}$ with a numerator of 2.

Then, compare the denominators. 10 < 12, so $\frac{2}{10}>\frac{2}{12}$.

Since $\frac{1}{5}$ is equivalent to $\frac{2}{10}$, $\frac{1}{5}>\frac{2}{12}$.