Question

compare the fraction models below using <, >, or =

Explanation:

Step1: Analyze the first fraction model (circle)

The left circle is divided into 4 equal parts, and 3 parts are shaded. So the fraction is $\frac{3}{4}$. The right circle is divided into 6 equal parts, and 5 parts are shaded. So the fraction is $\frac{5}{6}$. To compare them, find a common denominator. The least common denominator of 4 and 6 is 12. Convert the fractions: $\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}$, $\frac{5}{6}=\frac{5\times2}{6\times2}=\frac{10}{12}$. Since $9 < 10$, $\frac{3}{4}<\frac{5}{6}$.

Step2: Analyze the second fraction model (rectangle)

The left rectangle is divided into 5 equal parts, and 4 parts are shaded. So the fraction is $\frac{4}{5}$. The right rectangle is divided into 4 equal parts, and 3 parts are shaded. So the fraction is $\frac{3}{4}$. Find a common denominator, which is 20. Convert the fractions: $\frac{4}{5}=\frac{4\times4}{5\times4}=\frac{16}{20}$, $\frac{3}{4}=\frac{3\times5}{4\times5}=\frac{15}{20}$. Since $16 > 15$, $\frac{4}{5}>\frac{3}{4}$.

Answer:

For the circle models: $\frac{3}{4}<\frac{5}{6}$; For the rectangle models: $\frac{4}{5}>\frac{3}{4}$