Use the area models to answer the question.

Question

The fraction of area model A is 4/12
. The fraction of area model B is 3/9
. Compare the two fractions and write an equation or inequality to show how the two fractions are related. Use <, >, or =.

Two rectangles are shown. The left rectangle is divided into 12 equal parts and arranged in 3 rows of 4 cells each. 4 of these cells are colored yellow. The right rectangle is divided into 9 equal parts and arranged in 3 rows of 3 cells each. 3 of these cells are colored yellow.

(2 points)

Answer 1

To compare the two fractions \( \frac{4}{12} \) and \( \frac{3}{9} \), we can simplify both fractions to see if they are equal or which one is greater.

1. Simplifying \( \frac{4}{12} \): \[ \frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3} \]

2. Simplifying \( \frac{3}{9} \): \[ \frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{1}{3} \]

Since both fractions simplify to \( \frac{1}{3} \), we can conclude that: \[ \frac{4}{12} = \frac{3}{9} \]

Thus, the relationship between the two fractions can be written as: \[ \frac{4}{12} = \frac{3}{9} \]

This indicates that the two fractions are equal.