Question

partition each area model again to make like units.

Explanation:

Step1: Analyze the first area model

The first rectangle is divided into 5 equal vertical strips, with 1 strip shaded (purple). To make like units with the second model, we need to find a common denominator. The second rectangle is divided into 4 horizontal strips, with 3 shaded. The least common multiple of 5 and 4 is 20. So we partition the first rectangle into 20 equal parts (by dividing each of the 5 strips into 4 smaller parts) and the second into 20 equal parts (dividing each of the 4 strips into 5 smaller parts).

Step2: Partition the first model

For the first rectangle (5 strips), each strip divided into 4 gives \(5\times4 = 20\) parts. The shaded part (1 strip) becomes \(1\times4=4\) parts out of 20.

Step3: Partition the second model

For the second rectangle (4 strips), each strip divided into 5 gives \(4\times5 = 20\) parts. The shaded part (3 strips) becomes \(3\times5 = 15\) parts out of 20.

Answer:

The first area model (5 - strip) is partitioned into 20 equal smaller rectangles (each original strip into 4), and the second (4 - strip) into 20 equal smaller rectangles (each original strip into 5), resulting in like units (20 - part models) with the first having 4 shaded and the second 15 shaded.