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 (representing $\frac{1}{5}$). To make like units with the second model, we need to find a common denominator. The second model is divided into 4 horizontal strips, with 3 shaded (representing $\frac{3}{4}$). The least common denominator of 5 and 4 is 20.

Step2: Partition the first model

For the first model (divided into 5 parts), we need to partition each strip into 4 smaller parts (since $5\times4 = 20$). So each of the 5 vertical strips will be divided into 4 horizontal sub - strips, resulting in a total of $5\times4=20$ small rectangles. The shaded area (1 strip) will now be $1\times4 = 4$ small rectangles, so it represents $\frac{4}{20}$.

Step3: Partition the second model

For the second model (divided into 4 parts), we need to partition each strip into 5 smaller parts (since $4\times5 = 20$). So each of the 4 horizontal strips will be divided into 5 vertical sub - strips, resulting in a total of $4\times5 = 20$ small rectangles. The shaded area (3 strips) will now be $3\times5=15$ small rectangles, so it represents $\frac{15}{20}$.

(Note: Since the problem is about partitioning area models for fraction operations, the subfield of Mathematics here is likely related to Fractions, which can be considered under the broader subfields like Algebra or more specifically under the "Others" or as a part of basic arithmetic which is foundational to Mathematics subfields. But the key is the process of partitioning to get like units for fraction addition or subtraction.)

Answer:

The first area model (with 5 vertical strips) should be partitioned into 20 equal parts (by dividing each of the 5 strips into 4 sub - strips), and the second area model (with 4 horizontal strips) should be partitioned into 20 equal parts (by dividing each of the 4 strips into 5 sub - strips) to make like units (with a common denominator of 20).