Question

partition the area models to make common units.
\\(\frac{4}{5}\\)
\\(\frac{3}{4}\\)

Explanation:

Step1: Find common denominator

To make common units (common denominator) for $\frac{4}{5}$ and $\frac{3}{4}$, find the least common multiple (LCM) of 5 and 4. LCM(5,4) = 20.

Step2: Partition first model

For $\frac{4}{5}$, to get denominator 20, multiply numerator and denominator by 4: $\frac{4\times4}{5\times4}=\frac{16}{20}$. So partition each of the 5 original parts into 4 smaller parts (since 5×4 = 20). The blue parts (4 original) will become 4×4 = 16 smaller parts.

Step3: Partition second model

For $\frac{3}{4}$, to get denominator 20, multiply numerator and denominator by 5: $\frac{3\times5}{4\times5}=\frac{15}{20}$. So partition each of the 4 original parts into 5 smaller parts (since 4×5 = 20). The blue parts (3 original) will become 3×5 = 15 smaller parts.

Answer:

After partitioning, $\frac{4}{5}=\frac{16}{20}$ (16 out of 20 smaller parts) and $\frac{3}{4}=\frac{15}{20}$ (15 out of 20 smaller parts). The common unit is 20 - part partition.