Question

3/4 + 4/5
partition each area model again to make like units.

Explanation:

Step1: Find common denominator

To add \(\frac{3}{4}\) and \(\frac{4}{5}\), find the least common denominator (LCD) of 4 and 5. The LCD of 4 and 5 is \(4\times5 = 20\).

Step2: Rewrite fractions

Rewrite \(\frac{3}{4}\) with denominator 20: \(\frac{3\times5}{4\times5}=\frac{15}{20}\).
Rewrite \(\frac{4}{5}\) with denominator 20: \(\frac{4\times4}{5\times4}=\frac{16}{20}\).

Step3: Add the fractions

Now add the two fractions: \(\frac{15}{20}+\frac{16}{20}=\frac{15 + 16}{20}=\frac{31}{20}\) (or \(1\frac{11}{20}\)).

For the area models:

• The first model (representing \(\frac{3}{4}\)): Partition each of the 4 columns into 5 smaller parts (since LCD is 20, \(4\times5 = 20\) parts total). The shaded area will have \(3\times5 = 15\) small parts.
• The second model (representing \(\frac{4}{5}\)): Partition each of the 5 rows into 4 smaller parts (since \(5\times4 = 20\) parts total). The shaded area will have \(4\times4 = 16\) small parts.

Answer:

The sum of \(\frac{3}{4}+\frac{4}{5}\) is \(\frac{31}{20}\) (or \(1\frac{11}{20}\)). For the area models, partition the first into 5 sub - parts per column and the second into 4 sub - parts per row to make 20 like units each, with shaded parts 15 and 16 respectively.