Question

2/7 + 2/3 partition each area model again to make like units.

Explanation:

Step1: Find a common denominator

To add \(\frac{2}{7}\) and \(\frac{2}{3}\), we first find the least common denominator (LCD) of 7 and 3. The LCD of 7 and 3 is \(7\times3 = 21\).

Step2: Rewrite the fractions

Rewrite \(\frac{2}{7}\) with denominator 21: \(\frac{2\times3}{7\times3}=\frac{6}{21}\).
Rewrite \(\frac{2}{3}\) with denominator 21: \(\frac{2\times7}{3\times7}=\frac{14}{21}\).

Step3: Add the fractions

Now add the two fractions: \(\frac{6}{21}+\frac{14}{21}=\frac{6 + 14}{21}=\frac{20}{21}\).

For the area models:

• The first rectangle (representing \(\frac{2}{7}\)) is divided into 7 parts. To make the denominator 21, we need to divide each of the 7 parts into 3 smaller parts, so the total number of parts becomes \(7\times3 = 21\). The shaded parts will then be \(2\times3 = 6\) parts out of 21.
• The second rectangle (representing \(\frac{2}{3}\)) is divided into 3 parts. To make the denominator 21, we need to divide each of the 3 parts into 7 smaller parts, so the total number of parts becomes \(3\times7 = 21\). The shaded parts will then be \(2\times7 = 14\) parts out of 21.

Answer:

The sum of \(\frac{2}{7}+\frac{2}{3}\) is \(\frac{20}{21}\). For the area models, partition the first (7 - part) rectangle into 21 parts (by dividing each of the 7 columns into 3 smaller columns) and the second (3 - part) rectangle into 21 parts (by dividing each of the 3 rows into 7 smaller rows) to have like units (21 - part models), with 6 and 14 shaded parts respectively, which add up to 20 shaded parts in the 21 - part model.