Question

1/3 + 4/5 partition each area model again to make like units.

Explanation:

Step1: Find a common denominator

To add \(\frac{1}{3}\) and \(\frac{4}{5}\), we need a common denominator. The least common denominator of 3 and 5 is \(3\times5 = 15\).

Step2: Rewrite the fractions

For \(\frac{1}{3}\), multiply numerator and denominator by 5: \(\frac{1\times5}{3\times5}=\frac{5}{15}\).
For \(\frac{4}{5}\), multiply numerator and denominator by 3: \(\frac{4\times3}{5\times3}=\frac{12}{15}\).

Step3: Add the fractions

Now that the denominators are the same, add the numerators: \(\frac{5}{15}+\frac{12}{15}=\frac{5 + 12}{15}=\frac{17}{15}\) (or \(1\frac{2}{15}\)).

For the area models:

• The first rectangle (representing \(\frac{1}{3}\)) is divided into 3 parts. To make 15 parts (since \(3\times5 = 15\)), we need to partition each of the 3 vertical strips into 5 smaller horizontal strips. This will create \(3\times5 = 15\) small rectangles, and the shaded part (1 strip) will become 5 small shaded rectangles (representing \(\frac{5}{15}\)).
• The second rectangle (representing \(\frac{4}{5}\)) is divided into 5 parts. To make 15 parts (since \(5\times3 = 15\)), we need to partition each of the 5 horizontal strips into 3 smaller vertical strips. This will create \(5\times3 = 15\) small rectangles, and the shaded parts (4 strips) will become \(4\times3 = 12\) small shaded rectangles (representing \(\frac{12}{15}\)).

Answer:

The sum of \(\frac{1}{3}+\frac{4}{5}\) is \(\frac{17}{15}\) (or \(1\frac{2}{15}\)). For the area models, partition the first into 15 parts (5 per original part) and the second into 15 parts (3 per original part) to show \(\frac{5}{15}\) and \(\frac{12}{15}\) respectively.