5. Draw a tape diagram to represent and answer the question: What fraction of \( 1 \frac{1}{2} \) is \( 4 / 5 \) ?

We start by writing the whole \(1\frac{1}{2}\) as an improper fraction: \[ 1\frac{1}{2}=\frac{3}{2}. \] The question “What fraction of \(1\frac{1}{2}\) is \(\frac{4}{5}\)?” can be set up as a division: \[ \text{Fraction}=\frac{\frac{4}{5}}{\frac{3}{2}}. \] Multiplying by the reciprocal we have: \[ \frac{4}{5}\times\frac{2}{3}=\frac{8}{15}. \] Thus, \(\frac{4}{5}\) is \(\frac{8}{15}\) of \(1\frac{1}{2}\). A tape diagram can help visualize this relationship. Below is a diagram showing a tape divided into 15 equal parts (each part represents \(\frac{1}{15}\) of the whole \(1\frac{1}{2}\)). Since we found that \(\frac{4}{5}\) corresponds to \(\frac{8}{15}\), we shade 8 out of the 15 parts. ``` Whole tape (represents 1½ = 15/15): _______________________________________ |■■■■■■■■|□□□□□□□| | 8 parts | 7 parts | --------------------------------------- ``` In this diagram: - The entire tape is divided into 15 equal segments. - The shaded 8 segments represent \(\frac{8}{15}\) of \(1\frac{1}{2}\), which is equal to \(\frac{4}{5}\). Thus, the final answer is \(\boxed{\frac{8}{15}}\).