Question

use the model to find 128 ÷ 8. first, find the missing side lengths.

Explanation:

Step1: Find the side length of the orange rectangle

The area of a rectangle is \(A = l\times w\). For the orange rectangle, \(A = 80\) and \(w = 8\). Using the formula \(l=\frac{A}{w}\), we have \(l=\frac{80}{8}\).
$$\frac{80}{8}=10$$

Step2: Find the side length of the pink rectangle

For the pink rectangle, \(A = 48\) and \(w = 8\). Using the formula \(l=\frac{A}{w}\), we have \(l=\frac{48}{8}\).
$$\frac{48}{8}=6$$

Step3: Calculate \(128\div8\)

Since \(128=80 + 48\), then \(128\div8=(80 + 48)\div8\). By the distributive property \((a + b)\div c=a\div c + b\div c\), so \(128\div8=(80\div8)+(48\div8)\).
We know \(80\div8 = 10\) and \(48\div8=6\), then \(10 + 6=16\).

Answer:

The side - length of the orange rectangle is \(10\), the side - length of the pink rectangle is \(6\), and \(128\div8 = 16\).