Question

3 scale up or scale down to determine each unknown quantity. b) \\(\frac{12\text{ inches}}{1\text{ foot}} = \frac{?}{18\text{ feet}}\\)

Explanation:

Step1: Identify the proportion relationship

We have a proportion \(\frac{12\ \text{inches}}{1\ \text{foot}}=\frac{x}{18\ \text{feet}}\), where \(x\) is the unknown quantity. Since the ratio of inches to feet should be consistent, we can solve for \(x\) by cross - multiplying or by scaling up the numerator as we scale up the denominator.

Step2: Scale up the numerator

The denominator is scaled up from \(1\) foot to \(18\) feet. To find the factor by which the denominator is scaled, we calculate \(\frac{18\ \text{feet}}{1\ \text{foot}} = 18\). So we also scale up the numerator (which represents inches) by the same factor. The original numerator is \(12\) inches. So we multiply \(12\) inches by \(18\).
\(x=12\times18\)
\(x = 216\)

Answer:

\(216\) inches