Question

find the number that makes the ratio equivalent to 24:72. 2:□

Explanation:

Step1: Find the scale factor

To find the number that makes the ratio \(2:\square\) equivalent to \(24:72\), we first find the scale factor by dividing the first term of the new ratio (\(2\)) by the first term of the original ratio (\(24\)). So the scale factor \(k=\frac{2}{24}=\frac{1}{12}\).

Step2: Apply the scale factor to the second term

Now we apply this scale factor to the second term of the original ratio (\(72\)) to find the missing term. Let the missing term be \(x\). We know that \(\frac{2}{24}=\frac{x}{72}\) (cross - multiplying or using the scale factor). Using the scale factor method, \(x = 72\times\frac{1}{12}\) or we can also think of it as since \(24\div12 = 2\), then \(72\div12=6\). So \(2:6\) is equivalent to \(24:72\) because \(\frac{24}{72}=\frac{24\div12}{72\div12}=\frac{2}{6}\).

Answer:

\(6\)