Question

find the number that makes the ratio equivalent to 2:18. \boxed{}:54

Explanation:

Step1: Analyze the ratio relationship

We know that in a ratio \(a:b = c:d\), the product of the extremes (\(a\times d\)) equals the product of the means (\(b\times c\)). Here, the original ratio is \(2:18\) and the new ratio is \(\square:54\). Let the unknown number be \(x\), so we have the proportion \(2:18=x:54\).

Step2: Solve for the unknown

Using the proportion property, we get \(18\times x = 2\times54\). First, calculate the right - hand side: \(2\times54 = 108\). Then, solve for \(x\) by dividing both sides of the equation \(18x = 108\) by 18. So \(x=\frac{108}{18}=6\). We can also think about the scale factor. The second term of the ratio changes from 18 to 54. The scale factor is \(\frac{54}{18}=3\). So we multiply the first term of the original ratio (2) by 3, \(2\times3 = 6\).

Answer:

6