Question

lily is using the equivalent ratios \\(\frac{7}{100} = \frac{77}{\square}\\) to find the unknown whole value. what factor should she multiply 100 by? explain how you found the factor. select the answers from the drop - down lists to correctly complete the sentence. show hints i would multiply by \\(\boldsymbol{\
abla}\\) because \\(\boldsymbol{\
abla}\\).

Explanation:

Step1: Analyze the numerators

We have the fraction \(\frac{7}{100}\) and \(\frac{77}{\square}\). The numerator changes from \(7\) to \(77\). To find the factor, we calculate \(\frac{77}{7}\).
\(\frac{77}{7} = 11\)

Step2: Determine the factor for the denominator

In equivalent fractions, if we multiply the numerator by a factor, we must multiply the denominator by the same factor to keep the ratio equivalent. Since the numerator \(7\) is multiplied by \(11\) to get \(77\), the denominator \(100\) should also be multiplied by \(11\).

Answer:

I would multiply by \(11\) because \(7\times11 = 77\), so to keep the ratio equivalent, \(100\) must be multiplied by \(11\) as well.