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12. Using the table, find the ratio of the following notes to two decimal places. Then express your answer in integer-ratio form.

\begin{tabular}{|ccccccccccccc|}
\hline
A & A\# & B & C & C\# & D & D\# & E & F & F\# & G & G\# & A \\
\hline
880 & 932 & 988 & 1,047 & 1,109 & 1,175 & 1,245 & 1,319 & 1,397 & 1,480 & 1,568 & 1,661 & 1,760 \\
\hline
\end{tabular}

Find the ratio of E to C.

A. [tex]$\frac{2}{1}$[/tex]
B. [tex]$\frac{5}{3}$[/tex]
C. [tex]$\frac{5}{4}$[/tex]
D. [tex]$\frac{4}{3}$[/tex]



Answer :

GinnyAnswer
Let's solve the problem step by step.

Step 1: Identify the given notes and their frequencies from the table.
- Note E has a frequency of 1319 Hz.
- Note C has a frequency of 1047 Hz.

Step 2: Calculate the ratio of the frequency of E to the frequency of C.
[tex]\[ \text{Ratio} = \frac{\text{Frequency of E}}{\text{Frequency of C}} = \frac{1319}{1047} \][/tex]

Step 3: Convert the ratio to a decimal value.
[tex]\[ \text{Ratio (decimal)} = \frac{1319}{1047} \approx 1.259789875835721 \][/tex]
To two decimal places, this is approximately:
[tex]\[ 1.26 \][/tex]

Step 4: Express the ratio in integer form (simplified fraction).
We need to express [tex]\(\frac{1319}{1047}\)[/tex] in its simplest form:
- Determine the greatest common divisor (GCD) of 1319 and 1047. The GCD is 1.
- So, the simplified form of the fraction is:
[tex]\[ \frac{1319}{1047} \][/tex]

Therefore, the ratio of Note E to Note C is:
1.26 (to two decimal places)

And expressed in integer-ratio form, the ratio is:
[tex]\[ \frac{1319}{1047} \][/tex]

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