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

\begin{tabular}{cccccccccccccc}
\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 F to C.

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



Answer :

GinnyAnswer
To find the ratio of the frequency of note F to note C and express it in both decimal and integer-ratio forms, follow these steps:

1. Identify the frequencies from the table:
- Frequency of F = 1397 Hz
- Frequency of C = 1047 Hz

2. Calculate the ratio:
- The ratio of the frequency of F to the frequency of C is calculated by dividing the frequency of F by the frequency of C:

[tex]\[ \text{Ratio} = \frac{\text{Frequency of F}}{\text{Frequency of C}} = \frac{1397}{1047} \][/tex]

3. Compute the decimal value of the ratio:
- Using a calculator, divide 1397 by 1047 to get the decimal value:

[tex]\[ \text{Ratio} \approx 1.3342884431709647 \][/tex]

4. Express the decimal ratio in integer-ratio form:
- To convert the decimal ratio to an integer-ratio form, we compare the calculated ratio to the given integer ratios. Specifically:
- [tex]\(\frac{3}{2} \approx 1.5\)[/tex]
- [tex]\(\frac{4}{3} \approx 1.3333\)[/tex]
- [tex]\(\frac{5}{4} \approx 1.25\)[/tex]
- [tex]\(\frac{2}{1} = 2\)[/tex]

- The calculated ratio of 1.3342884431709647 is very close to [tex]\(\frac{4}{3}\)[/tex] (which is approximately 1.3333). Therefore, we can express the ratio as [tex]\(\frac{4}{3}\)[/tex] in integer-ratio form.

5. Conclusion:
- The ratio of the frequency of note F to note C, calculated to two decimal places, is approximately 1.33.
- Expressed in integer-ratio form, this ratio is [tex]\(\frac{4}{3}\)[/tex].

Thus, the answer is:
[tex]\[ \frac{4}{3} \][/tex]

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