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Given the nonsensical nature of the original content, it is necessary to clarify the intended mathematical operation. Below is a sensible and well-formatted math problem:

Simplify the following expressions:

[tex]\[
\frac{4}{32} \cdot \frac{47}{72} \cdot r
\][/tex]

[tex]\[
\frac{40}{72} \cdot r
\][/tex]

[tex]\[
\frac{57}{72} \cdot 1
\][/tex]

Choose the correct simplifications from the following options:

A. [tex]\(\frac{1}{64}\)[/tex]

B. [tex]\(\frac{9}{64} \cdot r\)[/tex]

C. [tex]\(\frac{50}{64} \cdot r\)[/tex]

D. [tex]\(\frac{55}{64}\)[/tex]



Answer :

GinnyAnswer
Let's solve this step-by-step, considering the three different expressions provided.

### Step 1: Simplify Each Fraction Expression

#### Expression 1
For the first fraction:
[tex]\[ \frac{4}{32} \cdot \frac{47}{72} \cdot 1 \][/tex]
We simply multiply the fractions:
[tex]\[ = \frac{4 \cdot 47}{32 \cdot 72} \][/tex]
Here, the final result is:
[tex]\[ 0.08159722222222222 \][/tex]

#### Expression 2
For the second fraction:
[tex]\[ \frac{40}{72} \cdot 1 \][/tex]
We have:
[tex]\[ \frac{40}{72} = \frac{5}{9} \][/tex]
And multiplying by 1, we get:
[tex]\[ = \frac{5}{9} \][/tex]
The result is:
[tex]\[ 0.5555555555555556 \][/tex]

#### Expression 3
For the third fraction:
[tex]\[ \frac{57}{72} \cdot 1 \][/tex]
We have:
[tex]\[ \frac{57}{72} = \frac{19}{24} \][/tex]
And multiplying by 1, we get:
[tex]\[ = \frac{19}{24} \][/tex]
The result is:
[tex]\[ 0.7916666666666666 \][/tex]

### Summarized Results
So, evaluating the given expressions:
1. [tex]\(\frac{4}{32} \cdot \frac{47}{72} \cdot 1 \approx 0.08159722222222222\)[/tex]
2. [tex]\(\frac{40}{72} \cdot 1 \approx 0.5555555555555556\)[/tex]
3. [tex]\(\frac{57}{72} \cdot 1 \approx 0.7916666666666666\)[/tex]

These are the steps and their corresponding results. Please let me know if you need further details or explanations!

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