Gibbs Savage
07/03/2024 · Middle School
\( 4\frac{5}{4}.\frac{8^{2}}{5^{4}}= \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the expression \( 4\frac{5}{4} \cdot \frac{8^{2}}{5^{4}} \), we will first convert the mixed number \( 4\frac{5}{4} \) into an improper fraction.
1. Convert \( 4\frac{5}{4} \):
\[
4\frac{5}{4} = 4 + \frac{5}{4} = \frac{4 \cdot 4}{4} + \frac{5}{4} = \frac{16}{4} + \frac{5}{4} = \frac{16 + 5}{4} = \frac{21}{4}
\]
2. Now, we need to calculate \( 8^2 \) and \( 5^4 \):
\[
8^2 = 64
\]
\[
5^4 = 625
\]
3. Substitute these values into the expression:
\[
\frac{21}{4} \cdot \frac{64}{625}
\]
4. Multiply the fractions:
\[
= \frac{21 \cdot 64}{4 \cdot 625}
\]
5. Calculate \( 21 \cdot 64 \):
\[
21 \cdot 64 = 1344
\]
6. Now calculate \( 4 \cdot 625 \):
\[
4 \cdot 625 = 2500
\]
7. Now we have:
\[
\frac{1344}{2500}
\]
8. To simplify \( \frac{1344}{2500} \), we can check for common factors. The greatest common divisor (GCD) of 1344 and 2500 is 4.
9. Divide both the numerator and the denominator by 4:
\[
\frac{1344 \div 4}{2500 \div 4} = \frac{336}{625}
\]
Thus, the final answer is:
\[
\boxed{\frac{336}{625}}
\]
Quick Answer
The simplified expression is \( \frac{336}{625} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
(0)
Ask Real Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
PREV 
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
