Weston Knight
02/17/2024 · Junior High School
nd \( \frac{6}{7} 4 \frac{2}{9} \)
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Tutor-Verified Answer
Step-by-step Solution
To perform the operation \( \frac{6}{7} \times 4 \frac{2}{9} \), we first need to convert the mixed number \( 4 \frac{2}{9} \) into an improper fraction.
1. Convert \( 4 \frac{2}{9} \) to an improper fraction:
\[
4 \frac{2}{9} = 4 + \frac{2}{9} = \frac{4 \times 9}{9} + \frac{2}{9} = \frac{36}{9} + \frac{2}{9} = \frac{36 + 2}{9} = \frac{38}{9}
\]
2. Now we can multiply \( \frac{6}{7} \) by \( \frac{38}{9} \):
\[
\frac{6}{7} \times \frac{38}{9} = \frac{6 \times 38}{7 \times 9} = \frac{228}{63}
\]
3. Next, we simplify \( \frac{228}{63} \). We can find the greatest common divisor (GCD) of 228 and 63. The GCD is 9.
4. Divide both the numerator and the denominator by their GCD:
\[
\frac{228 \div 9}{63 \div 9} = \frac{25.3333}{7} \approx \frac{76}{21}
\]
Thus, the final answer is:
\[
\frac{76}{21}
\] or approximately \( 3 \frac{13}{21} \) if you want it in mixed number form.
Quick Answer
The final answer is \( \frac{76}{21} \) or approximately \( 3 \frac{13}{21} \).
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