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Answer :
Sure! Let's break down the question step-by-step.
Problem Statement:
Charlie makes a rectangular flag that has a triangular section. Charlie claims that the area of the triangle is [tex]\(\frac{16}{24}\)[/tex] of the area of the entire flag. We need to determine if Charlie's claim is correct.
1. Understand Charlie's Claim:
Charlie claims that the area of the triangle section is [tex]\(\frac{16}{24}\)[/tex] of the area of the flag.
2. Simplify the Fraction:
Let's simplify the fraction [tex]\(\frac{16}{24}\)[/tex].
To simplify [tex]\(\frac{16}{24}\)[/tex], we find the greatest common divisor (GCD) of 16 and 24. The GCD of 16 and 24 is 8.
Now, divide both the numerator and the denominator by 8:
[tex]\[
\frac{16 \div 8}{24 \div 8} = \frac{2}{3}
\][/tex]
3. Compare the Simplified Fraction:
After simplification, the fraction [tex]\(\frac{16}{24}\)[/tex] becomes [tex]\(\frac{2}{3}\)[/tex].
4. Conclusion:
Since [tex]\(\frac{16}{24}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex], Charlie's claim that the area of the triangle is [tex]\(\frac{16}{24}\)[/tex] of the area of the flag is correct.
So, yes, I agree with Charlie's claim because [tex]\(\frac{16}{24}\)[/tex] is indeed [tex]\(\frac{2}{3}\)[/tex] after simplification.
Problem Statement:
Charlie makes a rectangular flag that has a triangular section. Charlie claims that the area of the triangle is [tex]\(\frac{16}{24}\)[/tex] of the area of the entire flag. We need to determine if Charlie's claim is correct.
1. Understand Charlie's Claim:
Charlie claims that the area of the triangle section is [tex]\(\frac{16}{24}\)[/tex] of the area of the flag.
2. Simplify the Fraction:
Let's simplify the fraction [tex]\(\frac{16}{24}\)[/tex].
To simplify [tex]\(\frac{16}{24}\)[/tex], we find the greatest common divisor (GCD) of 16 and 24. The GCD of 16 and 24 is 8.
Now, divide both the numerator and the denominator by 8:
[tex]\[
\frac{16 \div 8}{24 \div 8} = \frac{2}{3}
\][/tex]
3. Compare the Simplified Fraction:
After simplification, the fraction [tex]\(\frac{16}{24}\)[/tex] becomes [tex]\(\frac{2}{3}\)[/tex].
4. Conclusion:
Since [tex]\(\frac{16}{24}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex], Charlie's claim that the area of the triangle is [tex]\(\frac{16}{24}\)[/tex] of the area of the flag is correct.
So, yes, I agree with Charlie's claim because [tex]\(\frac{16}{24}\)[/tex] is indeed [tex]\(\frac{2}{3}\)[/tex] after simplification.
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