Answer :
It looks like we're dealing with a problem involving fraction equivalency and simplification. Let's break down the process step-by-step:
1. Understanding Fraction Equivalence:
- The fractions we're examining are [tex]\(\frac{24}{30}\)[/tex] and [tex]\(\frac{\pi}{5}\)[/tex].
- To check if two fractions are equivalent, we can cross-multiply. Multiply the numerator of one fraction by the denominator of the other and see if both products are equal:
- [tex]\(24 \times 5\)[/tex] for the first fraction.
- [tex]\(\pi \times 30\)[/tex] for the second fraction.
2. Cross-Multiplication Check:
- Calculating [tex]\(24 \times 5\)[/tex] gives us 120.
- Calculating [tex]\(\pi \times 30\)[/tex], since [tex]\(\pi \approx 3.14159\)[/tex], results in approximately 94.25.
- Since 120 is not equal to 94.25, these fractions are not equivalent.
3. Simplifying the Fraction [tex]\(\frac{24}{30}\)[/tex]:
- To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator.
- The GCD of 24 and 30 is 6.
- Divide both the numerator and the denominator by the GCD:
- [tex]\(\frac{24}{6} = 4\)[/tex]
- [tex]\(\frac{30}{6} = 5\)[/tex]
- So, the fraction [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
4. Final Observations:
- The simplified form of [tex]\(\frac{24}{30}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].
- The original fraction [tex]\(\frac{24}{30}\)[/tex] is not equivalent to [tex]\(\frac{\pi}{5}\)[/tex] because their cross-multiplication results differ.
In conclusion, [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex] and is not equivalent to [tex]\(\frac{\pi}{5}\)[/tex].
1. Understanding Fraction Equivalence:
- The fractions we're examining are [tex]\(\frac{24}{30}\)[/tex] and [tex]\(\frac{\pi}{5}\)[/tex].
- To check if two fractions are equivalent, we can cross-multiply. Multiply the numerator of one fraction by the denominator of the other and see if both products are equal:
- [tex]\(24 \times 5\)[/tex] for the first fraction.
- [tex]\(\pi \times 30\)[/tex] for the second fraction.
2. Cross-Multiplication Check:
- Calculating [tex]\(24 \times 5\)[/tex] gives us 120.
- Calculating [tex]\(\pi \times 30\)[/tex], since [tex]\(\pi \approx 3.14159\)[/tex], results in approximately 94.25.
- Since 120 is not equal to 94.25, these fractions are not equivalent.
3. Simplifying the Fraction [tex]\(\frac{24}{30}\)[/tex]:
- To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator.
- The GCD of 24 and 30 is 6.
- Divide both the numerator and the denominator by the GCD:
- [tex]\(\frac{24}{6} = 4\)[/tex]
- [tex]\(\frac{30}{6} = 5\)[/tex]
- So, the fraction [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
4. Final Observations:
- The simplified form of [tex]\(\frac{24}{30}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].
- The original fraction [tex]\(\frac{24}{30}\)[/tex] is not equivalent to [tex]\(\frac{\pi}{5}\)[/tex] because their cross-multiplication results differ.
In conclusion, [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex] and is not equivalent to [tex]\(\frac{\pi}{5}\)[/tex].
