Answer :
Sure! Let's go through this step-by-step to understand which statement is true about the product of [tex]\(\frac{6}{5}\)[/tex] and 94.
1. Understanding the Fraction [tex]\(\frac{6}{5}\)[/tex]:
- The fraction [tex]\(\frac{6}{5}\)[/tex] is greater than 1 because 6 is greater than 5. This means that multiplying any number by [tex]\(\frac{6}{5}\)[/tex] will increase the number.
2. Calculate the Product:
- We want to find the product of [tex]\(\frac{6}{5}\)[/tex] and 94. Multiplying 94 by [tex]\(\frac{6}{5}\)[/tex] is essentially increasing 94.
3. Comparison:
- Since [tex]\(\frac{6}{5}\)[/tex] is greater than 1, the product of [tex]\(\frac{6}{5}\)[/tex] and 94 will be greater than 94 itself.
- This is because by multiplying by a number greater than 1, we increase the original number.
4. Conclusion:
- Therefore, the correct statement is:
- A. The product of [tex]\(\frac{6}{5}\)[/tex] and 94 is greater than 94, because [tex]\(\frac{6}{5}\)[/tex] is greater than 1.
This logical reasoning, based on the properties of the fraction and multiplication, shows why statement A is the true statement regarding the comparison.
1. Understanding the Fraction [tex]\(\frac{6}{5}\)[/tex]:
- The fraction [tex]\(\frac{6}{5}\)[/tex] is greater than 1 because 6 is greater than 5. This means that multiplying any number by [tex]\(\frac{6}{5}\)[/tex] will increase the number.
2. Calculate the Product:
- We want to find the product of [tex]\(\frac{6}{5}\)[/tex] and 94. Multiplying 94 by [tex]\(\frac{6}{5}\)[/tex] is essentially increasing 94.
3. Comparison:
- Since [tex]\(\frac{6}{5}\)[/tex] is greater than 1, the product of [tex]\(\frac{6}{5}\)[/tex] and 94 will be greater than 94 itself.
- This is because by multiplying by a number greater than 1, we increase the original number.
4. Conclusion:
- Therefore, the correct statement is:
- A. The product of [tex]\(\frac{6}{5}\)[/tex] and 94 is greater than 94, because [tex]\(\frac{6}{5}\)[/tex] is greater than 1.
This logical reasoning, based on the properties of the fraction and multiplication, shows why statement A is the true statement regarding the comparison.
