Answer :
To determine which expression is equivalent to the fraction [tex]\(\frac{24}{17}\)[/tex], we need to evaluate each option and see which one matches the fraction.
Let's analyze each option:
A. [tex]\(17 \div 24\)[/tex]: This expression means dividing 17 by 24, which is not the same as [tex]\(24 \div 17\)[/tex].
B. [tex]\(24 \cdot 17\)[/tex]: This expression means multiplying 24 by 17. Multiplying two numbers is different from dividing them, so this is not equivalent to [tex]\(\frac{24}{17}\)[/tex].
C. 24.17: This is a decimal number and does not represent division. It is not equivalent to [tex]\(\frac{24}{17}\)[/tex].
D. [tex]\(17 - 24\)[/tex]: This is a subtraction operation resulting in [tex]\(-7\)[/tex]. Subtraction does not equal the division of these numbers, so it's not equivalent.
E. [tex]\(24 + 17\)[/tex]: This represents addition and results in 41. Adding these numbers is not the same as dividing them.
F. [tex]\(24 \div 17\)[/tex]: This expression represents the division of 24 by 17, which is exactly what the fraction [tex]\(\frac{24}{17}\)[/tex] represents.
From the evaluation, option F ([tex]\(24 \div 17\)[/tex]) is indeed the same as the original fraction [tex]\(\frac{24}{17}\)[/tex]. When you perform this division, it results in approximately [tex]\(1.411764705882353\)[/tex], which matches the value of the fraction. Thus, the correct answer is option F.
Let's analyze each option:
A. [tex]\(17 \div 24\)[/tex]: This expression means dividing 17 by 24, which is not the same as [tex]\(24 \div 17\)[/tex].
B. [tex]\(24 \cdot 17\)[/tex]: This expression means multiplying 24 by 17. Multiplying two numbers is different from dividing them, so this is not equivalent to [tex]\(\frac{24}{17}\)[/tex].
C. 24.17: This is a decimal number and does not represent division. It is not equivalent to [tex]\(\frac{24}{17}\)[/tex].
D. [tex]\(17 - 24\)[/tex]: This is a subtraction operation resulting in [tex]\(-7\)[/tex]. Subtraction does not equal the division of these numbers, so it's not equivalent.
E. [tex]\(24 + 17\)[/tex]: This represents addition and results in 41. Adding these numbers is not the same as dividing them.
F. [tex]\(24 \div 17\)[/tex]: This expression represents the division of 24 by 17, which is exactly what the fraction [tex]\(\frac{24}{17}\)[/tex] represents.
From the evaluation, option F ([tex]\(24 \div 17\)[/tex]) is indeed the same as the original fraction [tex]\(\frac{24}{17}\)[/tex]. When you perform this division, it results in approximately [tex]\(1.411764705882353\)[/tex], which matches the value of the fraction. Thus, the correct answer is option F.
