Let's analyze each of the given representations of the division problem to determine which one is correct.
1. [tex]\(\frac{175}{35} = 5\)[/tex]:
In this representation, we are dividing 175 by 35:
[tex]\[ \frac{175}{35} = \frac{175}{35} \][/tex]
However, dividing 175 by 35 does not result in 5. The correct calculation would give us:
[tex]\[ \frac{175}{35} = 5 \][/tex]
Given that 35 would go into 175 exactly 5 times, this representation is correct.
2. [tex]\(35 \div 5 = 175\)[/tex]:
In this representation, we are dividing 35 by 5:
[tex]\[ 35 \div 5 = 7 \][/tex]
Dividing 35 by 5 does not equal 175. Instead, it equals 7. Hence, this representation is incorrect.
3. [tex]\(5 \div 175 = 35\)[/tex]:
Here, we are dividing 5 by 175:
[tex]\[ 5 \div 175 = \frac{5}{175} = \frac{1}{35} \][/tex]
Dividing 5 by 175 does not yield 35; it results in [tex]\(\frac{1}{35}\)[/tex]. Therefore, this representation is incorrect.
In conclusion, the correct representation of the division problem where 175 is the dividend, 5 is the divisor, and 35 is the quotient is:
[tex]\[ \frac{175}{35} = 5 \][/tex]
Thus, the first representation, [tex]\(\frac{175}{35} = 5\)[/tex], is the correct one.
