Marci performed a division. 175 was the dividend, 5 was the divisor, and 35 was the quotient. Which is a correct representation of this problem?

A. [tex]$\frac{175}{35}=5$[/tex]

B. [tex]$35 \div 5=175$[/tex]

C. [tex]$5 \div 175=35$[/tex]

D. [tex]$\frac{175}{5}=35$[/tex]



Answer :

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.