Let's carefully examine each of the given options to determine which one correctly shows the quotient of [tex]\(75\)[/tex] divided by [tex]\(5\)[/tex].
1. Option 1: [tex]\(75 \div 5 = 70\)[/tex]
To verify this, we need to divide [tex]\(75\)[/tex] by [tex]\(5\)[/tex].
[tex]\[
75 \div 5 = 15
\][/tex]
So, [tex]\(75 \div 5\)[/tex] does not equal [tex]\(70\)[/tex]. Therefore, this option is incorrect.
2. Option 2: [tex]\(\frac{5}{75} = 12\)[/tex]
To evaluate this, we divide [tex]\(5\)[/tex] by [tex]\(75\)[/tex].
[tex]\[
\frac{5}{75} = \frac{1}{15}
\][/tex]
This result is clearly not [tex]\(12\)[/tex]. Therefore, this option is incorrect.
3. Option 3: [tex]\(\frac{75}{5} = 15\)[/tex]
To verify this, we divide [tex]\(75\)[/tex] by [tex]\(5\)[/tex].
[tex]\[
\frac{75}{5} = 15
\][/tex]
This result is correct. Therefore, this option is correct.
4. Option 4: [tex]\(75 \div 5 = 25\)[/tex]
To verify this, we divide [tex]\(75\)[/tex] by [tex]\(5\)[/tex].
[tex]\[
75 \div 5 = 15
\][/tex]
So, [tex]\(75 \div 5\)[/tex] does not equal [tex]\(25\)[/tex]. Therefore, this option is incorrect.
Having verified each option, the correct one is:
[tex]\[
\boxed{3 : \frac{75}{5} = 15}
\][/tex]
