Sure, let’s break down the problem step-by-step to form the correct algebraic expression that corresponds to "ten less than a number divided by twelve".
1. Identify Key Words and Their Replacements:
- "ten" is replaced with 10.
- "less than" indicates subtraction, so it will be represented by the minus sign (-).
- "a number" will be represented by the variable [tex]\( n \)[/tex].
- "divided by" will be represented by the division sign (/).
- "twelve" is replaced with 12.
2. Construct the Algebraic Expression:
- Start with "a number divided by twelve" which corresponds to [tex]\(\frac{n}{12}\)[/tex].
- Now we need "ten less than [tex]\(\frac{n}{12}\)[/tex]". "Less than" indicates subtraction, so we subtract 10 from [tex]\(\frac{n}{12}\)[/tex].
After combining these parts, the expression becomes:
[tex]\[
\frac{n}{12} - 10
\][/tex]
3. Verification with Given Choices:
Let's match this expression with the given options:
- [tex]\(\frac{n}{12} - 10\)[/tex]
- [tex]\(\frac{12}{n} - 10\)[/tex]
- [tex]\(10 - \frac{n}{12}\)[/tex]
- [tex]\(10 - \frac{12}{n}\)[/tex]
The correct match is:
[tex]\[
\frac{n}{12} - 10
\][/tex]
Thus, the algebraic expression that represents "ten less than a number divided by twelve" is:
[tex]\[
\frac{n}{12} - 10
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\frac{n}{12} - 10}
\][/tex]
