Question
Represent the following phrase as an algebraic expression, where "a number" is the letter \( x \). You do not need to simplify. The quotient of 1 and the square of a number.
Ask by Gordon Mejia. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The algebraic expression is \( \frac{1}{x^2} \).
Solution
To represent the phrase **"The quotient of 1 and the square of a number"** algebraically, follow these steps:
1. **Identify the components:**
- **Quotient of 1 and something**: This implies a division where 1 is the numerator.
- **Square of a number (x)**: This means \( x^2 \).
2. **Combine them into an expression:**
The quotient (division) of 1 by \( x^2 \) is written as:
\[
\frac{1}{x^2}
\]
Alternatively, it can be expressed using the division symbol:
\[
1 \div x^2 \quad \text{or} \quad 1 / x^2
\]
**Final Algebraic Expression:**
\[
\frac{1}{x^2}
\]
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Simplify this solution Beyond the Answer
The mathematical expression for the phrase "the quotient of 1 and the square of a number" can be represented as \( \frac{1}{x^2} \). This means you take 1 and divide it by the square of \( x \), which is the variable representing "a number". Now, let's add a touch of fun: imagine you have a magic number (your 'x') that gets a little squarier every time you multiply it by itself. When you split 1 by its square, you’re basically taking a tiny piece of that magic and seeing how many times you can fit it into that larger square! Voilà, algebraic magic at play!
