To determine which equation represents the word sentence "The quotient of a number \(b\) and 0.3 equals negative 10", let's carefully analyze the arithmetic expression described in the sentence.
1. Understanding the term "quotient":
- The "quotient" refers to the result of division.
2. Identifying the quantities involved:
- The number \(b\).
- The number \(0.3\).
3. Setting up the equation:
- According to the sentence, the quotient of \(b\) and \(0.3\) is given as negative 10.
- Mathematically, this can be expressed as:
[tex]\[
\frac{b}{0.3} = -10
\][/tex]
4. Analyzing the options:
- Option A: \(0.3b = 10\) does not match because it represents multiplying \(b\) by \(0.3\) and setting it equal to \(10\), which is not a quotient.
- Option B: \(\frac{b}{0.3} = -10\) correctly represents the division of \(b\) by \(0.3\) and equates it to \(-10\).
- Option C: \(\frac{0.3}{b} = -10\) incorrectly represents the division of \(0.3\) by \(b\), which is not the quotient described in the sentence.
- Option D: \(\frac{b}{0.3} = 10\) represents the division of \(b\) by \(0.3\) but equates it to positive 10, not negative 10.
Thus, the correct equation that represents the word sentence "The quotient of a number \(b\) and \(0.3\) equals negative 10" is:
[tex]\[
\boxed{\frac{b}{0.3} = -10}
\][/tex]
