Pregunta
\begin{tabular}{l} Select a counterexample to the statement. \\ The product of an integer and a decimal number will never be an integer. \\ Answer 2 Points \\ Prev \\ Keyboard Shortcut \\ R \( 8 \cdot 1.4=11.2 \) \\ \hline \( 2 \cdot 1.3=2.6 \) \\ \hline \( 2 \cdot 1.5=3 \)\end{tabular}
Ask by Salazar Zimmerman. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( 2 \cdot 1.5 = 3 \) is a counterexample.
Solución
The statement to evaluate is:
**"The product of an integer and a decimal number will never be an integer."**
Let's examine each option to find a counterexample:
1. **\( 8 \cdot 1.4 = 11.2 \)**
- **Product:** 11.2 (not an integer)
- **Does not serve as a counterexample.**
2. **\( 2 \cdot 1.3 = 2.6 \)**
- **Product:** 2.6 (not an integer)
- **Does not serve as a counterexample.**
3. **\( 2 \cdot 1.5 = 3 \)**
- **Product:** 3 (an integer)
- **This **_is_** a counterexample** because multiplying the integer 2 by the decimal 1.5 results in the integer 3, which contradicts the original statement.
**Answer:** \( 2 \cdot 1.5 = 3 \)
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Extra Insights
Here’s a fun twist on exploring this mathematical statement! The statement claims that multiplying an integer by a decimal will never yield an integer, but consider \(2 \cdot 1.5 = 3\). Boom! That’s a counterexample, and it’s a whole number! Another classic example is \(3 \cdot 1.0 = 3\). In this case, multiplying by a decimal that represents a whole number (like 1.0) results in an integer! So don’t let that statement fool you! There are certainly instances where the product is, indeed, an integer!
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