To identify the appropriate conversion factor to convert feet to inches using multiplication, we need to determine how many inches are contained in one foot.
1. Understanding the relationship between feet and inches:
- By definition, one foot consists of 12 inches.
2. Choosing the correct conversion factor:
- When we need to convert a measurement in feet to inches, we multiply the number of feet by the number of inches in one foot.
- This means the conversion factor should allow us to multiply the measurement in feet by 12 to get the measurement in inches.
3. Examining the given options:
- [tex]$\frac{12 in }{1 ft }$[/tex]: This represents 12 inches per one foot, which matches our understanding that one foot is equal to 12 inches.
- [tex]$\frac{12 ft }{1 in }$[/tex]: This suggests 12 feet per one inch, which is not correct.
- [tex]$\frac{1 ft }{12 in }$[/tex]: This suggests one foot per 12 inches, which implies division rather than multiplication and is therefore not suitable for converting from feet to inches.
- [tex]$\frac{1 \text{ in }}{12 ft }$[/tex]: This suggests one inch per 12 feet, which is also not correct.
4. Conclusion:
- The appropriate conversion factor to convert feet to inches by multiplication is [tex]\(\frac{12 in }{1 ft }\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{12 in }{1 ft }}
\][/tex]
