How many inches are equivalent to 5 1/2 feet?
The Correct Answer and Explanation is:
To convert feet to inches, we need to use the conversion factor that 1 foot is equivalent to 12 inches. Therefore, to find out how many inches are in 5 1/2 feet, we first need to convert the feet measurement into a fraction or decimal and then multiply by 12.
- Convert the mixed number to an improper fraction:
- The mixed number 5 1/2 can be converted to an improper fraction. The whole number 5 is converted as follows:
[
5 \text{ (whole number)} \times 2 \text{ (denominator)} + 1 \text{ (numerator)} = 10 + 1 = 11.
] - Thus, 5 1/2 can be expressed as:
[
\frac{11}{2} \text{ feet}.
]
- Multiply the improper fraction by the conversion factor:
- To find the equivalent in inches, we multiply the number of feet by 12 inches per foot:
[
\frac{11}{2} \text{ feet} \times 12 \text{ inches/foot} = \frac{11 \times 12}{2} \text{ inches} = \frac{132}{2} \text{ inches} = 66 \text{ inches}.
]
Therefore, 5 1/2 feet is equivalent to 66 inches.
Explanation
Understanding conversions between different units of measurement is crucial in various fields, including mathematics, engineering, and everyday life. In this case, converting feet to inches involves using a simple ratio, where 1 foot is consistently defined as 12 inches. When dealing with mixed numbers, it is often easier to convert them into improper fractions for calculations, as this allows for straightforward multiplication.
After converting 5 1/2 feet to (\frac{11}{2}) feet, we multiply by the conversion factor (12 inches per foot). This method ensures that we maintain accuracy and clarity in our calculations. After carrying out the multiplication, we arrive at 66 inches, demonstrating the practical application of unit conversion in real-world contexts, such as measuring height, furniture dimensions, or construction projects. Accurate conversions are essential for ensuring that measurements are consistent and usable across different applications, helping to avoid errors that can arise from miscalculating or misunderstanding unit relationships.