3 5/6 ft equals how many inches
The Correct Answer and Explanation is:
To convert 3 5/6 feet to inches, we can follow a simple step-by-step approach.
Step 1: Understanding the Conversion Factor
We know that:
- 1 foot = 12 inches.
Thus, to convert feet to inches, we multiply the number of feet by 12.
Step 2: Convert the Mixed Number to an Improper Fraction
The given value is a mixed number: 3 5/6 feet. To simplify the calculation, we first convert this mixed number into an improper fraction.
- 3 5/6 can be written as:
[
3 + \frac{5}{6} = \frac{18}{6} + \frac{5}{6} = \frac{23}{6}
]
So, 3 5/6 feet is equivalent to (\frac{23}{6}) feet.
Step 3: Convert Feet to Inches
Now, multiply the improper fraction by 12 to convert feet to inches:
[
\frac{23}{6} \times 12 = \frac{23 \times 12}{6} = \frac{276}{6} = 46
]
Thus, 3 5/6 feet equals 46 inches.
Step 4: Final Answer
The correct answer is 46 inches.
Explanation
This conversion relies on two fundamental concepts in measurement:
- Understanding mixed numbers and fractions: The original measurement was in the form of a mixed number (3 5/6), which we converted to an improper fraction ((\frac{23}{6})) for easier multiplication.
- Feet to inches conversion: We used the basic conversion factor of 1 foot = 12 inches, which is a standard measurement equivalence. Multiplying the total number of feet by 12 allows us to find the equivalent length in inches.
This method ensures accurate conversion from one unit of length to another, using basic arithmetic and understanding of fractional operations.