To convert the improper fraction [tex]\( \frac{7}{4} \)[/tex] into a mixed number, follow these steps:
1. Divide the numerator by the denominator:
- [tex]\( 7 \div 4 \)[/tex] equals 1 with a remainder of 3.
2. Determine the integer part:
- The quotient from the division, which is 1, is the integer part of the mixed number.
3. Determine the fractional part:
- The remainder from the division is 3, and the denominator remains 4.
- Hence, the fractional part is [tex]\( \frac{3}{4} \)[/tex].
4. Combine the integer and fractional parts:
- The mixed number is [tex]\( 1 \frac{3}{4} \)[/tex].
Now, let's compare this to the given answer choices:
- A. [tex]\( \frac{17}{4} \)[/tex] - This is incorrect because 17 divided by 4 does not equal to 1 with a remainder of 3.
- B. [tex]\( 1\frac{3}{4} \)[/tex] - This is correct as it matches our result.
- C. [tex]\( \frac{3}{4} \)[/tex] - This is incorrect because it lacks the integer part.
- D. [tex]\( 1 \frac{1}{4} \)[/tex] - This is incorrect because 1 with a remainder of 1 over 4 is not the correct mixed number.
Thus, the best answer is:
B. [tex]\( 1 \frac{3}{4} \)[/tex]
