18 = 4 Convert the improper fraction to a mixed number.
The correct answer and explanation is:
To convert the improper fraction 18/4 to a mixed number, follow these steps:
- Divide the numerator by the denominator:
Divide 18 by 4, which gives a quotient of 4 (this is the whole number part of the mixed number) and a remainder of 2. - Write the whole number and the fraction:
The quotient, 4, is the whole number part of the mixed number. The remainder, 2, becomes the numerator of the fractional part, and the denominator remains the same, 4. - Final mixed number:
So, 18/4 as a mixed number is 4 2/4. - Simplify the fraction (optional):
The fraction 2/4 can be simplified. Since 2 and 4 have a common factor of 2, divide both the numerator and denominator by 2. This gives 1/2.
Thus, the final simplified mixed number is 4 1/2.
Why is this method correct?
When you divide an improper fraction, you are essentially splitting the total into whole parts and fractions. The quotient gives the number of whole parts, and the remainder represents the leftover fraction. By converting the remainder to a fraction, you retain the exact value of the improper fraction while expressing it in a more understandable mixed number format.
This process works for any improper fraction, ensuring clarity in representation. It’s also a good way to simplify fractions, especially when you encounter remainders that can be simplified further. In cases where the fraction part cannot be simplified, it remains in its original form, making the mixed number still a valid and accurate representation of the improper fraction.