What is 14 divided by 3 as a fraction than in mixed numbers?
The Correct Answer and Explanation is:
To divide 14 by 3 and express the result as a fraction and a mixed number, we can break the process down step by step.
1. Division as a Fraction
When you divide 14 by 3, you can write it as the fraction:
[
\frac{14}{3}
]
This fraction represents the result of dividing 14 (the numerator) by 3 (the denominator). The fraction shows the exact relationship between the two numbers.
2. Simplifying the Fraction
The fraction (\frac{14}{3}) is already in its simplest form. Since 14 and 3 do not have any common factors other than 1, the fraction cannot be simplified further. The next step is to express this improper fraction as a mixed number.
3. Converting to a Mixed Number
A mixed number combines a whole number with a proper fraction. To convert (\frac{14}{3}) into a mixed number, we need to perform the division:
- Divide 14 by 3. The quotient is 4, because 3 goes into 14 four times (since (3 \times 4 = 12)).
- The remainder is 2, because when 12 is subtracted from 14, 2 remains.
So, we can express (\frac{14}{3}) as:
[
4 \frac{2}{3}
]
This is the mixed number form, where 4 is the whole number, and (\frac{2}{3}) is the proper fraction.
4. Explanation of the Process
The conversion process from an improper fraction to a mixed number involves two parts:
- Finding how many times the denominator (3) fits into the numerator (14): This gives the whole number (quotient).
- Determining the remainder: The remainder, which is the part that doesn’t fully divide by the denominator, becomes the new numerator in the proper fraction, while the denominator remains the same.
Therefore, (\frac{14}{3}) as a mixed number is (4 \frac{2}{3}), and this gives us both an exact fraction and a more intuitive mixed number form.