Dividing a Mixed Number by a Whole Number: 1 1/3 / 3
This article will guide you through the process of dividing the mixed number 1 1/3 by the whole number 3.
Understanding Mixed Numbers
A mixed number combines a whole number and a fraction. In our example, 1 1/3 represents one whole and one-third.
Converting to an Improper Fraction
Before dividing, we need to convert the mixed number 1 1/3 into an improper fraction. To do this:
- Multiply the whole number (1) by the denominator of the fraction (3): 1 * 3 = 3
- Add the numerator of the fraction (1): 3 + 1 = 4
- Keep the same denominator (3): This gives us the improper fraction 4/3.
Dividing Fractions
Now we have the problem: 4/3 / 3.
Dividing by a whole number is the same as multiplying by its reciprocal. The reciprocal of 3 is 1/3.
So, our problem becomes: (4/3) * (1/3).
Multiplying Fractions
To multiply fractions, we multiply the numerators and the denominators:
- Numerators: 4 * 1 = 4
- Denominators: 3 * 3 = 9
This gives us the fraction 4/9.
Simplifying the Answer
The fraction 4/9 is already in its simplest form, as there are no common factors between 4 and 9.
Conclusion
Therefore, 1 1/3 / 3 = 4/9.