9 3/4 Divided by 4 1/8 as a Fraction
This problem involves dividing mixed numbers, which can be a bit tricky. Here's how to solve it step-by-step:
1. Convert Mixed Numbers to Improper Fractions
- 9 3/4: Multiply the whole number (9) by the denominator (4) and add the numerator (3): 9 * 4 + 3 = 39. Keep the same denominator (4). So 9 3/4 becomes 39/4.
- 4 1/8: Multiply the whole number (4) by the denominator (8) and add the numerator (1): 4 * 8 + 1 = 33. Keep the same denominator (8). So 4 1/8 becomes 33/8.
2. Change Division to Multiplication
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 33/8 is 8/33.
Therefore, our problem becomes: 39/4 * 8/33
3. Simplify (If Possible)
Before multiplying, check if any numbers can be simplified by finding common factors:
- 39 and 33 share a common factor of 3.
- 4 and 8 share a common factor of 4.
Simplify by dividing:
- 39/3 = 13
- 33/3 = 11
- 4/4 = 1
- 8/4 = 2
Now our problem is: 13/1 * 2/11
4. Multiply the Numerators and Denominators
- Numerators: 13 * 2 = 26
- Denominators: 1 * 11 = 11
This gives us 26/11.
5. Convert Back to a Mixed Number (Optional)
The answer can be left as an improper fraction (26/11), or converted back to a mixed number:
- Divide the numerator (26) by the denominator (11): 26 ÷ 11 = 2 with a remainder of 4.
- The whole number is 2. The remainder (4) becomes the numerator of the fraction. The denominator stays the same.
Therefore, 9 3/4 divided by 4 1/8 as a fraction is 26/11 or 2 4/11.
