To express the improper fraction 31/8 as a mixed number, we need to follow a straightforward process:
1. **Divide the numerator by the denominator**: First, take 31 (the numerator) and divide it by 8 (the denominator). When you perform the division, you find that:
31 ÷ 8 = 3 remainder 7
2. **Determine the whole number and the remainder**: The result of the division tells us that 8 fits into 31 a total of 3 times, which becomes the whole number part of our mixed number. The remainder, 7, will be utilized to form the fractional part.
3. **Form the fractional part**: The remainder (7) will be placed over the original denominator (8). Thus, the fraction part of our mixed number will be:
7/8
4. **Combine the whole number and the fraction**: Now that we have both parts, we can write our mixed number. Combining the whole number and the fraction gives us:
3 7/8
In summary, the mixed number representation for the improper fraction 31/8 is 3 7/8.