To multiply the fractions \( \frac{7}{8} \) and \( 3 \frac{1}{2} \), we first need to convert the mixed number \( 3 \frac{1}{2} \) into an improper fraction.
-
Convert \( 3 \frac{1}{2} \): \[ 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \]
-
Now we can multiply \( \frac{7}{8} \) by \( \frac{7}{2} \): \[ \frac{7}{8} \times \frac{7}{2} = \frac{7 \times 7}{8 \times 2} = \frac{49}{16} \]
-
Next, convert \( \frac{49}{16} \) to a mixed number:
- Divide \( 49 \) by \( 16 \):
- \( 16 \) goes into \( 49 \) \( 3 \) times because \( 16 \times 3 = 48 \).
- The remainder is \( 49 - 48 = 1 \).
- Divide \( 49 \) by \( 16 \):
Thus, \( \frac{49}{16} \) can be expressed as: \[ 3 \frac{1}{16} \]
Therefore, the answer is: 3 1/16