To multiply \( \frac{7}{8} \) by \( 3 \frac{1}{2} \), we first need to convert the mixed number \( 3 \frac{1}{2} \) to an improper fraction.
- Convert \( 3 \frac{1}{2} \):
\[ 3 \frac{1}{2} = 3 \cdot 2 + 1 = 6 + 1 = 7 \]
So, \( 3 \frac{1}{2} = \frac{7}{2} \).
- Now, multiply the two fractions:
\[ \frac{7}{8} \times \frac{7}{2} = \frac{7 \times 7}{8 \times 2} = \frac{49}{16} \]
- Next, convert \( \frac{49}{16} \) to a mixed number:
To convert \( \frac{49}{16} \) to a mixed number, divide 49 by 16.
\[ 49 \div 16 = 3 \quad \text{(the quotient)} \]
Now, calculate the remainder:
\[ 49 - (16 \times 3) = 49 - 48 = 1 \]
So, the mixed number is:
\[ 3 \frac{1}{16} \]
Thus, the product of \( \frac{7}{8} \) and \( 3 \frac{1}{2} \) is:
\[ \boxed{3 \frac{1}{16}} \]
1 answer