To find [tex]\( 1 \frac{1}{2} \cdot 3 \frac{1}{2} \)[/tex] and express the product as a mixed number, follow these steps:
1. Convert the mixed numbers to improper fractions:
- For [tex]\(1 \frac{1}{2}\)[/tex]:
- Multiply the whole number part by the denominator: [tex]\(1 \cdot 2 = 2\)[/tex].
- Add the numerator: [tex]\(2 + 1 = 3\)[/tex].
- The improper fraction is [tex]\(\frac{3}{2}\)[/tex].
- For [tex]\(3 \frac{1}{2}\)[/tex]:
- Multiply the whole number part by the denominator: [tex]\(3 \cdot 2 = 6\)[/tex].
- Add the numerator: [tex]\(6 + 1 = 7\)[/tex].
- The improper fraction is [tex]\(\frac{7}{2}\)[/tex].
2. Multiply the improper fractions:
- First, multiply the numerators: [tex]\(3 \cdot 7 = 21\)[/tex].
- Then, multiply the denominators: [tex]\(2 \cdot 2 = 4\)[/tex].
- The product of the fractions is [tex]\(\frac{21}{4}\)[/tex].
3. Convert the product to a mixed number:
- Divide the numerator by the denominator to find the whole number part:
- [tex]\(21 \div 4 = 5\)[/tex] (quotient, which is the whole number) with a remainder of [tex]\(1\)[/tex].
- The remainder becomes the new numerator, with the denominator remaining the same: [tex]\(\frac{1}{4}\)[/tex].
4. Express as a mixed number:
- Combine the whole number and the fraction part:
- [tex]\(5\)[/tex] (whole number) and [tex]\(\frac{1}{4}\)[/tex] (fraction).
Therefore, the product of [tex]\(1 \frac{1}{2} \cdot 3 \frac{1}{2}\)[/tex] expressed as a mixed number is:
[tex]\[ 5 \frac{1}{4} \][/tex]
So, the correct answer is:
[tex]\[ \boxed{5 \frac{1}{4}} \][/tex]
