To solve the multiplication of the mixed numbers [tex]\(-2 \frac{1}{4} \cdot 1 \frac{1}{2}\)[/tex], follow these steps:
1. Convert mixed numbers to improper fractions:
- [tex]\(-2 \frac{1}{4}\)[/tex] can be converted as follows:
[tex]\[
\text{Multiply the whole number by the denominator and add the numerator:}
\][/tex]
[tex]\[
-2 \cdot 4 + 1 = -8 + 1 = -7
\][/tex]
[tex]\[
\text{So,} \quad -2 \frac{1}{4} = -\frac{7}{4}
\][/tex]
- Similarly, [tex]\(1 \frac{1}{2}\)[/tex] can be converted as follows:
[tex]\[
\text{Multiply the whole number by the denominator and add the numerator:}
\][/tex]
[tex]\[
1 \cdot 2 + 1 = 2 + 1 = 3
\][/tex]
[tex]\[
\text{So,} \quad 1 \frac{1}{2} = \frac{3}{2}
\][/tex]
2. Multiply the improper fractions:
- Multiply the numerators:
[tex]\[
-7 \cdot 3 = -21
\][/tex]
- Multiply the denominators:
[tex]\[
4 \cdot 2 = 8
\][/tex]
- So, the product of the fractions is:
[tex]\[
-\frac{21}{8}
\][/tex]
3. Convert the improper fraction back to a mixed number:
- Divide the numerator by the denominator:
[tex]\[
21 \div 8 = 2 \quad \text{remainder} \quad 5
\][/tex]
- So, the quotient is 2 and the remainder is 5, which means:
[tex]\[
-\frac{21}{8} = -2 \frac{5}{8}
\][/tex]
Thus, the product of [tex]\(-2 \frac{1}{4} \cdot 1 \frac{1}{2}\)[/tex] is [tex]\(-2 \frac{5}{8}\)[/tex].
Alternatively, if we were to convert this fraction to a decimal for verification, [tex]\(-2 \frac{5}{8}\)[/tex] is equivalent to [tex]\( -2.625 \)[/tex]. The multiplication could also be checked directly by converting as done earlier:
[tex]\[
-2.25 \times 1.5 = -3.375
\][/tex]
However, the most precise answer is:
[tex]\(-2 \frac{5}{8}\)[/tex].
