Let's find the product of [tex]\(4 \frac{2}{3}\)[/tex] and [tex]\(11 \frac{1}{4}\)[/tex] step-by-step.
Step 1: Convert the mixed numbers to improper fractions.
For [tex]\( 4 \frac{2}{3} \)[/tex]:
- The whole number part is [tex]\(4\)[/tex].
- The fractional part is [tex]\(\frac{2}{3}\)[/tex].
To convert this mixed number to an improper fraction:
[tex]\[ 4 \frac{2}{3} = 4 + \frac{2}{3} = \frac{12}{3} + \frac{2}{3} = \frac{14}{3} \][/tex]
For [tex]\( 11 \frac{1}{4} \)[/tex]:
- The whole number part is [tex]\(11\)[/tex].
- The fractional part is [tex]\(\frac{1}{4}\)[/tex].
To convert this mixed number to an improper fraction:
[tex]\[ 11 \frac{1}{4} = 11 + \frac{1}{4} = \frac{44}{4} + \frac{1}{4} = \frac{45}{4} \][/tex]
Step 2: Multiply the improper fractions.
To find the product of [tex]\(\frac{14}{3}\)[/tex] and [tex]\(\frac{45}{4}\)[/tex]:
[tex]\[ \frac{14}{3} \times \frac{45}{4} = \frac{14 \times 45}{3 \times 4} = \frac{630}{12} \][/tex]
Step 3: Simplify the resulting fraction.
First, let's divide the numerator and the denominator by their greatest common divisor (GCD). The GCD of 630 and 12 is 6.
[tex]\[ \frac{630 \div 6}{12 \div 6} = \frac{105}{2} \][/tex]
Step 4: Convert the improper fraction to a mixed number.
To convert [tex]\(\frac{105}{2}\)[/tex] to a mixed number:
[tex]\[ 105 \div 2 = 52 \text{ R } 1 \][/tex]
So, this is:
[tex]\[ 52 \frac{1}{2} \][/tex]
Final Answer:
The product of [tex]\(4 \frac{2}{3}\)[/tex] and [tex]\(11 \frac{1}{4}\)[/tex] is [tex]\(52 \frac{1}{2}\)[/tex].
Therefore, the correct choice is:
C. [tex]\(52 \frac{1}{2}\)[/tex]
