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What is the product of [tex]$4 \frac{2}{3}$[/tex] and [tex]$11 \frac{1}{4}$[/tex]?

A. [tex]\frac{83}{7}[/tex]

B. [tex]44 \frac{2}{12}[/tex]

C. [tex]52 \frac{1}{2}[/tex]

D. [tex]\frac{56}{135}[/tex]


Sagot :

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]