IDNLearn.com offers a unique blend of expert answers and community insights. Get accurate and comprehensive answers to your questions from our community of knowledgeable professionals.
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]
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]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.