Answer :
Sure, let's work through the problem step by step:
1. Understanding the problem: We need to determine how many [tex]\(\frac{1}{4}\)[/tex]-pound hamburgers Kate can make if she has [tex]\(7 \frac{1}{4}\)[/tex] pounds of hamburger meat.
2. Converting the mixed number to an improper fraction: The total amount of hamburger meat Kate has is [tex]\(7 \frac{1}{4}\)[/tex] pounds. We need to convert this mixed number to an improper fraction.
- Multiply the whole number part (7) by the denominator of the fraction part (4): [tex]\(7 \times 4 = 28\)[/tex].
- Add the numerator of the fraction part (1) to this result: [tex]\(28 + 1 = 29\)[/tex].
- So, [tex]\(7 \frac{1}{4}\)[/tex] as an improper fraction is [tex]\(\frac{29}{4}\)[/tex].
3. Dividing to find the number of hamburgers: Each hamburger weighs [tex]\(\frac{1}{4}\)[/tex] pound. We need to find out how many [tex]\(\frac{1}{4}\)[/tex]-pound hamburgers can be made with [tex]\(\frac{29}{4}\)[/tex] pounds of meat.
- Divide [tex]\(\frac{29}{4}\)[/tex] by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{29}{4} \div \frac{1}{4} = \frac{29}{4} \times \frac{4}{1} = \frac{29 \times 4}{4} = 29
\][/tex]
4. Conclusion: Kate can make 29 [tex]\(\frac{1}{4}\)[/tex]-pound hamburgers with her [tex]\(7 \frac{1}{4}\)[/tex] pounds of hamburger meat.
Therefore, the correct answer is:
D. 29
1. Understanding the problem: We need to determine how many [tex]\(\frac{1}{4}\)[/tex]-pound hamburgers Kate can make if she has [tex]\(7 \frac{1}{4}\)[/tex] pounds of hamburger meat.
2. Converting the mixed number to an improper fraction: The total amount of hamburger meat Kate has is [tex]\(7 \frac{1}{4}\)[/tex] pounds. We need to convert this mixed number to an improper fraction.
- Multiply the whole number part (7) by the denominator of the fraction part (4): [tex]\(7 \times 4 = 28\)[/tex].
- Add the numerator of the fraction part (1) to this result: [tex]\(28 + 1 = 29\)[/tex].
- So, [tex]\(7 \frac{1}{4}\)[/tex] as an improper fraction is [tex]\(\frac{29}{4}\)[/tex].
3. Dividing to find the number of hamburgers: Each hamburger weighs [tex]\(\frac{1}{4}\)[/tex] pound. We need to find out how many [tex]\(\frac{1}{4}\)[/tex]-pound hamburgers can be made with [tex]\(\frac{29}{4}\)[/tex] pounds of meat.
- Divide [tex]\(\frac{29}{4}\)[/tex] by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{29}{4} \div \frac{1}{4} = \frac{29}{4} \times \frac{4}{1} = \frac{29 \times 4}{4} = 29
\][/tex]
4. Conclusion: Kate can make 29 [tex]\(\frac{1}{4}\)[/tex]-pound hamburgers with her [tex]\(7 \frac{1}{4}\)[/tex] pounds of hamburger meat.
Therefore, the correct answer is:
D. 29
