We appreciate your visit to Problem 1 Select all statements that show correct reasoning for finding tex frac 14 15 div frac 7 5 tex A Multiplying tex frac 14. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve the problem of finding [tex]\(\frac{14}{15} \div \frac{7}{5}\)[/tex], we need to understand that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the division problem:
[tex]\[
\frac{14}{15} \div \frac{7}{5} = \frac{14}{15} \times \frac{5}{7}
\][/tex]
Now, let's go through each option to see which statements show correct reasoning for this calculation:
A. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then by [tex]\(\frac{1}{7}\)[/tex].
This is correct because multiplying by 5 is part of finding the reciprocal of [tex]\(\frac{7}{5}\)[/tex], then [tex]\(\frac{1}{7}\)[/tex] adjusts the second fraction correctly.
B. Dividing [tex]\(\frac{14}{15}\)[/tex] by 5, and then multiplying by [tex]\(\frac{1}{7}\)[/tex].
This isn't correct. Dividing by 5 is not part of getting the reciprocal of [tex]\(\frac{7}{5}\)[/tex].
C. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 7, and then multiplying by [tex]\(\frac{1}{5}\)[/tex].
This isn't correct because it doesn't represent multiplying by the reciprocal [tex]\(\frac{5}{7}\)[/tex].
D. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then dividing by 7.
This is correct, as multiplying by 5 and dividing by 7 is equivalent to multiplying by [tex]\(\frac{5}{7}\)[/tex].
E. Multiplying [tex]\(\frac{15}{14}\)[/tex] by 7 and then dividing by 5.
This isn't correct. This statement involves flipping the first fraction, which is not how division is solved here.
Based on the correct reasoning, the solution shows that option D is correct for solving [tex]\(\frac{14}{15} \div \frac{7}{5}\)[/tex].
[tex]\[
\frac{14}{15} \div \frac{7}{5} = \frac{14}{15} \times \frac{5}{7}
\][/tex]
Now, let's go through each option to see which statements show correct reasoning for this calculation:
A. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then by [tex]\(\frac{1}{7}\)[/tex].
This is correct because multiplying by 5 is part of finding the reciprocal of [tex]\(\frac{7}{5}\)[/tex], then [tex]\(\frac{1}{7}\)[/tex] adjusts the second fraction correctly.
B. Dividing [tex]\(\frac{14}{15}\)[/tex] by 5, and then multiplying by [tex]\(\frac{1}{7}\)[/tex].
This isn't correct. Dividing by 5 is not part of getting the reciprocal of [tex]\(\frac{7}{5}\)[/tex].
C. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 7, and then multiplying by [tex]\(\frac{1}{5}\)[/tex].
This isn't correct because it doesn't represent multiplying by the reciprocal [tex]\(\frac{5}{7}\)[/tex].
D. Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then dividing by 7.
This is correct, as multiplying by 5 and dividing by 7 is equivalent to multiplying by [tex]\(\frac{5}{7}\)[/tex].
E. Multiplying [tex]\(\frac{15}{14}\)[/tex] by 7 and then dividing by 5.
This isn't correct. This statement involves flipping the first fraction, which is not how division is solved here.
Based on the correct reasoning, the solution shows that option D is correct for solving [tex]\(\frac{14}{15} \div \frac{7}{5}\)[/tex].
Thanks for taking the time to read Problem 1 Select all statements that show correct reasoning for finding tex frac 14 15 div frac 7 5 tex A Multiplying tex frac 14. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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