Answer :
To find [tex]\(\frac{14}{15} \div \frac{7}{5}\)[/tex], we need to remember that dividing by a fraction is the same as multiplying by its reciprocal. So, [tex]\(\frac{14}{15} \div \frac{7}{5}\)[/tex] is equivalent to [tex]\(\frac{14}{15} \times \frac{5}{7}\)[/tex].
Let's examine each statement to see if they correctly represent this process:
A) Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then by [tex]\(\frac{1}{7}\)[/tex]:
- This is correct because [tex]\(\frac{14}{15} \times 5 \times \frac{1}{7} = \frac{14}{15} \times \frac{5}{7}\)[/tex].
B) Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then dividing by 7:
- This is also correct. When you multiply by 5, you get [tex]\(\frac{14}{15} \times 5\)[/tex], and dividing by 7 is the same as multiplying by [tex]\(\frac{1}{7}\)[/tex], resulting in [tex]\(\frac{14}{15} \times \frac{5}{7}\)[/tex].
C) Multiplying [tex]\(\frac{15}{14}\)[/tex] by 7 and then dividing by 5:
- This statement is incorrect because it starts with [tex]\(\frac{15}{14}\)[/tex] instead of [tex]\(\frac{14}{15}\)[/tex], and you're multiplying by 7 and dividing by 5, which is the reverse order needed for the reciprocal.
D) Dividing [tex]\(\frac{14}{15}\)[/tex] by 5, and then multiplying by [tex]\(\frac{1}{7}\)[/tex]:
- This is not correct. Dividing by 5 first changes the operation and does not align with multiplying by the reciprocal of [tex]\(\frac{7}{5}\)[/tex].
E) Multiplying [tex]\(\frac{14}{15}\)[/tex] by 7, and then multiplying by [tex]\(\frac{1}{5}\)[/tex]:
- This is correct as well. Multiplying by 7 and then by [tex]\(\frac{1}{5}\)[/tex] effectively accomplishes the same thing as multiplying by [tex]\(\frac{5}{7}\)[/tex].
The correct statements are A, B, and E.
Let's examine each statement to see if they correctly represent this process:
A) Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then by [tex]\(\frac{1}{7}\)[/tex]:
- This is correct because [tex]\(\frac{14}{15} \times 5 \times \frac{1}{7} = \frac{14}{15} \times \frac{5}{7}\)[/tex].
B) Multiplying [tex]\(\frac{14}{15}\)[/tex] by 5 and then dividing by 7:
- This is also correct. When you multiply by 5, you get [tex]\(\frac{14}{15} \times 5\)[/tex], and dividing by 7 is the same as multiplying by [tex]\(\frac{1}{7}\)[/tex], resulting in [tex]\(\frac{14}{15} \times \frac{5}{7}\)[/tex].
C) Multiplying [tex]\(\frac{15}{14}\)[/tex] by 7 and then dividing by 5:
- This statement is incorrect because it starts with [tex]\(\frac{15}{14}\)[/tex] instead of [tex]\(\frac{14}{15}\)[/tex], and you're multiplying by 7 and dividing by 5, which is the reverse order needed for the reciprocal.
D) Dividing [tex]\(\frac{14}{15}\)[/tex] by 5, and then multiplying by [tex]\(\frac{1}{7}\)[/tex]:
- This is not correct. Dividing by 5 first changes the operation and does not align with multiplying by the reciprocal of [tex]\(\frac{7}{5}\)[/tex].
E) Multiplying [tex]\(\frac{14}{15}\)[/tex] by 7, and then multiplying by [tex]\(\frac{1}{5}\)[/tex]:
- This is correct as well. Multiplying by 7 and then by [tex]\(\frac{1}{5}\)[/tex] effectively accomplishes the same thing as multiplying by [tex]\(\frac{5}{7}\)[/tex].
The correct statements are A, B, and E.
