Certainly! Let's address the problem step-by-step:
### Part (a):
Imagine Priya made a mistake in her calculations. Without knowing the specific details of her mistake, a common error when multiplying fractions is not multiplying the numerators and the denominators correctly. Another possible mistake could be not simplifying the fraction at the end. Therefore, a potential sentence describing her mistake could be:
"Priya might have mistakenly added the fractions instead of multiplying them, or she did not correctly multiply the numerators and denominators."
### Part (b):
Now let's calculate the correct answer to [tex]\(\frac{5}{7} \times \frac{10}{11}\)[/tex]:
1. Multiply the numerators:
The numerators are [tex]\(5\)[/tex] and [tex]\(10\)[/tex].
[tex]\[
5 \times 10 = 50
\][/tex]
2. Multiply the denominators:
The denominators are [tex]\(7\)[/tex] and [tex]\(11\)[/tex].
[tex]\[
7 \times 11 = 77
\][/tex]
3. Combine the results into a fraction:
So the product of [tex]\(\frac{5}{7}\)[/tex] and [tex]\(\frac{10}{11}\)[/tex] is:
[tex]\[
\frac{50}{77}
\][/tex]
4. Simplify the fraction (if possible):
The fraction [tex]\(\frac{50}{77}\)[/tex] is already in its simplest form, as there are no common factors between 50 and 77 other than 1.
Therefore, the correct answer is:
[tex]\[
\frac{50}{77}
\][/tex]
Thus, the correct answer to [tex]\(\frac{5}{7} \times \frac{10}{11}\)[/tex] is [tex]\(\frac{50}{77}\)[/tex].
