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Answer :
Let's look into the given problem and break it down step by step. The main task here involves understanding the operations of division and multiplication.
(a) For the expression:
[tex]\frac{2772}{1161} \times 1162 \times 1163 \times 1164 \times 1165 \times 1166 \times 1167 \times 1168 \times 1169 \times 11610 \times 11620 \times 11630 \times 11640 \times 11650 \times 11660 \times 11670 \times 11680 \times 11690 \times 116b[/tex]
This seems to involve a repetitive pattern of multiplication, and the main point of interest for simplification might lie within the division [tex]\frac{2772}{1161}[/tex].
To simplify:
- Divide [tex]2772[/tex] by [tex]1161[/tex]:
[tex]\frac{2772}{1161} \approx 2.39[/tex]
However, without the full set of multipliers, we're left with seeing that this segment simplifies to [tex]2.39[/tex] as its primary contribution.
(b) For the second expression:
[tex]\frac{2829}{1231} \times 1232 \times 1233 \times 1234 \times 1235 \times 1236 \times 1237 \times 1238 \times 1239 \times 12310 \times 12320 \times 12330 \times 12340 \times 12350 \times 12360 \times 12370 \times 12380 \times 12390 \times 123[/tex]
Similarly, begin with the division:
- Divide [tex]2829[/tex] by [tex]1231[/tex]:
[tex]\frac{2829}{1231} \approx 2.30[/tex]
Again, without the entire context or specific instructions on how to treat each multiplication factor, the division is the primary simplification insight.
In both expressions, the key aspect is the initial division as it simplifies the starting point before continuing the multiplication. As each multiplication relies on extending results, having an accurate division outcome provides a fundamental base.
To expand more effectively, verification or further context is needed around the multiplicatives for precise results.
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