To calculate the total cost of 24 candy bars at 69 cents each using partial products, we can break down the multiplication into more manageable parts.
First, let's express 69 as \( 60 + 9 \). Thus, we can calculate:
\[ 24 \times 69 = 24 \times (60 + 9) = 24 \times 60 + 24 \times 9 \]
Now, we can find each partial product:
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Calculating \( 24 \times 60 \): \[ 24 \times 60 = 1440 \]
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Calculating \( 24 \times 9 \): \[ 24 \times 9 = 216 \]
Now, we can add these two partial products together:
\[ 1440 + 216 = 1656 \]
So, the total cost in cents is 1656 cents.
The potential partial products for the multiplication of \( 24 \times 69 \) should include:
- \( 24 \times 60 = 1440 \)
- \( 24 \times 9 = 216 \)
Any other product that is not equal to 1440 or 216 (or does not logically fit into those calculations) would not be a valid partial product for \( 24 \times 69 \). For example, products like \( 24 \times 70 \), \( 30 \times 60 \), or some other calculation that goes beyond the breakdown would not count as partial products for this multiplication.
If you have a list of options, you can identify which of them are not valid partial products by comparing them with 1440 and 216, or any reasonable intermediate steps in this multiplication breakdown. Please provide the options if you want specific analysis on them!