Answer:
3. (5x600)+(5x80)
Explanation:
You want to choose an expression that shows how to evaluate 5×680 using mental math.
Choices
As with many multiple-choice problems, you can eliminate the choices that are false or not consistent with problem requirements. This leaves you with choosing between options 1 and 3.
1. 5 × (600 +80) = 5×680, the original problem. Offers no gain in speed or simplicity
2. = 5×608 . . . . incorrect result
3. (5 × 600) +(5 × 80) reduces to single-digit products, an appropriate approach
4. (5 × 600) +(6 × 80) = 3480 . . . . incorrect result
5. (5 × 70) -(5 × 20) = 250 . . . . incorrect result
The only choice that makes any sense is ...
3. (5 × 600) +(5 × 80)
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Additional comment
For almost anything involving multiplication or division by 5, it works well to use 10/2 instead. That is ...
5 × 680 = 10 × (680/2) = 10 × 340 = 3400
Usually, doubling or halving a number is easier than multiplication or division by 5.
The expression of choice 3 is identical to the "long multiplication" approach usually taught for multiplying multi-digit numbers. Yes, you can do it mentally, but there is no particular saving of effort.
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