When using partial quotients for division, the goal is to choose a number that makes the subtraction manageable while getting as close as possible to the dividend (the number being divided), without exceeding it.
Here we need to divide 9,176 by 31. Let's analyze the options:
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6,200: This is a bit more than 6 times 31 (which is 186), but that seems too large compared to 9,176.
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9,000: This is a larger amount that would cover a lot of the dividend (31 goes into 9,000 about 290 times), but it's a round number to subtract which may make the calculations cumbersome.
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620: This is a manageable number to subtract. Specifically, 31 goes into 620 about 20 times (since \(31 \times 20 = 620\)).
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9,300: This is above 9,176, so it can't be subtracted.
From these options, 620 would be the best choice for the first number to subtract in the division problem \(9,176 \div 31\). It keeps the calculation straightforward and gets the result closer to the quotient.