Okay, so Remmy wants to divide 10 by 2/3, but he's fuzzy on the exact steps. Let me try to recall how division of fractions works. Hmm, dividing by a fraction is the same as multiplying by its reciprocal, right? So if you have a problem like 10 ÷ (2/3), you can flip the 2/3 to 3/2 and then multiply 10 by 3/2. That should give the answer. But wait, Remmy is asking by what number he should multiply 10 to get the answer. So maybe he's trying to remember if there's a direct multiplication factor instead of doing the division step-by-step?

Let me think again. When you divide by a fraction, you indeed multiply by its reciprocal. So 10 divided by (2/3) is 10 multiplied by 3/2. Therefore, the number he needs to multiply 10 by is 3/2. But let me verify this with an example. If I take 10 divided by 2/3, that's 10 * (3/2) = 15. Alternatively, if I were to multiply 10 by 3/2, that's 15 as well. So yes, that seems to check out.

But maybe there's another way to approach this. Let's consider what dividing by a fraction means. Dividing by a number is the same as multiplying by 1 over that number. So 10 divided by (2/3) is 10 * (3/2). So the multiplier is 3/2. Alternatively, if we express 3/2 as 1.5, then multiplying 10 by 1.5 also gives 15. Both methods lead to the same result, so that's consistent.

Wait, but maybe Remmy is confused about why it's the reciprocal. Let me explain it in another way. If you have 10 divided by (2/3), you can think of it as asking "how many 2/3s are in 10?" So if each 2/3 is a portion, how many portions fit into 10. Since each portion is smaller than 1, you would expect more portions. Multiplying by 3/2 (which is 1.5) makes sense because 10 times 1.5 is 15, which is indeed larger than 10, which fits the expectation.

Let me also check with a different example to make sure. Suppose we have 4 divided by (1/2). According to the rule, we multiply by 2/1, so 4 * 2 = 8. And indeed, 4 divided by (1/2) is 8 because there are 8 halves in 4. So the same rule applies here. Therefore, in the original problem, 10 divided by (2/3) should be 10 * (3/2) = 15.

Alternatively, if Remmy were to use the method of multiplying numerator and denominator by the reciprocal, he would invert the divisor and multiply. So 10 ÷ (2/3) = 10 * (3/2). So the number he needs to multiply by is 3/2. That seems straightforward.

I think that's the answer. But let me just confirm once again. If we take 10 multiplied by 3/2, that's (10*3)/2 = 30/2 = 15. And 10 divided by (2/3) is indeed 15. So both methods give the same result. Therefore, the multiplier is 3/2.

Wait, but the question is asking "By what number should he multiply 10 to get the answer?" So the answer is 3/2, which is 1.5. But should it be expressed as a fraction or a decimal? The question doesn't specify, but since the original numbers are fractions, maybe expressing it as a fraction is better. So 3/2 is the number he needs to multiply by. Therefore, the final answer is 3/2.
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