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To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Rewrite the problem as a multiplication:
Step 2: Multiply the numerators and the denominators:
Step 3: This fraction is already in its simplest form. Looking at the answer choices, we can conclude the correct answer is .
Therefore, the correct solution to the problem is .
\( \frac{1}{2}:3= \)\( \)\( \)\( \)
Division by a whole number is the same as multiplication by its reciprocal! When you divide by 3, you're asking "how many groups of 3 fit into this fraction?" - which is the same as multiplying by .
The reciprocal of any whole number is 1 divided by that number. So the reciprocal of 3 is , the reciprocal of 5 is , and so on.
Let's check! The greatest common factor of 2 and 21 is 1, since 2 and 21 share no common factors other than 1. This means is already in simplest form.
That's exactly right! When you divide a number, you get a smaller result. Since is smaller than , your division worked correctly.
Remember this key difference: multiplying fractions makes them smaller (unless multiplying by something greater than 1), while dividing by whole numbers also makes them smaller. Both operations here should give you a result smaller than .
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