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Consider this complex fraction. Which division problem is represented in the picture?

10 ÷ 3
3 ÷ 2
2 ÷ 1
1 ÷ 3

1 Answer

3 votes

Final answer:

To find out which division problem a complex fraction represents, we need to understand the concept of dividing by a number being the same as multiplying by its reciprocal. The student's question involves interpreting a complex fraction and linking it to a division problem.

Step-by-step explanation:

The student is asking about how to interpret a complex fraction and relate it to a division problem. To determine which of the given division problems is represented by a complex fraction in the picture, there are a few concepts we need to understand. First, a complex fraction is simply a fraction where the numerator, the denominator, or both, are also fractions.

Now consider the relationship between division and multiplication when it comes to fractions. Dividing by a number is the same as multiplying by its reciprocal. So in the context of fractions, for example, dividing by \( \frac{2}{3} \) is equivalent to multiplying by \( \frac{3}{2} \) as you are just flipping the fraction.

Additionally, when multiplying fractions, you simply multiply the numerators together and the denominators together. But when you divide by a fraction, you are multiplying by its reciprocal. Thus, if we see a complex fraction where we have one fraction over another, such as \( \frac{1}{2} \div \frac{3}{4} \), we would actually multiply \( \frac{1}{2} \) by \( \frac{4}{3} \).

User Tim Delaney
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