To write a fraction multiplication problem as an addition problem, Nick can use the concept of repeated addition. For instance, if he wants to multiply two fractions \( \frac{a}{b} \) and \( \frac{c}{d} \), he can represent the multiplication of \( \frac{a}{b} \) by \( c \) as follows:
\[ \frac{a}{b} \times c = \frac{a}{b} + \frac{a}{b} + \ldots + \frac{a}{b} \quad \text{(c times)} \]
However, since we are dealing with two fractions, a specific example could be:
For example, if Nick wants to calculate \( \frac{1}{2} \times 3 \):
- He can express this as \( \frac{1}{2} + \frac{1}{2} + \frac{1}{2} \) (1/2 added together to represent multiplication by 3).
If it’s specifically about two fractions like \( \frac{1}{2} \times \frac{1}{3} \):
- He can convert it into \( \frac{1}{3} + \frac{1}{3} \) and relate this back to fractions (but this is usually only conceptually for smaller fractions).
So, if Nick wants to demonstrate multiplication of \( \frac{1}{2} \) and \( 3 \) as addition, he can show:
\[ \frac{1}{2} \times 3 = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} \quad \text{(three times)} \]
This demonstrates the concept of fraction multiplication as repeated addition.
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