To convert a fraction multiplication problem into an addition problem, Nick can use the concept of logarithms or exponents to express multiplication in terms of addition. However, if we’re simply looking at the multiplication of fractions (with fractions expressed as decimals), he can transform the multiplication into an addition form by using the logarithmic identity:
If \( a \) and \( b \) are two numbers, \[ \log(a \times b) = \log(a) + \log(b) \]
For example, if Nick wants to multiply \( \frac{1}{2} \) and \( \frac{1}{3} \), he can express this as:
\[ \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} \]
And then use logarithms:
\[ \log\left(\frac{1}{2} \times \frac{1}{3}\right) = \log\left(\frac{1}{2}\right) + \log\left(\frac{1}{3}\right) \]
This is how multiplication can be represented in an addition manner in terms of logarithmic properties.
However, if you're looking for a simpler way or perhaps a specific example or context Nick could use—like combining fractions instead of converting them mathematically—please provide more details for a targeted response or example!
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