The product of a fraction and a whole number is not greater than both of its factors when that fraction is less than or equal to 1.
To illustrate, let's break this down:
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Understanding Factors: When you multiply a fraction \( \frac{a}{b} \) by a whole number \( c \), the product is \( c \times \frac{a}{b} = \frac{ac}{b} \).
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When is the Product Not Greater?:
- If \( \frac{a}{b} \) is less than 1 (i.e., \( a < b \)), then \( c \times \frac{a}{b} < c \) because you're taking a fraction of \( c \).
- This means that the product \( \frac{ac}{b} \) will not exceed either \( c \) (the whole number factor) or the fraction \( \frac{a}{b} \) (considering that it is less than 1).
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When \( \frac{a}{b} = 1 \): If the fraction equals 1 (meaning \( a = b \)), then the product equals \( c \). At this point, the product is equal to one of the factors but not greater than both.
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Conclusion: The product \( c \times \frac{a}{b} \) is not greater than both factors when \( \frac{a}{b} \leq 1 \) (or, equivalently, when \( a \leq b \) if we are considering positive integers).
In summary, when multiplying a fraction by a whole number, the product will not be greater than both factors when the fraction is less than or equal to 1.
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