Multiply 4/17 by a fraction smaller than one. is the product smaller than 4/17, larger, or equal to?

1 answer

When you multiply a fraction by another fraction that is smaller than one, the product will always be smaller than the original fraction.

In this case, you are multiplying \( \frac{4}{17} \) by a fraction smaller than one (let's call it \( \frac{a}{b} \) where \( 0 < \frac{a}{b} < 1 \)). The multiplication can be expressed as:

\[ \frac{4}{17} \times \frac{a}{b} = \frac{4a}{17b} \]

Since \( \frac{a}{b} < 1\), we know that \( 4a < 4b \) (because multiplying both sides of the inequality by 4, which is positive, preserves the inequality). Therefore:

\[ \frac{4a}{17b} < \frac{4}{17} \]

This means that the product \( \frac{4}{17} \times \frac{a}{b} \) is smaller than \( \frac{4}{17} \).

So, the answer is that the product is smaller than \( \frac{4}{17} \).