When you multiply fractions why do you multiply the fractions across?

When you multiply fractions, you multiply the numerators together and the denominators together because each fraction represents a part of a whole. This process reflects finding a part of a part, which is achieved by combining the two ratiOS. For example, multiplying (\frac{a}{b}) by (\frac{c}{d}) gives (\frac{a \cdot c}{b \cdot d}), accurately representing the new proportion of the whole. This method ensures that the relationship between the parts and wholes is maintained.