Final answer:
When multiplying fractions, multiply the numerators and denominators separately and simplify if possible.
Step-by-step explanation:
Rules for Multiplying Fractions
When multiplying fractions or mixed numbers, the correct approach involves multiplying the numerators (top numbers) of the fractions together and multiplying the denominators (bottom numbers) together. Simplification by common factors is usually the next step to reduce the fraction to its simplest form. It's important to note that unlike addition, where you need a common denominator, for multiplication, you directly multiply across both numerators and denominators.
For example, to multiply ⅓ by ⅔, you would multiply the numerators (2 x 3) to get 6, and the denominators (3 x 4) to get 12, resulting in the fraction ⅖, which simplifies to ⅒ after dividing both the numerator and denominator by the common factor 6.
This process is different from addition, where a common denominator is necessary to add the numerators. Multiplication of fractions is straightforward in that it doesn't require matching the denominators. Always remember that multiplication and division are closely linked; division by a number is the same as multiplication by its reciprocal. Thus, following these rules ensures maintaining the equality of an equation when both sides are multiplied or divided by the same number.