Final answer:
To multiply rational numbers, multiply the numerators together to find the new numerator and the denominators together for the new denominator. Scientific notation follows a similar multiplication rule but includes adding exponents. These rules assist in quick mental arithmetic and in tackling more complex math problems.
Step-by-step explanation:
The general rule for multiplying two fractions is to multiply the numerators (the top numbers) together to get the new numerator, and multiply the denominators (the bottom numbers) together to get the new denominator. For example, to multiply ½ by ⅓, you would multiply 1 (the numerator of the first fraction) by 2 (the numerator of the second fraction) to get 2, and 2 (the denominator of the first fraction) by 3 (the denominator of the second fraction) to get 6, resulting in the product ⅔. This principle applies to all rational numbers, including whole numbers (which can be thought of as having a denominator of 1).
When working with scientific notation, the process is similar but includes an additional step of adding exponents when the base is the same. In decimal form, for example, we can consider 24 × 5 by using reciprocals to recognize that it is similar to dividing 24 by 2, which gives us 12, and then multiplying by 10 to reach 120.