Final answer:
In solving multiplication and division of rational numbers, applying the concept of reciprocals can simplify the process. For instance, finding a fraction of a number or handling numbers in scientific notation involves specific rules for multiplying and dividing base numbers and their exponents.
Step-by-step explanation:
When solving word problems about multiplying and dividing rational numbers, we use the concepts of reciprocals and simplification extensively. For instance, understanding that dividing by a number is akin to multiplying by its reciprocal can simplify the process. Let's take a scenario where we are working with the fraction 15 and we want to find out ¼ of it. According to our multiplication rules, we would multiply 15 by 4 to find the reciprocal and then 30 in the numerator and 120 in the denominator, which simplifies to ¼ or 1.
Furthermore, in scientific notation, multiplying and dividing involve handling the base numbers (N) and their exponents (n) differently than when adding and subtracting. For multiplication, you multiply the base numbers and add the exponents, while for division, you divide the base numbers and subtract the exponents.
For example, consider money examples which can make these concepts easier to grasp. If you have $24 and you need to multiply it by ⅔, instead of doing complex fraction multiplication, you can recognize that multiplying by ⅔ is the same as dividing by 2, which quickly gives you $12—or, with a decimal adjustment, $120 when multiplying it by 5.