Final answer:
The algebraic expressions 5m+5p and 10m can represent real-world scenarios such as the total cost of 5 movie tickets and 5 popcorns, and 10 movie tickets, respectively. Money examples like these help illustrate how multiplication and addition of variables can apply in everyday contexts.
Step-by-step explanation:
To give a real-world meaning to the algebraic expressions 5m+5p and 10m, let's consider an example involving money, which is often easier for students to grasp. Imagine that 'm' represents the cost of a single movie ticket and 'p' represents the price of a popcorn. The expression 5m+5p could represent the total cost of purchasing 5 movie tickets and 5 popcorns, whereas the expression 10m could represent the total cost of purchasing 10 movie tickets. In this scenario, we simply apply the rules of multiplication to combine like terms and calculate the total costs.
When we multiply meters together or any units, we treat them as variables following the same rules. In the context of our example, multiplying ticket prices or popcorn prices by the quantity doesn't change the units; only the totals are affected. It's also worth noting that according to the multiplication rules for signs, the result of multiplying two positive numbers, like ticket prices or quantities, always yields a positive result, indicating a positive total cost.