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Understanding how to calculate ratios is crucial in determining how to distribute profits fairly based on investments. A ratio is a way to compare quantities. In this problem, we are comparing the investments of partners A, B, and C. By putting B's investment over the total investment, we get a ratio that shows B's portion of the whole investment. First, sum up all the partners' investments to get a total of \$ 12,000. Then, B's investment, \$ 4,500, is considered in proportion to this total. This is expressed as a fraction: \(\frac{4,500}{12,000}\). Simplifying the ratio, we use the greatest common divisor to reduce \(\frac{4,500}{12,000}\) to \(\frac{3}{8}\). This simplified ratio tells us B's part in the investment and consequently in the total profit distribution.

Investment distribution is about how each partner's money is represented in the total invested. In this case, partner A invested \$ 5,000, B \$ 4,500, and C \$ 2,500. To find out the share of each partner, we first find the total investment: \(\text{Total Investment} = 5,000 + 4,500 + 2,500 = 12,000\) dollars. The next step is to understand what fraction each partner's investment is of this total. B's share is found by dividing B's investment by the total investment, resulting in \(\frac{4,500}{12,000}\). This tells us the part of the total sum each partner has contributed, thereby setting the stage for how the profit will be split. Simplifying fractions is a key step here, converting \(\frac{4,500}{12,000}\) to \(\frac{3}{8}\).

After understanding ratios and investment distribution, the next part is profit sharing based on these figures. The process involves distributing the total profit, \$ 3,600, in the same proportions as the investments. B’s share of the profit can be determined by taking B’s ratio of the investment, which we simplified to \(\frac{3}{8}\), and multiplying it by the total profit. Therefore, we calculate B’s share of the profit as: \(\frac{3}{8} \times 3,600\). This equals \$ 1,350. Hence, B gets \$ 1,350 as their portion from the \$ 3,600 profit. This kind of proportional distribution ensures that each partner receives an amount of profit corresponding to their initial investment, maintaining fairness in the division.