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One common technique for solving rational equations is cross-multiplication. This method makes it easier to solve for unknown variables by eliminating the fractions. When you have an equation in the form of \(\frac{a}{b} = \frac{c}{d}\), you can cross-multiply to get \(a \times d = b \times c\).
In our exercise, we start with the equation \( \frac{2.8}{k} = \frac{2.1}{1.5} \). By cross-multiplying, we eliminate the fractions and get a simpler equation: \(2.8 \times 1.5 = 2.1 \times k\). This results in: \ 4.2 = 2.1k\.
Cross-multiplying helps you work with whole numbers or simple decimals, making it easier to solve for unknowns.

Ratios show the relative size of two quantities, and proportions show that two ratios are equal. In the given exercise, \( \frac{2.8}{k} = \frac{2.1}{1.5} \) signifies that the ratio of 2.8 to k is the same as the ratio of 2.1 to 1.5.
Simplifying the right side, \( \frac{2.1}{1.5} \) becomes \( \frac{7}{5} \). This gives us a clear equivalent proportion: \( \frac{2.8}{k} = \frac{7}{5} \).
Understanding ratios and proportions helps you see the consistency between different sets of numbers, making it easier to solve the equation.

Simplifying fractions is another critical concept for solving rational equations. The goal is to simplify fractions to their simplest form so that equations become easier to manage.
In our example, simplifying \( \frac{2.1}{1.5} \) to \( \frac{7}{5} \) allows us to work with smaller, more comprehensible numbers.
Here's how it works: \( 2.1/1.5 \) can be written as \( 21/15 \) (multiplying both the numerator and denominator by 10). Then, simplify by dividing both 21 and 15 by their greatest common divisor, which is 3, to get \( 7/5 \).
Simplifying fractions reduces complexity, making the overall problem easier to solve. It also helps in identifying equivalent ratios and in verifying solutions once the equation is solved.