Equations with Fractions

In this section, we learn how to solve a linear equation in one variable with fractions or decimals. When we solve equations with fractions, we have the option to clear the equation of fractions. We do this by multiplying both sides of the equation by the LCD of all fractions involved in the equation. This is legal because of the multiplication property of equality; we are multiplying both sides of the equation by the same non-zero number. The result of this process is a fraction free equation that we can solve using our four-step process. When we encounter an equation with decimals, we also have the option to clear the equation of decimals. We can clear the decimals by multiplying both sides of the equation by the appropriate power of ten. Once we have executed this process, we will have an equation that is free of decimals. In both cases, these procedures are optional. We can solve an equation without clearing the fractions or decimals with the four-step method.