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Fractions are numbers that represent a part of a whole. They have two components: a numerator and a denominator. The numerator is the top number, which signifies how many parts we have, while the denominator, the bottom number, shows how many parts the whole is divided into. Understanding fractions is critical when dealing with anything less than one, or when parts of a whole are involved in equations. For instance, in our problem, the term \(-\frac{4}{b}\) is a fraction because it has a numerator (-4) and a denominator (b). This means we are looking at -4 parts of some value b.

Solving equations with fractions involves finding the value of the unknown variable that makes the equation true. The presence of a fraction can often complicate this process. Here are some steps to help:

• First, isolate the fractional term. You want the fraction to be by itself on one side of the equation, as it is easier to manipulate fractions when they're isolated. In our example, we subtracted 18 from both sides to isolate the fractional term.
• Next, remove the fraction by eliminating negative signs or performing operations. In the worked solution, multiplying by -1 helped simplify the fraction.
• Finally, multiply both sides by the denominator to get rid of the fraction entirely. This helps to turn the equation into a simpler, more straightforward equation that can be solved easily. In the example, multiplying both sides by the value of the denominator, b, and then dividing by 8, helped find the value of b as \(\frac{1}{2}\).

Inverse operations in equations are like the reverse actions used to solve problems. They help in undoing the operations one at a time to solve for the variable. Whenever you are solving equations such as \(18 - \frac{4}{b} = 10\), the goal is to completely isolate the variable by using inverse operations. These operations include:- **Addition and Subtraction**: These are inverse operations. If an equation has addition or subtraction, you can perform the opposite operation to both sides to eliminate those terms.- **Multiplication and Division**: When a variable is multiplied or divided by a number, you can undo this using the opposite operation.In the example, to eliminate the fraction, we multiplied by \(-1\), which is the inverse of subtracting. Similarly, to solve for \(b\), dividing by 8 is the inverse of multiplying by 8. Using these inverse operations effectively simplifies the equation and eases the process of finding a solution.