Content - Algebraic Fractions

Algebraic Fractions

For most people, the goal of driving a car is to go from point A to point B. Before you can operate a car, you have to learn the function of each individual major component such as the steering wheel, brake, and gear selector. After you become familiar with each individual part, you use them simultaneously to perform the real task - driving your car.

Similarly, the individual components in algebra problem solving include the monomial arithmetic, polynomial arithmetic, and operations with algebraic fractions. In this section, algebraic fractions are our focus point.

Algebraic fractions are fractions having a variable(s) in the numerator, or denominator, or both, such as x/2, 1/y, or (1-y)/(x-4). It is understood that both the numerator and the denominator will never make the fraction invalid. That is, in the fraction 1/y, y will not be equal to 0; in the fraction (1-y)/(x-4), x will not be equal to 4. When dealing with algebraic fractions, remember these types of restrictions.

Reducing Algebraic Fractions

The rules and reasons for the treatment of algebraic fractions in algebra are the same as that in arithmetic.

In arithmetic, when both the numerator and denominator of the fraction contain a common factor, the fraction can be reduced by this factor. For instance,

When the same rule applies to algebraic fractions, we have

Multiplying Algebraic Fractions

To multiply fractions in arithmetic, simply multiply numerators, then multiply the denominators. Reduce the resulting fraction to lowest terms if necessary. For example,

When the same rule applies to multiplying algebraic fractions, we have

Dividing Algebraic Fractions

To divide fractions in arithmetic, turn the second fraction upside down and multiply. This reduces a division problem to a multiplication problem, which has been solved previously. Then reduce the result, if necessary. For example,

When the same rule applies to dividing algebraic fractions, we have

Adding and Subtracting Algebraic Fractions

To add fractions in arithmetic, first, change all denominators to their lowest common denominator, which is the lowest number that can be divided evenly by all the original denominators in the problem. When all the denominators become the same, add or subtract the numerators. Write the resulting sum or difference over the common denominator. Reduce the resulting fraction to lowest terms if necessary. For example,

When the same rule applies to adding or subtracting algebraic fractions, we have

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