Unlike Fractions

Definition

Unlike fractions are fractions that have different denominators, meaning the bottom numbers of the fractions are not the same. These fractions cannot be directly added or subtracted without first finding a common denominator.

5 Must Know Facts For Your Next Test

1. Unlike fractions cannot be directly added or subtracted without first finding a common denominator.
2. To add or subtract unlike fractions, you must first convert them to equivalent fractions with the same denominator.
3. The common denominator is the least common multiple (LCM) of the denominators of the unlike fractions.
4. Once the fractions have a common denominator, you can add or subtract the numerators and keep the common denominator.
5. Rational expressions, which involve fractions with variables, also require finding a common denominator to perform operations.

Review Questions

• Explain the importance of finding a common denominator when adding or subtracting unlike fractions.
  • Finding a common denominator is crucial when adding or subtracting unlike fractions because the denominators must be the same in order to perform these operations. Unlike fractions have different denominators, meaning the bottom numbers are not the same. By converting the fractions to equivalent fractions with a common denominator, you can then add or subtract the numerators while keeping the same denominator. This ensures that the fractions are being compared and combined properly, resulting in a valid final answer.
• Describe the process of finding the least common multiple (LCM) to determine the common denominator for a set of unlike fractions.
  • To find the common denominator for a set of unlike fractions, you need to determine the least common multiple (LCM) of the denominators. The LCM is the smallest positive integer that is divisible by all the denominators. Once the LCM is found, you can convert each fraction to an equivalent fraction with the LCM as the new denominator. This is done by multiplying the numerator and denominator of each fraction by the same number, so that the new denominator becomes the LCM. With all the fractions now having the same denominator, you can proceed to add or subtract the numerators.
• Analyze how the concept of unlike fractions extends to the addition and subtraction of rational expressions, and explain the importance of this connection.
  • The concept of unlike fractions is directly applicable to the addition and subtraction of rational expressions, which are algebraic expressions written as a ratio of two polynomial functions. Just as with unlike fractions, rational expressions cannot be directly added or subtracted unless they have a common denominator. To perform these operations on rational expressions, you must first find the least common multiple of the denominators to determine the common denominator. Then, you can convert the rational expressions to equivalent expressions with the common denominator, allowing you to add or subtract the numerators. Understanding the connection between unlike fractions and rational expressions is crucial, as it allows you to apply the same principles and strategies to manipulate and simplify a wide range of algebraic expressions involving fractions.

Related terms

Common Denominator: The lowest number that is a multiple of all the denominators in a set of fractions, allowing the fractions to be easily compared and combined.

Equivalent Fractions: Fractions that represent the same value, even though the numerator and denominator are different, by having the same ratio between the numerator and denominator.

Rational Expressions: Algebraic expressions that can be written as a ratio of two polynomial functions, where the denominator is not equal to zero.