Unlike Fractions

Definition

Unlike fractions are fractions that have different denominators, meaning the bottom numbers of the fractions are not the same. This makes it necessary to convert the fractions to equivalent fractions with a common denominator before they can be added or subtracted.

5 Must Know Facts For Your Next Test

1. Unlike fractions cannot be added or subtracted directly because they have different denominators.
2. To add or subtract unlike fractions, you must first convert them to equivalent fractions with a common denominator.
3. The common denominator is found by calculating 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. Simplifying the resulting fraction by reducing it to lowest terms is an important final step when adding or subtracting unlike fractions.

Review Questions

• Explain the purpose of finding a common denominator when adding or subtracting unlike fractions.
  • The purpose of finding a common denominator when adding or subtracting unlike fractions is to ensure that the fractions have the same basis for comparison. By converting the fractions to equivalent fractions with a common denominator, the numerators can be directly added or subtracted, as the denominators will be the same. This allows the operation to be performed correctly, as fractions can only be added or subtracted when they have the same denominator.
• Describe the process of finding the least common multiple (LCM) to determine the common denominator for unlike fractions.
  • To find the common denominator for unlike fractions, you must first determine the least common multiple (LCM) of the denominators. The LCM is the smallest positive integer that is divisible by all the denominators. This is done by listing the prime factors of each denominator and then taking the product of the highest powers of each prime factor. The resulting LCM becomes the common denominator that the unlike fractions are converted to, allowing the addition or subtraction operation to be performed.
• Analyze the importance of simplifying the resulting fraction after adding or subtracting unlike fractions with a common denominator.
  • Simplifying the resulting fraction after adding or subtracting unlike fractions with a common denominator is crucial because it ensures the final answer is in the simplest form possible. By reducing the fraction to its lowest terms, you eliminate any unnecessary factors in the numerator and denominator, making the fraction more concise and easier to work with. This step is important because it provides the most efficient and meaningful representation of the calculated value, which is essential for accurately interpreting the results of the operation.

Related terms

Common Denominator: The common denominator is the least common multiple of the denominators of the unlike fractions, which allows the fractions to be added or subtracted.

Equivalent Fractions: Equivalent fractions are fractions that represent the same numerical value, despite having different numerators and denominators.

Least Common Multiple (LCM): The least common multiple is the smallest positive integer that is divisible by all the denominators of the unlike fractions, which is used to find the common denominator.