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, which allows the fractions to have the same unit.

5 Must Know Facts For Your Next Test

1. Unlike fractions cannot be added or subtracted directly because they have different denominators, which represent different units.
2. To add or subtract unlike fractions, you must first find the least common multiple (LCM) of the denominators and convert the fractions 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. Converting unlike fractions to equivalent fractions with the same denominator allows you to add or subtract the numerators while maintaining the same unit.
5. Proper handling of unlike fractions is crucial for performing operations such as addition and subtraction of fractions with different denominators.

Review Questions

• Explain the importance of finding a common denominator when adding or subtracting unlike fractions.
  • Finding a common denominator is essential when working with unlike fractions because it allows the fractions to have the same unit. Without a common denominator, the fractions cannot be directly added or subtracted, as they represent different quantities. By converting the unlike fractions to equivalent fractions with the same denominator, you can then perform the addition or subtraction operation on the numerators while maintaining the same unit, ensuring the result is meaningful and accurate.
• Describe the process of converting unlike fractions to equivalent fractions with a common denominator.
  • To convert unlike fractions to equivalent fractions with a common denominator, you first need to find the least common multiple (LCM) of the denominators of the given fractions. This LCM will become the new common denominator. Then, you multiply the numerator and denominator of each fraction by the appropriate factor to obtain the equivalent fraction with the common denominator. This ensures that the new fractions represent the same quantities as the original fractions, allowing you to add or subtract them correctly.
• Analyze the relationship between the concept of unlike fractions and the process of adding or subtracting mixed numbers.
  • The concept of unlike fractions is closely tied to the process of adding or subtracting mixed numbers. Mixed numbers consist of a whole number and a fraction, and the fractions within the mixed numbers may have different denominators, making them unlike fractions. To add or subtract mixed numbers, you must first convert the unlike fractions to equivalent fractions with a common denominator. This allows you to perform the addition or subtraction on the fractional parts, and then combine the results with the whole number parts to obtain the final answer. Understanding the principles of unlike fractions is crucial for successfully navigating the operations of adding and subtracting mixed numbers.

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 by converting them to equivalent fractions with the same denominator.

Equivalent Fractions:

Equivalent fractions are fractions that have the same value, even though the numerator and denominator may be different. This allows unlike fractions to be converted to have the same denominator for addition and subtraction.

Least Common Multiple (LCM): The least common multiple (LCM) is the smallest positive integer that is divisible by two or more given numbers. The LCM is used to find the common denominator when adding or subtracting unlike fractions.