Subtraction of Fractions

Definition

Subtraction of fractions is the process of finding the difference between two fractions by aligning the fractions with a common denominator and then subtracting the numerators. This operation allows for the comparison and removal of fractional amounts from one another.

5 Must Know Facts For Your Next Test

1. To subtract fractions with different denominators, the fractions must first be converted to equivalent fractions with a common denominator.
2. The common denominator is found by determining the least common multiple (LCM) of the denominators of the fractions being subtracted.
3. Once the fractions have a common denominator, the numerators are subtracted, and the resulting fraction has the common denominator.
4. Subtracting fractions with the same denominator involves simply subtracting the numerators and keeping the same denominator.
5. Proper fractions, improper fractions, and mixed numbers can all be subtracted using the same process of finding a common denominator.

Review Questions

• Explain the purpose of finding a common denominator when subtracting fractions.
  • The purpose of finding a common denominator when subtracting fractions is to ensure that the fractions have the same unit value, allowing for a direct subtraction of the numerators. Without a common denominator, the fractions cannot be directly compared and subtracted, as they represent different fractional amounts. By converting the fractions to equivalent fractions with a common denominator, the subtraction can be performed accurately, resulting in a fraction that represents the true difference between the original fractions.
• Describe the process of finding the least common multiple (LCM) to determine the common denominator for subtracting fractions.
  • To find the common denominator for subtracting fractions, the least common multiple (LCM) of the denominators must be determined. The LCM is the smallest positive integer that is divisible by all the denominators of the fractions being subtracted. Once the LCM is found, it becomes the common denominator for the fractions, and the numerators are then adjusted to create equivalent fractions with the common denominator. This ensures that the fractions represent the same unit value, allowing for the accurate subtraction of the numerators to find the difference between the original fractions.
• Analyze the importance of understanding the concept of equivalent fractions in the context of subtracting fractions.
  • The understanding of equivalent fractions is crucial when subtracting fractions because it allows for the conversion of the fractions to a common denominator. Equivalent fractions represent the same fractional value but have different numerators and denominators. By recognizing that fractions with different denominators can be equivalent, the fractions can be adjusted to have a common denominator, which is necessary for performing the subtraction operation accurately. Without the concept of equivalent fractions, the subtraction of fractions with different denominators would not be possible, as the fractions would not be comparable. The ability to create equivalent fractions is the foundation for the successful subtraction of fractions with different denominators.

Related terms

Common Denominator:

The common denominator is the least common multiple of the denominators of the fractions being subtracted, which allows the fractions to be expressed with the same denominator for subtraction.

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

Equivalent Fractions:

Equivalent fractions are fractions that represent the same value, but have different numerators and denominators, which is necessary for aligning fractions with a common denominator during subtraction.