Subtraction of Fractions

Definition

Subtraction of fractions is the process of finding the difference between two or more fractions by finding a common denominator and then subtracting the numerators. It is an essential operation in working with fractions and is used to solve a variety of mathematical problems involving fractional quantities.

5 Must Know Facts For Your Next Test

1. To subtract fractions, the denominators must be the same. If the denominators are not the same, you must find a common denominator first.
2. The common denominator is the least common multiple (LCM) of the denominators of the fractions being subtracted.
3. Once the common denominator is found, you can convert the fractions to equivalent fractions with the common denominator.
4. After converting the fractions, you can subtract the numerators and keep the common denominator.
5. The final answer may need to be simplified by dividing the numerator and denominator by their greatest common factor.

Review Questions

• Explain the process of subtracting fractions with different denominators.
  • To subtract fractions with different denominators, you first need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the fractions being subtracted. Once you have the common denominator, you convert the fractions to equivalent fractions with the common denominator. Then, you can subtract the numerators and keep the common denominator. The final answer may need to be simplified by dividing the numerator and denominator by their greatest common factor.
• Describe the importance of finding a common denominator when subtracting fractions.
  • Finding a common denominator is a crucial step in subtracting fractions because the denominators must be the same in order to perform the subtraction operation. If the denominators are not the same, the fractions cannot be directly subtracted. By converting the fractions to equivalent fractions with a common denominator, you can then subtract the numerators and arrive at the correct difference. The common denominator ensures that the fractional values being subtracted are comparable and can be properly combined.
• Analyze the relationship between simplifying fractions and subtracting fractions.
  • The process of simplifying fractions is often necessary after subtracting fractions to ensure the final answer is in the simplest form possible. Simplifying involves reducing the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor. This step is important because it makes the fractional value easier to work with and interpret. By simplifying the result of a subtraction operation, you can present the final answer in the most concise and meaningful way. The ability to simplify fractions is a key skill in mastering fraction subtraction and other fraction operations.

Related terms

Common Denominator:

The common denominator is the least common multiple (LCM) of the denominators of the fractions being subtracted. Finding the common denominator is a crucial step in subtracting fractions.

Equivalent Fractions:

Equivalent fractions are fractions that represent the same fractional value, even though the numerators and denominators may be different. Equivalent fractions are used to find a common denominator for subtraction.

Simplifying Fractions: Simplifying fractions involves reducing the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor. This step may be necessary after subtracting fractions to ensure the final answer is in simplest form.