Subtraction of Fractions

Definition

Subtraction of fractions is the process of finding the difference between two or more fractions. It involves manipulating the fractions to have a common denominator, then subtracting the numerators while keeping the common denominator. This concept is essential for understanding how to add and subtract fractions with both common and different denominators.

5 Must Know Facts For Your Next Test

1. To subtract fractions with common denominators, you simply subtract the numerators and keep the common denominator.
2. When subtracting fractions with different denominators, you must first find the least common multiple (LCM) of the denominators to determine the common denominator.
3. Once the common denominator is found, you can convert the fractions to equivalent fractions with the common denominator and then subtract the numerators.
4. Proper subtraction of fractions is essential for solving more complex mathematical problems involving fractions, such as word problems and algebraic expressions.
5. Mastering the subtraction of fractions with both common and different denominators will provide a strong foundation for understanding more advanced fraction operations.

Review Questions

• Explain the process of subtracting fractions with common denominators.
  • To subtract fractions with common denominators, you simply need to subtract the numerators and keep the common denominator. For example, to subtract $\frac{3}{4} - \frac{1}{4}$, you would subtract the numerators: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4}$. This works because the denominators are the same, so you can directly subtract the numerators.
• Describe the steps involved in subtracting fractions with different denominators.
  • When subtracting fractions with different denominators, you must first find the least common multiple (LCM) of the denominators to determine the common denominator. Once the common denominator is found, you can convert the fractions to equivalent fractions with the common denominator and then subtract the numerators. For example, to subtract $\frac{1}{3} - \frac{1}{6}$, you would first find the LCM of 3 and 6, which is 6. Then, you would convert the fractions to $\frac{2}{6} - \frac{1}{6} = \frac{1}{6}$.
• Analyze the importance of mastering the subtraction of fractions in the context of more advanced mathematical concepts.
  • Proficiency in subtracting fractions, both with common and different denominators, is crucial for success in more advanced mathematical topics. The ability to accurately subtract fractions is foundational for solving word problems, working with algebraic expressions, and understanding higher-level concepts in mathematics. Mastering fraction subtraction provides a strong base for students to build upon, enabling them to tackle increasingly complex problems involving fractions and other mathematical operations. Developing this skill sets students up for success in their future mathematical studies and problem-solving endeavors.

Related terms

Common Denominator: The common denominator is the least common multiple of the denominators of the fractions being subtracted. This allows the fractions to be expressed with the same denominator, making the subtraction process easier.

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. The LCM is used to find the common denominator.

Equivalent Fractions: Equivalent fractions are fractions that represent the same value, but have different numerators and denominators. Equivalent fractions are used when subtracting fractions with different denominators.