Subtract.$ -\frac{9}{14} - \frac{1}{14} $ -\frac{9}{14} - \frac{1}{14} = \square $ (Type An Integer Or A Simplified Fraction.)
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Introduction
When it comes to subtracting fractions, it's essential to understand the basics of fraction operations. In this article, we'll delve into the world of subtracting fractions, exploring the steps and techniques required to perform this operation with ease. Whether you're a student, a teacher, or simply someone looking to brush up on their math skills, this guide is designed to provide you with a comprehensive understanding of subtracting fractions.
What are Fractions?
Before we dive into subtracting fractions, let's take a moment to understand what fractions are. A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). For example, the fraction 3/4 can be read as "three-fourths" or "three divided by four."
Subtracting Fractions: The Basics
When subtracting fractions, we need to follow a specific set of rules to ensure that we're performing the operation correctly. Here are the basics:
- Like denominators: When the denominators of the fractions are the same, we can simply subtract the numerators. For example, 3/4 - 1/4 = 2/4.
- Unlike denominators: When the denominators are different, we need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly. Once we have the LCM, we can convert both fractions to have the same denominator.
Subtracting Fractions with Unlike Denominators
Let's take a look at an example of subtracting fractions with unlike denominators:
In this example, the denominators are the same (14), so we can simply subtract the numerators:
Simplifying the Result
Now that we have the result of the subtraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 10 and 14 is 2.
Conclusion
Subtracting fractions may seem like a daunting task, but with the right techniques and a solid understanding of the basics, it's a breeze. By following the steps outlined in this article, you'll be able to subtract fractions with ease and confidence. Whether you're working with like or unlike denominators, you'll be able to simplify the result and arrive at the correct answer.
Frequently Asked Questions
Q: What is the difference between like and unlike denominators?
A: Like denominators are fractions that have the same denominator, while unlike denominators are fractions that have different denominators.
Q: How do I find the least common multiple (LCM) of two numbers?
A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.
Q: How do I simplify a fraction?
A: To simplify a fraction, you can divide both the numerator and the denominator by their greatest common divisor (GCD).
Final Answer
-\frac{9}{14} - \frac{1}{14} = -\frac{10}{14} = -\frac{5}{7}$<br/> # Subtracting Fractions: A Q&A Guide ===================================== ## Introduction ---------------- In our previous article, we explored the basics of subtracting fractions, including like and unlike denominators, and how to simplify the result. However, we know that math can be a complex and confusing subject, and sometimes it's helpful to have a Q&A guide to clarify any doubts or questions you may have. ## Q&A: Subtracting Fractions --------------------------- ### Q: What is the difference between subtracting fractions and subtracting whole numbers? A: Subtracting fractions is similar to subtracting whole numbers, but with fractions, we need to consider the denominators. When subtracting whole numbers, we simply subtract the numbers, but when subtracting fractions, we need to find a common denominator and then subtract the numerators. ### Q: How do I subtract fractions with unlike denominators? A: To subtract fractions with unlike denominators, you need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly. Once you have the LCM, you can convert both fractions to have the same denominator. ### Q: What is the least common multiple (LCM)? A: The LCM is the smallest number that both denominators can divide into evenly. For example, the LCM of 4 and 6 is 12, because both 4 and 6 can divide into 12 evenly. ### Q: How do I find the LCM of two numbers? A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists. Alternatively, you can use a formula to find the LCM. ### Q: What is the greatest common divisor (GCD)? A: The GCD is the largest number that both the numerator and the denominator can divide into evenly. For example, the GCD of 10 and 14 is 2, because both 10 and 14 can divide into 2 evenly. ### Q: How do I simplify a fraction? A: To simplify a fraction, you can divide both the numerator and the denominator by their greatest common divisor (GCD). This will give you a simplified fraction with the smallest possible numerator and denominator. ### Q: What is the difference between a proper fraction and an improper fraction? A: A proper fraction is a fraction where the numerator is less than the denominator, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator. ### Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. Then, you can write the result as an improper fraction. ### Q: What is the difference between subtracting fractions and adding fractions? A: Subtracting fractions is similar to adding fractions, but with subtracting fractions, we need to find a common denominator and then subtract the numerators. With adding fractions, we need to find a common denominator and then add the numerators. ## Conclusion ---------- We hope this Q&A guide has helped to clarify any doubts or questions you may have had about subtracting fractions. Remember, practice makes perfect, so be sure to try out the examples and exercises in this guide to reinforce your understanding of subtracting fractions. ## Final Answer -------------- $-\frac{9}{14} - \frac{1}{14} = -\frac{10}{14} = -\frac{5}{7}