Title: How to Add and Subtract Fractions: A Comprehensive Guide
Subtitle: A Step-by-Step Tutorial
Introduction
Adding and subtracting fractions can be a daunting task for many students. However, it doesn’t have to be! This comprehensive guide will provide you with a step-by-step tutorial to help you understand how to add and subtract fractions. We’ll cover everything from finding common denominators to simplifying fractions. At the end of this post, you’ll be able to confidently add and subtract fractions with ease.
Body
The first step to adding and subtracting fractions is to make sure that the fractions have the same denominator, or bottom number. This is called finding the common denominator. To do this, you’ll need to multiply the denominators of each fraction together. For example, if you have two fractions with denominators of 3 and 4, you would multiply 3 and 4 together to get 12. This means that the common denominator is 12.
Once you’ve found the common denominator, you can add or subtract the fractions. To add the fractions, you’ll need to add the numerators, or top numbers, of each fraction. For example, if you have two fractions with numerators of 2 and 3, you would add 2 and 3 together to get 5. This means that the numerator of the answer is 5.
To subtract the fractions, you’ll need to subtract the numerators of each fraction. For example, if you have two fractions with numerators of 4 and 3, you would subtract 3 from 4 to get 1. This means that the numerator of the answer is 1.
Once you’ve found the numerator, you’ll need to simplify the fraction. To do this, you’ll need to divide the numerator and denominator by the greatest common factor (GCF). The GCF is the largest number that can divide both the numerator and denominator. For example, if you have a fraction with a numerator of 10 and a denominator of 15, you would divide 10 and 15 by 5 to get 2 and 3. This means that the simplified fraction is 2/3.
Examples
Let’s look at a few examples of adding and subtracting fractions.
Example 1:
Add 2/3 and 3/4
Solution:
First, we need to find the common denominator. To do this, we multiply the denominators together, which gives us 12.
Next, we need to add the numerators. To do this, we add 2 and 3 together, which gives us 5.
Finally, we need to simplify the fraction. To do this, we divide the numerator and denominator by the greatest common factor, which is 3. This gives us 5/3, which is the simplified answer.
Example 2:
Subtract 4/5 and 2/3
Solution:
First, we need to find the common denominator. To do this, we multiply the denominators together, which gives us 15.
Next, we need to subtract the numerators. To do this, we subtract 2 from 4, which gives us 2.
Finally, we need to simplify the fraction. To do this, we divide the numerator and denominator by the greatest common factor, which is 5. This gives us 2/3, which is the simplified answer.
FAQ Section
Q: What is the common denominator?
A: The common denominator is the bottom number of the fractions that you are adding or subtracting. To find the common denominator, you need to multiply the denominators of each fraction together.
Q: What is the greatest common factor?
A: The greatest common factor (GCF) is the largest number that can divide both the numerator and denominator. To find the GCF, you need to divide the numerator and denominator by the greatest common factor.
Summary
Adding and subtracting fractions can be a daunting task for many students. However, it doesn’t have to be! This comprehensive guide provided you with a step-by-step tutorial to help you understand how to add and subtract fractions. We covered everything from finding common denominators to simplifying fractions. At the end of this post, you should be able to confidently add and subtract fractions with ease.
Conclusion
Adding and subtracting fractions doesn’t have to be a difficult task. With this comprehensive guide, you now have the tools to confidently add and subtract fractions. Just remember to find the common denominator, add or subtract the numerators, and simplify the fraction. With practice, you’ll be able to master this skill in no time!
