How Subtract Fractions with Different Denominators
Subtracting fractions with different denominators can sometimes be a challenging task for students, especially those who are new to the concept of fractions. However, with a few simple steps and a clear understanding of the basics, subtracting fractions with different denominators can become a straightforward process. In this article, we will explore the steps involved in subtracting fractions with different denominators and provide some practical examples to help you master this skill.
Understanding the Basics
Before we dive into the steps for subtracting fractions with different denominators, it’s essential to have a solid understanding of the basics. A fraction represents a part of a whole, where the numerator (the top number) indicates the number of parts we have, and the denominator (the bottom number) represents the total number of parts in the whole. When subtracting fractions, we are essentially finding the difference between two parts of a whole.
Step 1: Find a Common Denominator
To subtract fractions with different denominators, we first need to find a common denominator. A common denominator is a number that is a multiple of both denominators. This allows us to add or subtract the fractions by converting them into equivalent fractions with the same denominator.
To find a common denominator, you can use the least common multiple (LCM) of the two denominators. The LCM is the smallest positive integer that is divisible by both numbers. You can find the LCM by listing the multiples of each denominator and identifying the smallest common multiple.
Step 2: Convert the Fractions to Equivalent Fractions
Once you have found the common denominator, you need to convert the original fractions into equivalent fractions with the common denominator. To do this, multiply the numerator and denominator of each fraction by a number that will result in the common denominator.
For example, let’s say we want to subtract 1/3 from 2/5. The LCM of 3 and 5 is 15. To convert 1/3 to an equivalent fraction with a denominator of 15, we multiply the numerator and denominator by 5:
1/3 = (1 x 5) / (3 x 5) = 5/15
Similarly, to convert 2/5 to an equivalent fraction with a denominator of 15, we multiply the numerator and denominator by 3:
2/5 = (2 x 3) / (5 x 3) = 6/15
Now that both fractions have the same denominator, we can proceed to the next step.
Step 3: Subtract the Numerators
With the fractions now having the same denominator, subtract the numerators and keep the common denominator. In our example, we have:
5/15 – 6/15 = (5 – 6) / 15 = -1/15
The result is a fraction with a negative numerator, indicating that the first fraction is less than the second fraction.
Step 4: Simplify the Result (Optional)
In some cases, the resulting fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). However, in our example, -1/15 is already in its simplest form.
Conclusion
Subtracting fractions with different denominators can be broken down into a few simple steps: finding a common denominator, converting the fractions to equivalent fractions, subtracting the numerators, and simplifying the result if necessary. By following these steps, you can easily subtract fractions with different denominators and become more comfortable with this essential math skill.
