How to Subtract Fractions with Unlike Denominators
Before diving deep into the subtraction process with unlike denominators, it is imperative to understand some basic terminologies.
- Numerator: The number present above the fraction bar is called the numerator which represents the number of sections being used out of a whole.
- Denominator: The value displayed below the line is termed the denominator, determining into how many equal sections a single whole has been divided.
Steps for Subtraction
Step 1: Find the Least Common Denominator (LCD)
The first and foremost step when working with unlike denominators in subtraction is finding the Lowest Common Multiple (LCM) of denominators. To determine the LCM, we multiply the denominators of the two fractions in the given expression.
- For instance, suppose you need to subtract 1/4 from 3/5. The LCD is going to be (4 x 5) = 20.
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Step 2: Adjust Fractions to Equivalent Forms
With the Least Common Denominator acquired, express each fraction in an equivalent form having the LCM as its denominator. Multiply the old numerator by a factor that will match the new denominator.
- In the 1/4 – 3/5 example, multiply 1/4 by 5/5 and 3/5 by 4/4. This operation leads to 5/20 and 12/20 respectively adjusted fractions.
Step 3: Subtract Numerators
Now that you have equivalent fractions ready, go ahead and subtract the numerators of these fractions since the denominators are equal now. Given you have 5/20 and 12/20, subtract 5 from 12 to get -7 as the numerator of the fraction.
Step 4: Copy the Common Denominator
The next step is to transfer the least common denominator onto the resultant fraction. In the example we calculated above, the common denominator is 20, meaning your solution would be -7/20.
Step 5: Simplify the Final Fraction (if possible)
Assess if your final fraction can be further simplified. Look for any whole numbers or common denominators that may exist, then simplify accordingly. For example, if the resultant fraction is -14/28, you can divide both numbers by two to get -7/14 once simplified.
Expert Tips
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Cross Multiply: An advanced shortcut method to find the LCM is by cross-multiplying the numerator of one fraction by the denominator of the other fraction and vice versa. The products are then multiplied to acquire the LCD.
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Equivalent Fractions: Remember that any fraction remains unchanged when you multiply its numerator and denominator with the same number, which leads us to different forms of the same value without altering its value.
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Double-Checking: Always ensure double-checking your answer by adding the difference between the original fractions and the common denominator. This allows you to see if your resultant fraction equals the original starting fraction, validating the correctness of your solution.
Common Questions and Answers
How Do You Subtract Fractions With Unlike Denominators
Conclusion
Now that you’ve stepped through the detailed guide on subtracting fractions posed with unlike denominators, it is time to test your skills and practice the method with several examples. Constant practice aids in the development of comfort and confidence needed to tackle similar fraction problems effortlessly. Whether facing mathematical equations or practical problems requiring denominator manipulation, this technique serves as an invaluable tool when applied to the field of fractions.
Are you interested in pursuing further knowledge surrounding fractions? Explore our other articles covering various topics related to fractions from basic concepts to advanced applications
