Fraction Freedom! Get Rid of Fractions the Easy Way
Embark on a journey to Fraction Freedom! Ever wondered how do you get rid of a fraction and unlock a world of simpler calculations? Mastering this skill involves understanding the concept of the Least Common Multiple (LCM), a cornerstone of fraction manipulation. Applying the principles taught in resources like Khan Academy enables you to efficiently eliminate fractions in equations. Many students find that focusing on the methods taught by math educators, such as those using the PEMDAS rule, greatly helps in simplifying fractions. With these tools and techniques, achieving fraction freedom becomes an easily attainable goal.
Image taken from the YouTube channel Udacity , from the video titled Get Rid Of The Fraction - College Algebra .
Fraction Freedom! Conquer Fractions the Easy Way
Fractions can seem intimidating, but you can learn how to easily eliminate them from equations and problems. Let's explore the best and simplest methods! We'll primarily focus on answering the question, "How do you get rid of a fraction?" Don't worry, it's easier than you think!
Understanding the Challenge: Why Get Rid of Fractions?
Fractions, while mathematically sound, often complicate equations. Dealing with them can increase the chances of making errors. Simplifying expressions by removing fractions can make the overall problem more manageable and visually clearer.
- Simplified Equations: Easier to solve and understand.
- Reduced Errors: Less chance of making mistakes in calculations.
- Improved Clarity: More transparent problem-solving process.
The Magic Trick: Multiplying to Eliminate Fractions
The most common and effective technique is multiplying by the Least Common Multiple (LCM). This might sound complex, but we'll break it down step-by-step.
Finding the Least Common Multiple (LCM)
The LCM is the smallest number that all denominators in your fractions divide into evenly.
- Identify the Denominators: List all the denominators in your equation.
- Find the Multiples: Write out the multiples of each denominator until you find a common one. The smallest one is the LCM.
- Example:
- Fractions: 1/2, 1/3, 1/4
- Denominators: 2, 3, 4
- Multiples of 2: 2, 4, 6, 8, 10, 12...
- Multiples of 3: 3, 6, 9, 12...
- Multiples of 4: 4, 8, 12...
- LCM = 12
Multiplying the Entire Equation
Once you've found the LCM, multiply every term in the equation by that LCM. This is crucial!
- Identify Each Term: Recognize each distinct part of the equation, separated by "+" or "-" signs (or an "=" sign).
- Multiply Each Term: Multiply each term by the LCM.
- Simplify: Reduce each fraction by dividing the numerator by the denominator (or cancelling down). The denominators should disappear!
Example: Solving an Equation
Let's solve this equation: x/2 + 1/3 = 5/6
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Find the LCM: The denominators are 2, 3, and 6. The LCM is 6.
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Multiply Each Term by the LCM:
(6 x/2) + (6 1/3) = (6 * 5/6)
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Simplify:
- (6/2) x + (6/3) 1 = (6/6) * 5
- 3x + 2 = 5
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Solve for x (Now that Fractions are Gone):
- 3x = 3
- x = 1
Special Cases and Helpful Hints
While multiplying by the LCM is the general method, there are a few instances where you might adapt the approach.
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Single Fraction on One Side: If you only have one fraction on one side of the equation, you can multiply both sides by just the denominator of that fraction.
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Complex Fractions (Fractions Within Fractions): Start by simplifying the complex fraction itself first, then apply the LCM method to the entire equation.
Practice Makes Perfect!
Like any skill, mastering the art of eliminating fractions takes practice. Don't be discouraged if you make mistakes initially. The more problems you solve, the more confident you'll become!
Here are a few more to practice:
- x/4 + 2/5 = 1/2
- 3/7 = y/14
- (z + 1)/3 = 2/5
Video: Fraction Freedom! Get Rid of Fractions the Easy Way
Fraction Freedom FAQs: Simplifying Fractions for Everyone
These FAQs clarify some common questions about easily eliminating fractions in equations and expressions.
Why would I want to get rid of fractions?
Fractions, while useful, can make equations and expressions harder to solve and manipulate. Simplifying by eliminating them often makes the process much easier and less prone to errors.
What's the easiest way to get rid of a fraction in an equation?
The quickest way to get rid of a fraction in an equation is to multiply every term on both sides of the equation by the least common multiple (LCM) of all the denominators. This clears out the fractions, leaving you with whole numbers.
Does this method work for simplifying expressions, not just equations?
Yes, but with a key difference! When simplifying expressions (without an equals sign), you can't just multiply through without changing the value. Instead, find the LCM of the denominators and create a common denominator for all terms. Then, you can combine the terms into a single fraction, or potentially simplify further. The goal when simplifying expressions is not necessarily to get rid of all the fractions, but to express the expression in its simplest form. In some cases, you would only get rid of a fraction in a complex fraction.
How do you get rid of a fraction if there are multiple fractions in the equation?
The principle remains the same. First, identify all the denominators in the equation. Then, find the least common multiple (LCM) of all those denominators. Finally, multiply every single term on both sides of the equation by that LCM. This will effectively clear out all fractions in one step.