Clearing denominators is a technique used to eliminate fractions from an equation. This is achieved by multiplying both sides of the equation by the least common multiple (LCM) of all the denominators. By doing this, you transform the equation into one that is easier to solve, without fractions.
For example, consider the equation $\frac{x}{2} + \frac{1}{3} = 1$. The LCM of 2 and 3 is 6. Multiplying both sides by 6 gives $6(\frac{x}{2} + \frac{1}{3}) = 6(1)$, which simplifies to $3x + 2 = 6$. Now, you have a simple linear equation without any fractions!
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Least Common Multiple (LCM) | a. The process of eliminating fractions in an equation. |
| 2. Denominator | b. The number below the fraction bar. |
| 3. Numerator | c. The smallest multiple that is common to two or more numbers. |
| 4. Clearing Denominators | d. A statement that two expressions are equal. |
| 5. Equation | e. The number above the fraction bar. |
To clear ________, you must find the ________ of all the denominators in the equation. Once you find it, you ________ both sides of the equation by the LCM. This will ________ the fractions, making the equation easier to solve.
Why is clearing denominators a useful strategy when solving equations? Can you think of a situation where it might not be the most efficient approach?
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