When simplifying fractions, which operation is often used?

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When simplifying fractions, factoring out the greatest common divisor (GCD) is a fundamental operation that is often employed. The GCD is the largest number that can evenly divide both the numerator and the denominator. By dividing both parts of the fraction by this number, you reduce the fraction to its simplest form.

For example, in the fraction 8/12, the GCD of 8 and 12 is 4. By dividing both the numerator and the denominator by 4, you simplify the fraction to 2/3. This process ensures that the fraction retains its value while being represented in a more concise format.

Other options do not effectively simplify fractions. For instance, adding the numerator and denominator does not create a simplified form but rather changes the value of the fraction. Similarly, multiplying both the numerator and denominator by 10 will only change the fraction’s representation without simplifying it. Subtracting the numerator from the denominator would alter the original fraction, leading to a completely different value. Thus, using the GCD is the only viable operation for simplifying fractions properly.

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