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Simplifying fractions is the process of reducing a fraction to its lowest terms. It involves finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by that number. Understanding how to simplify fractions is vital in mathematics as it can make addition, subtraction, multiplication, and division of fractions much easier and the results more interpretable.

For instance, in the exercise solution, we simplified the fraction \( \frac{84}{140} \) by first identifying the GCD of 84 and 140, which is 28. We then divided both the numerator and the denominator by 28 to obtain \( \frac{3}{5} \) which is the fraction in its simplest form. Simplification does not change the value of the fraction, it only alters its appearance, making it neater and sometimes more useful in further calculations.

Dividing fractions may seem daunting, but it becomes straightforward with a simple trick: multiplying by the reciprocal. The reciprocal of a fraction is a way of finding an equivalent fraction that, when multiplied with the original, equals one.

Let’s take a closer look at our example: To divide \( \frac{4}{7} \) by \( \frac{20}{21} \) we rewrite the division as multiplication by the reciprocal. This means that we keep the first fraction the same (\

In mathematics, an inverse operation is an operation that reverses the effect of another operation. Multiplication and division are inverse operations. This understanding is key to performing division by fractions, as it's easier to multiply than to divide by a fraction.

In our exercise, instead of dividing \( \frac{4}{7} \) by \( \frac{20}{21} \), we multiply \( \frac{4}{7} \) by the inverse (reciprocal) of \( \frac{20}{21} \) which is \( \frac{21}{20} \). This turns the division problem into a multiplication problem, which is simpler to solve. Applying inverse operations correctly is a fundamental part of algebra and greatly simplifies many mathematical processes.