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Understanding how to invert fractions, also known as finding the reciprocal, is crucial in many math problems.
The reciprocal of a fraction is found by switching the numerator (top number) with the denominator (bottom number).
For example, the reciprocal of \(\frac{1}{2}\) is \(\frac{2}{1}\) or 2.
Similarly, for \(\frac{2}{3}\), the reciprocal is \(\frac{3}{2}\). This operation is often required when dividing fractions or solving equations involving fractions.
Always remember: the reciprocal of a fraction \(\frac{a}{b}\) is simply \(\frac{b}{a}\).
It helps to mentally note this flipping operation whenever you encounter the term 'inverse' with fractions.

When adding fractions, ensure they have the same denominator, called a common denominator.
In the exercise, after finding the reciprocals, you get 2 and \(\frac{3}{2}\).
To add these easily, convert 2 into a fraction. It can be written as \(\frac{4}{2}\), because multiplying the numerator and denominator by the same number doesn't change its value.
Now, adding \(\frac{4}{2}\) and \(\frac{3}{2}\) becomes straightforward:
\(\frac{4}{2} + \frac{3}{2} = \frac{7}{2}\).
The key here is converting whole numbers into fractions with the same denominator to simplify the addition process.

A common denominator is essential for adding or subtracting fractions.
It is a shared multiple of both fractions' denominators.
In the given exercise, you need to add 2 (written as \(\frac{4}{2}\)) and \(\frac{3}{2}\).
Notice both fractions now have the denominator 2, making them compatible for direct addition.
To find a common denominator generally, you can use the Least Common Multiple (LCM) of the denominators.
For instance, adding \(\frac{1}{4}\) and \(\frac{1}{6}\), the LCM of 4 and 6 is 12. So you'd convert: \(\frac{1}{4} = \frac{3}{12}\) and \(\frac{1}{6} = \frac{2}{12}\), and then add: \(\frac{3}{12} + \frac{2}{12} = \frac{5}{12}\).
Always ensure the fractions have a common denominator to make addition or subtraction smooth and accurate.