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In mathematics, the reciprocal of a number is its "flipped" version. This means that if your number is a fraction, you simply switch the numerator and the denominator to find its reciprocal. For example, the reciprocal of \(\frac{2}{39}\) is \(\frac{39}{2}\).
This concept is very useful in fraction division. Instead of dividing fractions directly, you multiply the first fraction by the reciprocal of the second fraction.
By using reciprocals, you convert the division problem into a multiplication problem, which is often simpler to solve.

Once you have converted the division into a multiplication problem using the reciprocal, you are ready to multiply fractions. Multiplying fractions is straightforward:

• Multiply the numerators together to get the new numerator.
• Multiply the denominators together to get the new denominator.

So, for \(\frac{4}{9} \times \frac{39}{2}\), you calculate \(4 \times 39\) to get the numerator, and \(9 \times 2\) to get the denominator.
This multiplication results in \(\frac{156}{18}\).
Remember to multiply straight across the top, and then straight across the bottom.

After multiplying, you often need to simplify the fraction you get. Simplifying a fraction involves reducing it to its simplest form.
Look for the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator evenly.
For example, the GCD of 156 and 18 is 6. Divide both the numerator and the denominator by their GCD, so \(\frac{156}{18}\) simplifies to \(\frac{26}{3}\) after division.
Sometimes, the simplified fraction still boils down to a decimal result that doesn’t seem "nice" or round. Double-check your steps when you notice an unexpected result to ensure there's no error in the division or multiplication process.