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Simplifying fractions is an essential step in fraction multiplication.
Once you have a resulting fraction from a multiplication problem, you should always check if it can be simplified.
Simplifying a fraction means making the numerator and the denominator as small as possible, while still keeping the value of the fraction the same.
To do this, find the greatest common divisor of both parts of the fraction and divide both by this number.
For example, in the problem above, we multiplied the fractions and got \( \frac{300}{45} \). This fraction is not in its simplest form.
We found the greatest common divisor of 300 and 45, which is 15.
Then, \( \frac{300}{45} \) was simplified to \( \frac{20}{3} \). Simplifying helps in making fractions easier to read and work with.

The Greatest Common Divisor (GCD) is the largest number that divides two numbers without leaving a remainder.
When simplifying fractions, finding the GCD is crucial.
Using the GCD ensures that the fraction is reduced to its simplest form.
To determine the GCD of two numbers, you can use various methods, such as:
1. **Listing Factors:** Write down all factors of both numbers and find the greatest common one.
2. **Prime Factorization:** Break down both numbers into their prime factors and multiply the common factors.
3. **Euclidean Algorithm:** Repeatedly subtract or divide the larger number by the smaller number until reaching the GCD.
In our example, the GCD of 300 and 45 is 15.
Prime factorizing, 300 is \( 2^2 \times 3 \times 5^2 \) and 45 is \( 3^2 \times 5 \).
The common prime factors are 3 and 5. Hence, GCD is \( 3 \times 5 = 15 \).

Understanding numerators and denominators is key to mastering fractions.
The **numerator** is the top part of a fraction and represents how many parts you have.
In the problem, the numerators were 50 and 6.
When multiplying fractions, you first multiply the numerators together.
The **denominator** is the bottom part of a fraction and shows how many parts make up a whole.
For our example, the denominators were 9 and 5.
You multiply these together next.
So, multiplying \( \frac{50}{9} \) and \( \frac{6}{5} \) means \( 50 \times 6 \) gives us 300, and \( 9 \times 5 \) gives us 45.
This product \( \frac{300}{45} \) is then simplified by dividing the numerator and denominator by their GCD, 15, resulting in \( \frac{20}{3} \).