91Ó°ÊÓ

When multiplying fractions, it is essential first to understand the process fully. In the given problem, we need to multiply the fraction \(\frac{6}{5}\) by the whole number 15.
Here is a straightforward approach:

• Write down the fractions or the whole number multiplied by writing 1 in the denominator, which simplifies it to just 15 (as the whole number). It becomes \(\frac{15}{1}\).
• Next, follow the rule of multiplying fractions by multiplying the numerators with each other and the denominators with each other.
• In this case, multiply 6 (numerator of the first fraction) by 15
  and 5 (denominator of the first fraction) by 1:
  \( \frac{6 \times 15}{5 \times 1} = \frac{90}{5}\).

This results in getting you the right multiplication result before simplification.

Simplifying fractions is an important step in fraction multiplication. Once you have multiplied the fractions, you need to check whether the resulting fraction can be reduced to a simpler form.
Here’s how to simplify the fraction \(\frac{90}{5}\):

• Look for common factors in the numerator and the denominator. The common factor of 90 (numerator) and 5 (denominator) is 5.
• Divide the numerator by the common factor: \ 90 ÷ 5 = 18\
• Divide the denominator by the same common factor: \ 5 ÷ 5 = 1 \

This simplifies the fraction to \(\frac{18}{1}\), which in reality is simply 18. Thus, simplification helps in reducing the complexity and making the fraction much simpler and easier to understand.

Understanding the components of a fraction is crucial for performing operations with them.

The Numerator: This is the top part of a fraction. It shows how many parts of a whole are being considered. In the exercise, for \( \frac{6}{5}\), 6 is the numerator.

The Denominator: This is the bottom part of a fraction. It indicates the total number of equal parts the whole is divided into. For \( \frac{6}{5}\), 5 is the denominator.
By multiplying the numerators and denominators separately, as shown before, we combine these parts effectively:

• Numerators combined: \(6 \times 15 = 90\)
• Denominators combined: \(5 \times 1 = 5\)

This highlighting of numerator and denominator helps in clearly visualizing why we get \( \frac{90}{5} \) in the process of fraction multiplication. With that clear understanding, further simplifying of fractions becomes much more intuitive.