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The distributive property is an essential concept in algebra. It helps simplify expressions involving multiplication distributed across addition or subtraction inside parentheses. This property states that multiplying a single term by terms inside a bracket applies to each term individually.

For example, in the expression \( a(b + c) \), the distributive property would allow you to rewrite this as \( ab + ac \).

This concept was used in the solution to handle the multiplication of 15 by the fraction \( \frac{4}{15}w \). Here, 15 is outside the parenthesis and thus gets multiplied with both terms within, simplifying through the cancellation of the common factor in the fraction.

Working with fractions can sometimes be confusing, but understanding the basics can make it much simpler. In the context of multiplication, it is essential to remember that every number can be written as a fraction by using 1 as its denominator.

When multiplying a whole number by a fraction as seen in \( 15 \times \frac{4}{15} \), you treat the whole number as \( \frac{15}{1} \). Multiplying fractions involves multiplying the numerators together and the denominators together. So, here it results in:

• Numerator: \( 15 \times 4 \)
• Denominator: \( 1 \times 15 \)

This simplifies to \( \frac{60}{15} \), and then further reduces to 4 after cancelling out common factors.

Coefficient multiplication occurs when a number (coefficient) is multiplied by a variable term, often involving other numbers or fractions. In our exercise, the coefficient 15 is multiplied by the term \( \frac{4}{15}w \).

The task is to find a product where the coefficient 15 multiplies the fraction. This is accomplished by multiplying directly across both the top (numerator) and bottom (denominator) of the fraction where possible.

Seeing common factors is crucial. Here, the 15 in the fraction's denominator cancels out with the 15, simplifying it to just 4. This leaves the multiplication of 4 and \( w \), resulting in \( 4w \). Since the coefficient simplifies entirely, you're left with a neater expression that is straightforward and easy to manage.