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Simplifying expressions is a crucial skill in algebra. It involves making an expression easier to understand or solve by combining like terms, applying properties, and removing any unnecessary parts. For example, in this exercise, you need to simplify the expression using the distributive property. Let's break it down step by step.
First, identify the expression within the parentheses, which is \( \frac{5}{9} y - \frac{1}{3} \).
Next, apply the distributive property by multiplying 9 by each term inside the parentheses. You will multiply 9 by \( \frac{5}{9} y \) and \( \frac{1}{3} \).
Finally, simplify each term individually: \( 9 \times \frac{5}{9} y \) simplifies to \( 5y \), and \( 9 \times \frac{1}{3} \) simplifies to 3.
The final simplified expression is \[ 5y - 3 \].

Multiplying fractions is another vital concept in algebra. When you multiply fractions, you multiply the numerators and the denominators. For example, to simplify \( 9 \times \frac{5}{9} y \), you multiply 9 (the numerator) by 5 (the numerator of the fraction), and then put the result over 9 (the denominator). This gives you \( \frac{45}{9} y \).
Breaking it down:

• Multiply the numerators: 9 and 5, which equals 45.
• Place this result over the original denominator, 9.
• Divide 45 by 9, which simplifies to 5. Thus, \( 9 \times \frac{5}{9} = 5 \).

This simplification shows how multiplying fractions can be straightforward when you follow these steps.
Also, understanding how to multiply fractions makes it easier to handle algebraic expressions and simplify them effectively.

Algebraic expressions are combinations of numbers, variables, and operations. They represent real-world scenarios and mathematical problems. In this exercise, the algebraic expression is simplified using the distributive property and multiplying fractions.
To understand the expression better, focus on:

• Identifying variables and constants: In this case, \( y \) is the variable, and the fractions \( \frac{5}{9} \) and \( \frac{1}{3} \) are constants.
• Applying the distributive property: Multiply 9 with each term inside the parentheses.
• Simplifying: Multiply and reduce fractions to their simplest form.

Let's revisit our example: The original expression is \( 9 \left( \frac{5}{9} y - \frac{1}{3} \right) \).
After applying the distributive property:
\( 9 \times \frac{5}{9} y - 9 \times \frac{1}{3} \).
Simplify each term to get:
\( 5y - 3 \).
Understanding these steps helps you manage more complex algebraic expressions with confidence.