Simplifying the Expression: 1/15 (15x - 40) - 1/3 (15x - 2y)

As a high school mathematics teacher, I often encounter questions where students are asked to simplify algebraic expressions. One such expression is: 1/15 (15x - 40) - 1/3 (15x - 2y). Let's break down the process of simplifying this expression step by step.

Step 1: Distribute the coefficients

The first step in simplifying this expression is to distribute the coefficients. This means that we will multiply the terms inside the parentheses by the coefficients outside the parentheses.

For the first term, 1/15 (15x - 40), we have:

• 1/15 × 15x = x
• 1/15 × (-40) = -8/3

For the second term, 1/3 (15x - 2y), we have:

• 1/3 × 15x = 5x
• 1/3 × (-2y) = -2/3y

Step 2: Combine like terms

Now that we have distributed the coefficients, we can combine the like terms. In this case, the like terms are the x terms and the constant terms.

The expression becomes:

• x - 8/3 - 5x + 2/3y

Step 3: Simplify the expression

To simplify the expression further, we can combine the x terms and the constant terms.

The x terms become:

• x - 5x = -4x

The constant terms become:

• -8/3 + 2/3y = -8/3 + 2/3y

Putting it all together, the simplified expression is:

• -4x - 8/3 + 2/3y

Therefore, the simplified expression is -4x - 8/3 + 2/3y.

I hope this step-by-step explanation helps you understand the process of simplifying algebraic expressions. If you have any further questions, feel free to ask!