Evaluating Algebraic Expressions -5/9x And -1/15y

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Hey guys! Today, we're diving into the exciting world of algebraic expressions and learning how to evaluate them. Specifically, we'll be tackling two expressions: -5/9x when x = -18, and -1/15y when y = -5. Don't worry, it sounds more complicated than it actually is. We'll break it down step by step, so you'll be a pro in no time! Let's get started!

Understanding Algebraic Expressions

Before we jump into the calculations, let's quickly recap what algebraic expressions are all about. Simply put, an algebraic expression is a combination of numbers, variables, and mathematical operations (like addition, subtraction, multiplication, and division). Variables are those letters (like x and y) that represent unknown values. Evaluating an expression means finding its numerical value by substituting the given values for the variables and performing the operations.

In our case, we have two expressions:

  1. -5/9x
  2. -1/15y

We are also given the values for the variables:

  • x = -18
  • y = -5

Our mission, should we choose to accept it (and we do!), is to substitute these values into the expressions and simplify them to get a numerical answer. So, let's put on our math hats and get to work!

The Importance of Understanding Order of Operations

Before we dive into the specifics, it's crucial to remember the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This order ensures we solve expressions correctly. In our examples, we primarily deal with multiplication, but remembering PEMDAS is vital for more complex problems.

Evaluating -5/9x when x = -18

Alright, let's start with the first expression: -5/9x when x = -18. This might look a bit intimidating with the fraction and the negative numbers, but trust me, it's totally manageable. The key here is to remember that -5/9x actually means -5/9 multiplied by x. So, let's rewrite the expression with the multiplication symbol to make it clearer:

-5/9 * x

Now, we substitute the value of x, which is -18:

-5/9 * (-18)

Okay, we've got a fraction multiplied by a whole number. How do we tackle this? Well, we can think of -18 as a fraction as well: -18/1. This makes the multiplication a bit easier to visualize:

-5/9 * (-18/1)

To multiply fractions, we simply multiply the numerators (the top numbers) and the denominators (the bottom numbers):

(-5 * -18) / (9 * 1)

Now, let's do the multiplication:

90 / 9

And finally, we simplify the fraction by dividing 90 by 9:

10

So, the value of the expression -5/9x when x = -18 is 10. Awesome! We've conquered the first one. Let's move on to the next expression.

Step-by-Step Breakdown of Evaluating -5/9x when x = -18

  1. Substitute the value of x: Replace x with -18 in the expression -5/9x, resulting in -5/9 * (-18).
  2. Rewrite as a fraction: Think of -18 as -18/1, making the expression -5/9 * (-18/1).
  3. Multiply numerators and denominators: Multiply the top numbers (-5 and -18) and the bottom numbers (9 and 1), giving us (90) / (9).
  4. Simplify: Divide 90 by 9 to get the final answer, which is 10.

Evaluating -1/15y when y = -5

Now, let's tackle the second expression: -1/15y when y = -5. This one is very similar to the first, so we can use the same steps and strategies. Again, remember that -1/15y means -1/15 multiplied by y. Let's rewrite the expression:

-1/15 * y

Substitute the value of y, which is -5:

-1/15 * (-5)

Just like before, let's think of -5 as a fraction: -5/1

-1/15 * (-5/1)

Multiply the numerators and the denominators:

(-1 * -5) / (15 * 1)

Perform the multiplication:

5 / 15

Now, we need to simplify this fraction. Both 5 and 15 are divisible by 5, so let's divide both the numerator and the denominator by 5:

(5 / 5) / (15 / 5)

This gives us:

1 / 3

So, the value of the expression -1/15y when y = -5 is 1/3. Fantastic! We've solved both expressions.

Step-by-Step Breakdown of Evaluating -1/15y when y = -5

  1. Substitute the value of y: Replace y with -5 in the expression -1/15y, resulting in -1/15 * (-5).
  2. Rewrite as a fraction: Think of -5 as -5/1, making the expression -1/15 * (-5/1).
  3. Multiply numerators and denominators: Multiply the top numbers (-1 and -5) and the bottom numbers (15 and 1), giving us (5) / (15).
  4. Simplify: Divide both the numerator and the denominator by their greatest common divisor, which is 5, resulting in 1/3.

Key Takeaways

Let's recap the key things we learned today:

  • Algebraic expressions are combinations of numbers, variables, and operations.
  • Evaluating expressions means finding their numerical value by substituting values for variables.
  • Remember the order of operations (PEMDAS).
  • Multiplying fractions involves multiplying the numerators and the denominators.
  • Simplifying fractions often involves dividing both the numerator and denominator by their greatest common factor.

Practice Makes Perfect

Now that we've walked through these examples, the best way to solidify your understanding is to practice! Try evaluating similar expressions with different values for the variables. You can even create your own expressions and challenge yourself. The more you practice, the more confident you'll become in your algebra skills.

Conclusion

And there you have it! We've successfully evaluated the expressions -5/9x when x = -18 and -1/15y when y = -5. We broke down each step, so you can see exactly how it's done. Remember, algebra might seem tricky at first, but with a little practice and a clear understanding of the fundamentals, you can conquer any expression that comes your way. Keep up the great work, guys!

Remember, the key to mastering math is practice. Try similar problems, and don't hesitate to ask for help if you get stuck. Keep practicing, and you'll be an algebra whiz in no time! This detailed breakdown should provide a comprehensive understanding of how to evaluate algebraic expressions. Good luck, and happy calculating!