Evaluate The Expression $8a - \frac{8a^2 - 3c}{a}$ Given $a = 15$ And \$c = 12$[/tex\].

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Introduction

In algebra, evaluating expressions is a crucial skill that helps us simplify complex mathematical statements. Given an algebraic expression and specific values for the variables, we can substitute these values into the expression and simplify it to obtain a numerical result. In this article, we will evaluate the expression $8a - \frac{8a^2 - 3c}{a}$ given $a = 15$ and $c = 12$. We will break down the process into manageable steps and provide a clear explanation of each step.

Step 1: Substitute the Given Values

The first step in evaluating the expression is to substitute the given values of $a$ and $c$ into the expression. We are given that $a = 15$ and $c = 12$. Substituting these values into the expression, we get:

8(15)−8(15)2−3(12)158(15) - \frac{8(15)^2 - 3(12)}{15}

Step 2: Simplify the Expression

Now that we have substituted the given values, we can simplify the expression by performing the arithmetic operations. Let's start by simplifying the terms inside the parentheses:

8(15)=1208(15) = 120

8(15)2=8(225)=18008(15)^2 = 8(225) = 1800

3(12)=363(12) = 36

Substituting these simplified values back into the expression, we get:

120−1800−3615120 - \frac{1800 - 36}{15}

Step 3: Simplify the Fraction

The next step is to simplify the fraction by performing the subtraction in the numerator:

1800−36=17641800 - 36 = 1764

Now, we can rewrite the expression as:

120−176415120 - \frac{1764}{15}

Step 4: Simplify the Fraction Further

To simplify the fraction further, we can divide the numerator by the denominator:

176415=117.6\frac{1764}{15} = 117.6

Now, we can rewrite the expression as:

120−117.6120 - 117.6

Step 5: Evaluate the Expression

The final step is to evaluate the expression by performing the subtraction:

120−117.6=2.4120 - 117.6 = 2.4

Therefore, the value of the expression $8a - \frac{8a^2 - 3c}{a}$ given $a = 15$ and $c = 12$ is $2.4$.

Conclusion

Evaluating algebraic expressions is an essential skill in mathematics that helps us simplify complex mathematical statements. By following the steps outlined in this article, we can evaluate expressions with ease. Remember to substitute the given values, simplify the expression, and perform the arithmetic operations to obtain the final result.

Example Use Cases

Evaluating algebraic expressions has numerous applications in various fields, including:

  • Science: Evaluating expressions helps scientists model real-world phenomena, such as the motion of objects or the behavior of chemical reactions.
  • Engineering: Evaluating expressions is crucial in engineering, where it helps designers and engineers create models of complex systems, such as bridges or buildings.
  • Finance: Evaluating expressions is essential in finance, where it helps investors and analysts model financial markets and make informed investment decisions.

Tips and Tricks

Here are some tips and tricks to help you evaluate algebraic expressions like a pro:

  • Read the expression carefully: Before starting to evaluate the expression, read it carefully to understand what it represents.
  • Substitute values carefully: When substituting values into the expression, make sure to use the correct values and units.
  • Simplify the expression step-by-step: Simplify the expression step-by-step, starting with the innermost parentheses and working your way outwards.
  • Check your work: Finally, check your work by plugging the final result back into the original expression to ensure that it is correct.

Introduction

In our previous article, we evaluated the expression $8a - \frac{8a^2 - 3c}{a}$ given $a = 15$ and $c = 12$. In this article, we will answer some frequently asked questions about evaluating algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical statement that contains variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the given values of the variables into the expression, simplify the expression, and perform the arithmetic operations to obtain the final result.

Q: What are the steps to evaluate an algebraic expression?

A: The steps to evaluate an algebraic expression are:

  1. Substitute the given values: Substitute the given values of the variables into the expression.
  2. Simplify the expression: Simplify the expression by performing the arithmetic operations.
  3. Check your work: Finally, check your work by plugging the final result back into the original expression to ensure that it is correct.

Q: What are some common mistakes to avoid when evaluating algebraic expressions?

A: Some common mistakes to avoid when evaluating algebraic expressions include:

  • Not substituting the correct values: Make sure to substitute the correct values of the variables into the expression.
  • Not simplifying the expression correctly: Simplify the expression step-by-step, starting with the innermost parentheses and working your way outwards.
  • Not checking your work: Finally, check your work by plugging the final result back into the original expression to ensure that it is correct.

Q: How do I handle fractions in algebraic expressions?

A: When handling fractions in algebraic expressions, you need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expressions inside the parentheses first.
  2. Exponents: Evaluate any exponents next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to evaluate algebraic expressions?

A: Yes, you can use a calculator to evaluate algebraic expressions. However, make sure to check your work by plugging the final result back into the original expression to ensure that it is correct.

Q: How do I evaluate algebraic expressions with negative numbers?

A: When evaluating algebraic expressions with negative numbers, you need to follow the same steps as before:

  1. Substitute the given values: Substitute the given values of the variables into the expression.
  2. Simplify the expression: Simplify the expression by performing the arithmetic operations.
  3. Check your work: Finally, check your work by plugging the final result back into the original expression to ensure that it is correct.

Conclusion

Evaluating algebraic expressions is an essential skill in mathematics that helps us simplify complex mathematical statements. By following the steps outlined in this article, you can evaluate expressions with ease. Remember to substitute the given values, simplify the expression, and perform the arithmetic operations to obtain the final result.

Example Use Cases

Evaluating algebraic expressions has numerous applications in various fields, including:

  • Science: Evaluating expressions helps scientists model real-world phenomena, such as the motion of objects or the behavior of chemical reactions.
  • Engineering: Evaluating expressions is crucial in engineering, where it helps designers and engineers create models of complex systems, such as bridges or buildings.
  • Finance: Evaluating expressions is essential in finance, where it helps investors and analysts model financial markets and make informed investment decisions.

Tips and Tricks

Here are some tips and tricks to help you evaluate algebraic expressions like a pro:

  • Read the expression carefully: Before starting to evaluate the expression, read it carefully to understand what it represents.
  • Substitute values carefully: When substituting values into the expression, make sure to use the correct values and units.
  • Simplify the expression step-by-step: Simplify the expression step-by-step, starting with the innermost parentheses and working your way outwards.
  • Check your work: Finally, check your work by plugging the final result back into the original expression to ensure that it is correct.

By following these tips and tricks, you can evaluate algebraic expressions with ease and confidence.