Evaluate $g + H + Np$ If $g = \frac{1}{4}$, $ H = − 1.45 H = -1.45 H = − 1.45 [/tex], $n = -\frac{2}{10}$, And $p = -\frac{2}{3}$. Express Your Answer As A Decimal. Use Bar Notation If Necessary.

Introduction

In mathematics, evaluating expressions is a crucial skill that helps us solve problems and understand complex concepts. In this article, we will focus on evaluating the expression $g + h + np$, where $g = \frac{1}{4}$, $h = -1.45$, $n = -\frac{2}{10}$, and $p = -\frac{2}{3}$. We will break down the problem step by step and use bar notation to simplify the expression.

Step 1: Substitute the Given Values

The first step is to substitute the given values of $g$, $h$, $n$, and $p$ into the expression $g + h + np$. This will give us:

$$\frac{1}{4} + (-1.45) + \left(-\frac{2}{10}\right)\left(-\frac{2}{3}\right)$$

Step 2: Simplify the Expression

Now, let's simplify the expression by evaluating the product of $n$ and $p$:

$$\left(-\frac{2}{10}\right)\left(-\frac{2}{3}\right) = \frac{4}{30} = \frac{2}{15}$$

So, the expression becomes:

$$\frac{1}{4} + (-1.45) + \frac{2}{15}$$

Step 3: Convert the Fraction to a Decimal

To make it easier to work with the fractions, let's convert them to decimals:

$$\frac{1}{4} = 0.25$$

$$\frac{2}{15} = 0.1333...$$

So, the expression becomes:

$$0.25 + (-1.45) + 0.1333...$$

Step 4: Add and Subtract the Decimals

Now, let's add and subtract the decimals:

$$0.25 + (-1.45) = -1.20$$

$$-1.20 + 0.1333... = -1.0666...$$

Conclusion

Therefore, the value of $g + h + np$ is:

$$-1.0666...$$

Bar Notation

In some cases, we may need to use bar notation to simplify the expression. Bar notation is a way of writing a repeating decimal as a fraction. For example, the decimal $0.1333...$ can be written as:

$$\frac{1}{7}$$

So, the expression becomes:

$$0.25 + (-1.45) + \frac{1}{7}$$

Evaluating the Expression with Bar Notation

Now, let's evaluate the expression using bar notation:

$$0.25 + (-1.45) = -1.20$$

$$-1.20 + \frac{1}{7} = -1.20 + 0.1428... = -1.0572...$$

Therefore, the value of $g + h + np$ is:

$$-1.0572...$$

Final Answer

In conclusion, the value of $g + h + np$ is:

$$-1.0666...$$

or

$$-1.0572...$$

depending on whether we use bar notation or not.

Discussion

Introduction

In our previous article, we discussed how to evaluate the expression $g + h + np$ using step-by-step instructions and bar notation. In this article, we will answer some frequently asked questions about evaluating expressions and provide additional tips and resources.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions 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: How do I simplify fractions?

A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. We can then divide both numbers by the GCD to simplify the fraction.

For example, let's simplify the fraction $\frac{12}{18}$:

1. Find the GCD of 12 and 18: 6
2. Divide both numbers by 6: $\frac{12}{6} = 2$ and $\frac{18}{6} = 3$
3. Simplify the fraction: $\frac{2}{3}$

Q: How do I convert fractions to decimals?

A: To convert a fraction to a decimal, we can divide the numerator by the denominator.

For example, let's convert the fraction $\frac{3}{4}$ to a decimal:

$$\frac{3}{4} = 3 \div 4 = 0.75$$

Q: What is bar notation?

A: Bar notation is a way of writing a repeating decimal as a fraction. For example, the decimal $0.3333...$ can be written as:

$$\frac{1}{3}$$

Q: How do I evaluate expressions with variables?

A: To evaluate an expression with variables, we need to substitute the values of the variables into the expression.

For example, let's evaluate the expression $2x + 3$, where $x = 4$:

1. Substitute the value of $x$ into the expression: $2(4) + 3$
2. Evaluate the expression: $8 + 3 = 11$

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

A: Here are some common mistakes to avoid when evaluating expressions:

1. Not following the order of operations
2. Not simplifying fractions
3. Not converting fractions to decimals
4. Not using bar notation for repeating decimals
5. Not substituting values of variables into the expression

Conclusion

Evaluating expressions is an essential skill in mathematics that helps us solve problems and understand complex concepts. In this article, we have answered some frequently asked questions about evaluating expressions and provided additional tips and resources. We hope this article has been helpful in improving your understanding of evaluating expressions.

Additional Resources

If you need additional help with evaluating expressions, here are some resources you can use:

1. Khan Academy: Khan Academy has a comprehensive section on evaluating expressions, including video lessons and practice exercises.
2. Mathway: Mathway is an online math problem solver that can help you evaluate expressions and solve math problems.
3. Wolfram Alpha: Wolfram Alpha is a powerful online calculator that can help you evaluate expressions and solve math problems.

Final Tips

Here are some final tips for evaluating expressions:

1. Always follow the order of operations
2. Simplify fractions and convert them to decimals when necessary
3. Use bar notation for repeating decimals
4. Substitute values of variables into the expression
5. Practice, practice, practice!

By following these tips and using the resources provided, you can become proficient in evaluating expressions and solving math problems.