Which Expression Is Equivalent To The One Shown Below? − 1.5 + 2 5 + ( − 7 ) + 2.6 -1.5+\frac{2}{5}+(-7)+2.6 − 1.5 + 5 2 ​ + ( − 7 ) + 2.6 A. ( − 5.5 + 2.6 ) + 2 5 (-5.5+2.6)+\frac{2}{5} ( − 5.5 + 2.6 ) + 5 2 ​ B. ( − 8.5 + 2.6 ) + 2 5 (-8.5+2.6)+\frac{2}{5} ( − 8.5 + 2.6 ) + 5 2 ​ C. ( − 1 5 + 2 5 ) + ( − 4.4 \left(-\frac{1}{5}+\frac{2}{5}\right)+(-4.4 ( − 5 1 ​ + 5 2 ​ ) + ( − 4.4 ] D.

Understanding the Problem

When dealing with algebraic expressions, it's essential to simplify them to make calculations easier and more manageable. In this article, we'll explore how to simplify the given expression: $-1.5+\frac{2}{5}+(-7)+2.6$. We'll examine each option and determine which one is equivalent to the original expression.

Breaking Down the Expression

To simplify the expression, we need to follow the order of operations (PEMDAS):

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

Option A: $(-5.5+2.6)+\frac{2}{5}$

Let's start by evaluating the expression inside the parentheses: $-5.5+2.6$. To do this, we'll subtract 5.5 from 2.6:

$-5.5+2.6 = -2.9$

Now, we can rewrite the expression as:

$-2.9+\frac{2}{5}$

To add a fraction to a decimal, we need to convert the fraction to a decimal with the same denominator. In this case, we can convert $\frac{2}{5}$ to a decimal by dividing the numerator by the denominator:

$\frac{2}{5} = 0.4$

Now, we can rewrite the expression as:

$-2.9+0.4$

To add these decimals, we'll align the decimal points and add the numbers:

$-2.9+0.4 = -2.5$

So, option A simplifies to $-2.5$.

Option B: $(-8.5+2.6)+\frac{2}{5}$

Let's start by evaluating the expression inside the parentheses: $-8.5+2.6$. To do this, we'll subtract 8.5 from 2.6:

$-8.5+2.6 = -5.9$

Now, we can rewrite the expression as:

$-5.9+\frac{2}{5}$

To add a fraction to a decimal, we need to convert the fraction to a decimal with the same denominator. In this case, we can convert $\frac{2}{5}$ to a decimal by dividing the numerator by the denominator:

$\frac{2}{5} = 0.4$

Now, we can rewrite the expression as:

$-5.9+0.4$

To add these decimals, we'll align the decimal points and add the numbers:

$-5.9+0.4 = -5.5$

So, option B simplifies to $-5.5$.

Option C: $\left(-\frac{1}{5}+\frac{2}{5}\right)+(-4.4)$

Let's start by evaluating the expression inside the parentheses: $-\frac{1}{5}+\frac{2}{5}$. To do this, we'll add the fractions by finding a common denominator:

$-\frac{1}{5}+\frac{2}{5} = \frac{1}{5}$

Now, we can rewrite the expression as:

$\frac{1}{5}+(-4.4)$

To add a fraction to a decimal, we need to convert the fraction to a decimal with the same denominator. In this case, we can convert $\frac{1}{5}$ to a decimal by dividing the numerator by the denominator:

$\frac{1}{5} = 0.2$

Now, we can rewrite the expression as:

$0.2+(-4.4)$

To add these decimals, we'll align the decimal points and add the numbers:

$0.2+(-4.4) = -4.2$

So, option C simplifies to $-4.2$.

Option D:

Unfortunately, option D is not provided, so we cannot evaluate it.

Conclusion

In conclusion, the correct answer is option B: $(-8.5+2.6)+\frac{2}{5}$. This option simplifies to $-5.5$, which is the same as the original expression.

Tips and Tricks

When simplifying algebraic expressions, it's essential to follow the order of operations (PEMDAS). This will ensure that you evaluate the expressions correctly and avoid any errors.

Additionally, when adding fractions to decimals, make sure to convert the fraction to a decimal with the same denominator. This will make it easier to add the numbers.

By following these tips and tricks, you'll be able to simplify algebraic expressions with ease and confidence.

Common Mistakes to Avoid

When simplifying algebraic expressions, there are several common mistakes to avoid:

• Not following the order of operations (PEMDAS)
• Not converting fractions to decimals with the same denominator
• Not aligning decimal points when adding decimals
• Not evaluating expressions inside parentheses correctly

By avoiding these common mistakes, you'll be able to simplify algebraic expressions accurately and efficiently.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. For example:

• In finance, simplifying algebraic expressions can help you calculate interest rates and investment returns.
• In science, simplifying algebraic expressions can help you model complex systems and make predictions.
• In engineering, simplifying algebraic expressions can help you design and optimize systems.

By mastering the art of simplifying algebraic expressions, you'll be able to tackle complex problems and make informed decisions in a variety of fields.

Final Thoughts

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying algebraic expressions. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next.
• Multiplication and Division: Evaluate multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify expressions with fractions and decimals?

A: When simplifying expressions with fractions and decimals, you need to convert the fraction to a decimal with the same denominator. For example, if you have the expression $-\frac{1}{5}+2.6$, you can convert the fraction to a decimal by dividing the numerator by the denominator:

$-\frac{1}{5} = -0.2$

Now, you can rewrite the expression as:

$-0.2+2.6$

To add these decimals, you'll align the decimal points and add the numbers:

$-0.2+2.6 = 2.4$

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. For example, $\frac{1}{2}$ represents one half of a whole. A decimal, on the other hand, is a way of expressing a fraction as a number with a decimal point. For example, $0.5$ represents one half of a whole.

Q: How do I simplify expressions with exponents?

A: When simplifying expressions with exponents, you need to evaluate the exponential expressions first. For example, if you have the expression $2^3+4$, you can evaluate the exponential expression first:

$2^3 = 8$

Now, you can rewrite the expression as:

$8+4$

To add these numbers, you'll simply add them together:

$8+4 = 12$

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. For example, $x$ is a variable. A constant, on the other hand, is a value that does not change. For example, $5$ is a constant.

Q: How do I simplify expressions with variables and constants?

A: When simplifying expressions with variables and constants, you need to combine like terms. For example, if you have the expression $2x+5+3x$, you can combine the like terms:

$2x+3x = 5x$

Now, you can rewrite the expression as:

$5x+5$

To simplify this expression, you can combine the constants:

$5x+5 = 5(x+1)$

Q: What is the difference between a linear expression and a quadratic expression?

A: A linear expression is an expression that can be written in the form $ax+b$, where $a$ and $b$ are constants. For example, $2x+3$ is a linear expression. A quadratic expression, on the other hand, is an expression that can be written in the form $ax^2+bx+c$, where $a$, $b$, and $c$ are constants. For example, $x^2+2x+1$ is a quadratic expression.

Q: How do I simplify expressions with linear and quadratic terms?

A: When simplifying expressions with linear and quadratic terms, you need to combine like terms. For example, if you have the expression $x^2+2x+1+3x^2$, you can combine the like terms:

$x^2+3x^2 = 4x^2$

Now, you can rewrite the expression as:

$4x^2+2x+1$

To simplify this expression, you can combine the constants:

$4x^2+2x+1 = 4x^2+2x+1$

Q: What is the difference between a rational expression and an irrational expression?

A: A rational expression is an expression that can be written in the form $\frac{p}{q}$, where $p$ and $q$ are polynomials. For example, $\frac{x+1}{x-1}$ is a rational expression. An irrational expression, on the other hand, is an expression that cannot be written in the form $\frac{p}{q}$, where $p$ and $q$ are polynomials. For example, $\sqrt{x}$ is an irrational expression.

Q: How do I simplify expressions with rational and irrational terms?

A: When simplifying expressions with rational and irrational terms, you need to combine like terms. For example, if you have the expression $\frac{x+1}{x-1}+\sqrt{x}$, you can combine the like terms:

$\frac{x+1}{x-1}+\sqrt{x}$

To simplify this expression, you can rewrite it as:

$\frac{x+1}{x-1}+\sqrt{x} = \frac{x+1}{x-1}+\sqrt{x}$

Note that this expression cannot be simplified further.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill that can be applied in a variety of contexts. By following the order of operations (PEMDAS) and avoiding common mistakes, you'll be able to simplify expressions with ease and confidence. Remember to practice regularly and apply your skills to real-world problems to become a master of algebraic expression simplification.