Which Expression Has The Same Value As The One Below? + ( − 32 +(-32 + ( − 32 ]A. 22 + ( − 22 ) + ( − 10 22+(-22)+(-10 22 + ( − 22 ) + ( − 10 ] B. 22 + ( 22 ) + ( − 10 22+(22)+(-10 22 + ( 22 ) + ( − 10 ] C. 22 + ( − 22 ) + ( 10 22+(-22)+(10 22 + ( − 22 ) + ( 10 ] D. 22 + 0 + 32 22+0+32 22 + 0 + 32

Understanding the Problem

In this article, we will explore the concept of simplifying algebraic expressions and apply it to a specific problem. The problem at hand is to find the expression that has the same value as the given expression: $22+(-32)$. We will analyze each option and determine which one is equivalent to the given expression.

The Given Expression

The given expression is $22+(-32)$. To simplify this expression, we need to combine the two terms. When we add a positive number and a negative number, we subtract the absolute value of the negative number from the positive number.

Simplifying the Given Expression

Let's simplify the given expression step by step:

1. The absolute value of -32 is 32.
2. To simplify the expression, we subtract 32 from 22: $22-32=-10$.

Therefore, the simplified form of the given expression is $-10$.

Analyzing the Options

Now that we have simplified the given expression, let's analyze each option and determine which one is equivalent to the given expression.

Option A: $22+(-22)+(-10)$

To simplify this expression, we need to combine the three terms. When we add a positive number and a negative number, we subtract the absolute value of the negative number from the positive number.

1. The absolute value of -22 is 22.
2. To simplify the expression, we subtract 22 from 22: $22-22=0$.
3. The expression now becomes $0+(-10)=-10$.

Therefore, option A is equivalent to the given expression.

Option B: $22+(22)+(-10)$

To simplify this expression, we need to combine the three terms. When we add a positive number and a positive number, we add the two numbers.

1. The expression now becomes $22+22=44$.
2. The expression now becomes $44+(-10)=-6$.

Therefore, option B is not equivalent to the given expression.

Option C: $22+(-22)+(10)$

To simplify this expression, we need to combine the three terms. When we add a positive number and a negative number, we subtract the absolute value of the negative number from the positive number.

1. The absolute value of -22 is 22.
2. To simplify the expression, we subtract 22 from 22: $22-22=0$.
3. The expression now becomes $0+(10)=10$.

Therefore, option C is not equivalent to the given expression.

Option D: $22+0+32$

To simplify this expression, we need to combine the three terms. When we add a positive number and a positive number, we add the two numbers.

1. The expression now becomes $22+32=54$.

Therefore, option D is not equivalent to the given expression.

Conclusion

In conclusion, the expression that has the same value as the given expression $22+(-32)$ is option A: $22+(-22)+(-10)$. This expression simplifies to $-10$, which is equivalent to the given expression.

Tips and Tricks

When simplifying algebraic expressions, it's essential 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 any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following the order of operations, you can simplify complex algebraic expressions and arrive at the correct solution.

Common Mistakes to Avoid

When simplifying algebraic expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

1. Not following the order of operations: Make sure to follow the order of operations (PEMDAS) to ensure that you simplify the expression correctly.
2. Not combining like terms: Combine like terms to simplify the expression.
3. Not evaluating expressions inside parentheses: Evaluate expressions inside parentheses first to ensure that you simplify the expression correctly.

By avoiding these common mistakes, you can simplify algebraic expressions with confidence and arrive at the correct solution.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. Here are a few examples:

1. Finance: Algebraic expressions are used to calculate interest rates, investment returns, and other financial metrics.
2. Science: Algebraic expressions are used to model physical systems, such as the motion of objects and the behavior of electrical circuits.
3. Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and buildings.

By understanding how to simplify algebraic expressions, you can apply this knowledge to real-world problems and make informed decisions.

Conclusion

Frequently Asked Questions

In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What is an algebraic expression?

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

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 simplifying an algebraic 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 an algebraic expression?

A: To simplify an algebraic expression, follow these steps:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponential expressions.
3. Evaluate any multiplication and division operations from left to right.
4. Evaluate any addition and subtraction operations from left to right.
5. Combine like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms because they both have the variable x and the same exponent (1).

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, 2x + 4x = 6x.

Q: What is a coefficient?

A: A coefficient is a number that is multiplied by a variable. For example, in the expression 2x, the coefficient is 2.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, follow these steps:

1. Simplify the fractions by finding the greatest common divisor (GCD) of the numerator and denominator.
2. Combine like terms.
3. Simplify the expression.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, use the following steps:

1. List the factors of each number.
2. Identify the common factors.
3. Multiply the common factors to find the GCD.

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

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

1. Not following the order of operations.
2. Not combining like terms.
3. Not evaluating expressions inside parentheses.
4. Not simplifying fractions.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by:

1. Working through practice problems.
2. Using online resources, such as algebraic expression simplifiers.
3. Asking a teacher or tutor for help.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill that has numerous real-world applications. By following the order of operations and combining like terms, you can simplify complex expressions and arrive at the correct solution. Remember to avoid common mistakes, such as not following the order of operations and not combining like terms. With practice and patience, you can become proficient in simplifying algebraic expressions and apply this knowledge to real-world problems.