Add The Following: 19 + ( − 7 19 + (-7 19 + ( − 7 ] 19 + ( − 7 ) = 19 + (-7) = 19 + ( − 7 ) =

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Introduction

In mathematics, algebraic expressions are a fundamental concept that helps us solve equations and represent real-world problems. One of the essential skills in algebra is simplifying expressions by combining like terms. In this article, we will focus on simplifying a simple algebraic expression: 19+(−7)19 + (-7).

Understanding the Expression

The given expression is 19+(−7)19 + (-7). To simplify this expression, we need to understand the concept of negative numbers and how they interact with positive numbers. A negative number is a number that is less than zero, and it is denoted by a minus sign (-). When we add a negative number to a positive number, we need to subtract the absolute value of the negative number from the positive number.

Simplifying the Expression

Now, let's simplify the expression 19+(−7)19 + (-7). To do this, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expression inside the parentheses: (−7)(-7).
  2. Add the result to 19.

The absolute value of -7 is 7, so we can rewrite the expression as:

19+(−7)=19−719 + (-7) = 19 - 7

Using the Commutative Property

The commutative property of addition states that the order of the numbers being added does not change the result. In other words, a+b=b+aa + b = b + a. We can use this property to rewrite the expression as:

19−7=7−1919 - 7 = 7 - 19

Simplifying the Expression Further

Now, let's simplify the expression 7−197 - 19. To do this, we need to subtract 19 from 7. Since 19 is greater than 7, the result will be a negative number.

7−19=−127 - 19 = -12

Conclusion

In conclusion, the simplified expression 19+(−7)19 + (-7) is equal to −12-12. We used the concept of negative numbers and the commutative property of addition to simplify the expression. This example illustrates the importance of understanding the basics of algebra and how to apply them to simplify complex expressions.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. For example, in finance, we use algebraic expressions to calculate interest rates and investment returns. In science, we use algebraic expressions to model population growth and chemical reactions. In engineering, we use algebraic expressions to design and optimize systems.

Tips and Tricks

Here are some tips and tricks to help you simplify algebraic expressions:

  • Use the commutative property: The commutative property of addition states that the order of the numbers being added does not change the result. Use this property to rewrite the expression and simplify it.
  • Use the associative property: The associative property of addition states that the order in which we add numbers does not change the result. Use this property to group numbers and simplify the expression.
  • Use the distributive property: The distributive property of multiplication states that we can multiply a number by a sum of numbers. Use this property to simplify expressions with multiple terms.

Common Mistakes

Here are some common mistakes to avoid when simplifying algebraic expressions:

  • Not using the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.
  • Not using the commutative property: The commutative property of addition states that the order of the numbers being added does not change the result. Use this property to rewrite the expression and simplify it.
  • Not simplifying expressions with multiple terms: Use the distributive property to simplify expressions with multiple terms.

Conclusion

Introduction

In our previous article, we discussed the basics of simplifying algebraic expressions. In this article, we will provide a Q&A guide to help you understand and apply the concepts of simplifying algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of 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 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 expression with multiple terms?

A: To simplify an expression with multiple terms, use the distributive property to multiply each term by the same value. Then, combine like terms by adding or subtracting the coefficients of the terms.

Q: What is the commutative property of addition?

A: The commutative property of addition states that the order of the numbers being added does not change the result. In other words, a + b = b + a.

Q: How do I use the commutative property to simplify an expression?

A: To use the commutative property to simplify an expression, rewrite the expression by changing the order of the numbers being added. Then, simplify the expression by combining like terms.

Q: What is the associative property of addition?

A: The associative property of addition states that the order in which we add numbers does not change the result. In other words, (a + b) + c = a + (b + c).

Q: How do I use the associative property to simplify an expression?

A: To use the associative property to simplify an expression, group numbers together and simplify the expression by combining like terms.

Q: What is the distributive property of multiplication?

A: The distributive property of multiplication states that we can multiply a number by a sum of numbers. In other words, a(b + c) = ab + ac.

Q: How do I use the distributive property to simplify an expression?

A: To use the distributive property to simplify an expression, multiply each term by the same value. Then, combine like terms by adding or subtracting the coefficients of the terms.

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

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

  • Not using the order of operations
  • Not using the commutative property
  • Not simplifying expressions with multiple terms
  • Not using the distributive property

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill in mathematics. By understanding the basics of algebra and applying the commutative property, associative property, and distributive property, we can simplify complex expressions and solve real-world problems. Remember to follow the order of operations and avoid common mistakes when simplifying algebraic expressions.

Practice Problems

Here are some practice problems to help you apply the concepts of simplifying algebraic expressions:

  1. Simplify the expression: 2x + 3y - 4x
  2. Simplify the expression: 5(2x + 3y) - 2(2x + 3y)
  3. Simplify the expression: (x + 2y) + (x - 2y)
  4. Simplify the expression: (x + 2y) - (x - 2y)
  5. Simplify the expression: 2x + 3y - 4x + 2y

Answer Key

  1. -2x + 3y
  2. 3(2x + 3y)
  3. 2x
  4. 4y
  5. -2x + 5y