Calculate The Following Expression: ${ -106 + (-45) = }$
Introduction
In mathematics, algebraic expressions are a fundamental concept that helps us solve equations and inequalities. One of the essential skills in algebra is simplifying expressions by combining like terms. In this article, we will focus on calculating the expression: ${-106 + (-45) = }$. We will break down the steps involved in simplifying this expression and provide a clear understanding of the process.
Understanding the Expression
The given expression is a simple addition problem involving two negative integers: ${-106 + (-45) = }$. To simplify this expression, we need to combine the two negative numbers.
Step 1: Combine Like Terms
Like terms are terms that have the same variable raised to the same power. In this case, we have two negative integers, so we can combine them by adding their absolute values and keeping the same sign.
Now that we have combined the like terms, we can simplify the expression by performing the subtraction.
{-106 - 45 = -151}$ **Conclusion** ---------- In conclusion, the expression ${-106 + (-45) = }$ simplifies to ${-151}$. By following the steps outlined above, we have successfully combined like terms and simplified the expression. **Why is Simplifying Algebraic Expressions Important?** -------------------------------------------- Simplifying algebraic expressions is an essential skill in mathematics that helps us solve equations and inequalities. By combining like terms, we can simplify complex expressions and make them easier to work with. This skill is also important in real-world applications, such as finance, engineering, and science. **Real-World Applications of Simplifying Algebraic Expressions** --------------------------------------------------------- Simplifying algebraic expressions has numerous real-world applications. For example: * In finance, simplifying algebraic expressions can help us calculate interest rates and investment returns. * In engineering, simplifying algebraic expressions can help us design and optimize complex systems. * In science, simplifying algebraic expressions can help us model and analyze complex phenomena. **Tips and Tricks for Simplifying Algebraic Expressions** --------------------------------------------------- Here are some tips and tricks for simplifying algebraic expressions: * Always combine like terms first. * Use the distributive property to simplify expressions. * Use the order of operations (PEMDAS) to simplify expressions. * Simplify expressions by canceling out common factors. **Common Mistakes to Avoid When Simplifying Algebraic Expressions** --------------------------------------------------------- Here are some common mistakes to avoid when simplifying algebraic expressions: * Failing to combine like terms. * Not using the distributive property. * Not following the order of operations (PEMDAS). * Not simplifying expressions by canceling out common factors. **Conclusion** ---------- In conclusion, simplifying algebraic expressions is an essential skill in mathematics that helps us solve equations and inequalities. By following the steps outlined above and using the tips and tricks provided, we can simplify complex expressions and make them easier to work with. Remember to always combine like terms first, use the distributive property, and follow the order of operations (PEMDAS) to simplify expressions.<br/> **Frequently Asked Questions: Simplifying Algebraic Expressions** =========================================================== **Q: What is the difference between like terms and unlike terms?** --------------------------------------------------------- A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or variables raised to different powers. **Q: How do I combine like terms?** ------------------------------ A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have the expression $2x + 3x$, you can combine the like terms by adding the coefficients: $2x + 3x = 5x$. **Q: What is the distributive property?** -------------------------------------- A: The distributive property is a rule that allows you to multiply a single term by multiple terms. For example, if you have the expression $a(b + c)$, you can use the distributive property to multiply $a$ by each term inside the parentheses: $a(b + c) = ab + ac$. **Q: How do I simplify expressions using the distributive property?** --------------------------------------------------------- A: To simplify expressions using the distributive property, you need to multiply each term inside the parentheses by the single term outside the parentheses. For example, if you have the expression $a(b + c)$, you can simplify it by multiplying $a$ by each term inside the parentheses: $a(b + c) = ab + ac$. **Q: What is the order of operations (PEMDAS)?** -------------------------------------------- A: The order of operations (PEMDAS) is a rule that tells you which operations to perform first when simplifying expressions. The acronym PEMDAS stands for: * **P**arentheses: Evaluate expressions inside parentheses first. * **E**xponents: Evaluate any exponential expressions next. * **M**ultiplication and **D**ivision: Evaluate any multiplication and division operations from left to right. * **A**ddition and **S**ubtraction: Finally, evaluate any addition and subtraction operations from left to right. **Q: How do I simplify expressions using the order of operations (PEMDAS)?** ------------------------------------------------------------------- A: To simplify expressions using the order of operations (PEMDAS), you need to follow the order of operations: 1. Evaluate any expressions inside parentheses. 2. Evaluate any exponential expressions. 3. Evaluate any multiplication and division operations from left to right. 4. Finally, evaluate any addition and subtraction operations from left to right. **Q: What is the difference between a coefficient and a variable?** --------------------------------------------------------- A: A coefficient is a number that is multiplied by a variable. A variable is a letter or symbol that represents a value that can change. **Q: How do I simplify expressions by canceling out common factors?** ---------------------------------------------------------------- A: To simplify expressions by canceling out common factors, you need to identify any common factors between the numerator and denominator of a fraction. You can then cancel out these common factors to simplify the expression. **Q: What are some common mistakes to avoid when simplifying algebraic expressions?** -------------------------------------------------------------------------------- A: Some common mistakes to avoid when simplifying algebraic expressions include: * Failing to combine like terms. * Not using the distributive property. * Not following the order of operations (PEMDAS). * Not simplifying expressions by canceling out common factors. **Q: How do I know when to simplify an algebraic expression?** --------------------------------------------------------- A: You should simplify an algebraic expression whenever possible to make it easier to work with. Simplifying expressions can help you: * Solve equations and inequalities more easily. * Understand complex concepts more clearly. * Make calculations more efficient. **Q: Can I simplify algebraic expressions with variables?** --------------------------------------------------- A: Yes, you can simplify algebraic expressions with variables. In fact, simplifying expressions with variables is an essential skill in algebra. By combining like terms and using the distributive property, you can simplify expressions with variables and make them easier to work with.</span></p>