Calculate The Following Expression:${ (4 - 20) \times 13 }$

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Introduction

In this article, we will delve into the world of mathematics and explore the process of solving a simple algebraic expression. The expression we will be working with is (4−20)×13(4 - 20) \times 13. This expression involves basic arithmetic operations such as subtraction and multiplication. Our goal is to simplify the expression and arrive at a final answer.

Understanding the Expression

Before we begin solving the expression, let's break it down and understand what it means. The expression (4−20)×13(4 - 20) \times 13 consists of two main parts: the subtraction operation and the multiplication operation.

  • The subtraction operation involves subtracting 20 from 4.
  • The multiplication operation involves multiplying the result of the subtraction operation by 13.

Step 1: Subtract 20 from 4

To solve the expression, we need to start by performing the subtraction operation. We subtract 20 from 4, which can be written as:

4−20=−164 - 20 = -16

Step 2: Multiply -16 by 13

Now that we have the result of the subtraction operation, we can proceed to the multiplication operation. We multiply -16 by 13, which can be written as:

−16×13=−208-16 \times 13 = -208

Conclusion

In conclusion, the expression (4−20)×13(4 - 20) \times 13 simplifies to -208. This is the final answer to the expression.

Why is this Important?

Solving algebraic expressions like this one is an essential skill in mathematics. It helps us to understand the underlying structure of mathematical operations and how they can be combined to solve complex problems. In real-world applications, algebraic expressions are used in a wide range of fields, including science, engineering, economics, and finance.

Real-World Applications

Algebraic expressions are used in many real-world applications, including:

  • Science: Algebraic expressions are used to model the behavior of physical systems, such as the motion of objects under the influence of gravity or friction.
  • Engineering: Algebraic expressions are used to design and optimize systems, such as electronic circuits or mechanical systems.
  • Economics: Algebraic expressions are used to model economic systems, such as the behavior of supply and demand or the impact of taxation on economic activity.
  • Finance: Algebraic expressions are used to model financial systems, such as the behavior of stock prices or the impact of interest rates on investment returns.

Tips and Tricks

Here are some tips and tricks to help you solve algebraic expressions like this one:

  • Follow the order of operations: When solving algebraic expressions, it's essential to follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • Use parentheses to group terms: Parentheses can be used to group terms and make it easier to solve the expression.
  • Simplify the expression: Simplifying the expression can make it easier to solve and reduce the risk of errors.

Conclusion

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Algebraic expressions are used to represent relationships between variables and can be used to solve equations and inequalities.

Q: What are the basic operations in algebraic expressions?

A: The basic operations in algebraic expressions are:

  • Addition: The process of combining two or more numbers or variables to get a sum.
  • Subtraction: The process of finding the difference between two numbers or variables.
  • Multiplication: The process of repeating a number or variable a certain number of times.
  • Division: The process of finding the quotient of two numbers or variables.

Q: How do I simplify an algebraic expression?

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

  1. Combine like terms: Combine terms that have the same variable and coefficient.
  2. Simplify fractions: Simplify fractions by dividing the numerator and denominator by their greatest common divisor.
  3. Remove parentheses: Remove parentheses by distributing the terms inside the parentheses to the terms outside.
  4. Simplify exponents: Simplify exponents by applying the rules of exponents.

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 there are multiple operations in 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 solve an equation with variables?

A: To solve an equation with variables, follow these steps:

  1. Isolate the variable: Get the variable by itself on one side of the equation.
  2. Use inverse operations: Use inverse operations to get rid of any coefficients or constants that are attached to the variable.
  3. Check your answer: Check your answer by plugging it back into the original equation.

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. A constant is a value that does not change.

Q: How do I evaluate an expression with multiple variables?

A: To evaluate an expression with multiple variables, follow these steps:

  1. Substitute the values: Substitute the values of the variables into the expression.
  2. Simplify the expression: Simplify the expression by combining like terms and applying the order of operations.
  3. Evaluate the expression: Evaluate the expression to get the final answer.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

  • Linear expressions: Expressions that have a single variable and a constant term, such as 2x + 3.
  • Quadratic expressions: Expressions that have a variable squared, such as x^2 + 4x + 4.
  • Polynomial expressions: Expressions that have multiple terms with variables and constants, such as 2x^2 + 3x - 4.

Conclusion

In conclusion, algebraic expressions are a fundamental concept in mathematics that can be used to represent relationships between variables and solve equations and inequalities. By understanding the basic operations, simplifying expressions, and following the order of operations, we can solve algebraic expressions and gain a deeper understanding of mathematical concepts.