Translate The Algebraic Expression That Follows Into A Written Expression: 5 ( 4 + M 5(4+m 5 ( 4 + M ]A. The Sum Of Five And 4 M 4m 4 M B. Five Times The Sum Of Four And M M M C. Five Times The Product Of Four And M M M D. Five Times Four Plus

Introduction

Algebraic expressions are a fundamental concept in mathematics, and understanding how to translate them into written expressions is crucial for solving mathematical problems. In this article, we will focus on translating the algebraic expression $5(4+m)$ into a written expression.

What is an Algebraic Expression?

An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be simple or complex, and they can be used to represent a wide range of mathematical concepts.

The Algebraic Expression $5(4+m)$

The algebraic expression $5(4+m)$ is a simple expression that consists of a constant, a variable, and a mathematical operation. The expression can be broken down into two parts: the constant $5$ and the variable $4+m$. The expression is enclosed in parentheses, which indicates that the operation inside the parentheses should be performed first.

Translating the Algebraic Expression

To translate the algebraic expression $5(4+m)$ into a written expression, we need to follow the order of operations (PEMDAS). The expression inside the parentheses should be evaluated first, and then the result should be multiplied by the constant $5$.

Option A: The Sum of Five and $4m$

Option A states that the algebraic expression $5(4+m)$ translates to "the sum of five and $4m$". This is a possible translation, but it is not the most accurate one. The expression $5(4+m)$ implies that the constant $5$ should be multiplied by the result of the expression inside the parentheses, not added to it.

Option B: Five Times the Sum of Four and $m$

Option B states that the algebraic expression $5(4+m)$ translates to "five times the sum of four and $m$". This is a more accurate translation, as it correctly implies that the constant $5$ should be multiplied by the result of the expression inside the parentheses.

Option C: Five Times the Product of Four and $m$

Option C states that the algebraic expression $5(4+m)$ translates to "five times the product of four and $m$". This is not a correct translation, as the expression inside the parentheses is a sum, not a product.

Option D: Five Times Four Plus

Option D states that the algebraic expression $5(4+m)$ translates to "five times four plus". This is not a correct translation, as it does not take into account the variable $m$ inside the parentheses.

Conclusion

In conclusion, the algebraic expression $5(4+m)$ translates to "five times the sum of four and $m$". This is the most accurate translation, as it correctly implies that the constant $5$ should be multiplied by the result of the expression inside the parentheses.

Tips and Tricks

• When translating algebraic expressions, always follow the order of operations (PEMDAS).
• Make sure to evaluate the expression inside the parentheses first, and then perform the operation outside the parentheses.
• Use the correct mathematical terminology, such as "sum" and "product", to describe the operation inside the parentheses.

Common Mistakes

• Adding the constant to the expression inside the parentheses, instead of multiplying it.
• Failing to evaluate the expression inside the parentheses first.
• Using incorrect mathematical terminology to describe the operation inside the parentheses.

Practice Problems

• Translate the algebraic expression $3(2x+y)$ into a written expression.
• Translate the algebraic expression $2(x+y)$ into a written expression.
• Translate the algebraic expression $4(3x-2)$ into a written expression.

Solutions

• The algebraic expression $3(2x+y)$ translates to "three times the sum of two $x$ and $y$".
• The algebraic expression $2(x+y)$ translates to "two times the sum of $x$ and $y$".
• The algebraic expression $4(3x-2)$ translates to "four times the difference of three $x$ and two".
  Algebraic Expressions: A Q&A Guide =====================================

Introduction

Algebraic expressions are a fundamental concept in mathematics, and understanding how to translate them into written expressions is crucial for solving mathematical problems. In this article, we will provide a Q&A guide to help you better understand algebraic expressions and how to translate them into written expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when evaluating an algebraic expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next.
• Multiplication and Division: Evaluate any 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 translate an algebraic expression into a written expression?

A: To translate an algebraic expression into a written expression, follow these steps:

1. Evaluate any expressions inside parentheses first.
2. Evaluate any exponential expressions next.
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 sum and a product?

A: A sum is the result of adding two or more numbers together, while a product is the result of multiplying two or more numbers together.

Q: How do I know whether to use the word "sum" or "product" in a written expression?

A: To determine whether to use the word "sum" or "product" in a written expression, look at the operation inside the parentheses. If the operation is addition, use the word "sum". If the operation is multiplication, use the word "product".

Q: Can you provide some examples of algebraic expressions and their written translations?

A: Here are some examples of algebraic expressions and their written translations:

• Algebraic expression: $3(2x+y)$ Written translation: "three times the sum of two $x$ and $y$"
• Algebraic expression: $2(x+y)$ Written translation: "two times the sum of $x$ and $y$"
• Algebraic expression: $4(3x-2)$ Written translation: "four times the difference of three $x$ and two"

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

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

• Adding the constant to the expression inside the parentheses, instead of multiplying it.
• Failing to evaluate the expression inside the parentheses first.
• Using incorrect mathematical terminology to describe the operation inside the parentheses.

Q: How can I practice translating algebraic expressions?

A: You can practice translating algebraic expressions by working through exercises and problems in your math textbook or online resources. You can also try creating your own algebraic expressions and translating them into written expressions.

Conclusion

In conclusion, algebraic expressions are a fundamental concept in mathematics, and understanding how to translate them into written expressions is crucial for solving mathematical problems. By following the order of operations (PEMDAS) and using the correct mathematical terminology, you can accurately translate algebraic expressions into written expressions. Remember to practice regularly to build your skills and confidence in translating algebraic expressions.