Translate The Phrase Into An Algebraic Expression: $k$ Dollars Per 28 Bottles.Select The Correct Answer Below:A. $\frac{28 \text{ Bottles }}{\$ K}$ B. $\frac{\$ K}{28 \text{ Bottles }}$C. $\$
Introduction
Algebraic expressions are a fundamental concept in mathematics, used to represent relationships between variables and constants. In this article, we will explore how to translate a given phrase into an algebraic expression, focusing on the example of translating the phrase "k dollars per 28 bottles" into an algebraic expression.
What is an Algebraic Expression?
An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is used to represent a relationship between variables and constants, and can be used to solve equations and inequalities. Algebraic expressions can be simple or complex, and can involve various mathematical operations such as addition, subtraction, multiplication, and division.
Translating the Phrase into an Algebraic Expression
To translate the phrase "k dollars per 28 bottles" into an algebraic expression, we need to identify the key components of the phrase. The phrase consists of two main components: the cost per bottle (k dollars) and the number of bottles (28 bottles).
Step 1: Identify the Cost per Bottle
The cost per bottle is represented by the variable k, which is in dollars. This means that the cost per bottle is a fixed amount, represented by the variable k.
Step 2: Identify the Number of Bottles
The number of bottles is represented by the number 28. This means that the phrase is referring to a specific quantity of bottles, which is 28.
Step 3: Translate the Phrase into an Algebraic Expression
Now that we have identified the key components of the phrase, we can translate it into an algebraic expression. The phrase "k dollars per 28 bottles" can be translated into the algebraic expression:
\frac{\$ k}{28 \text{ bottles }}
This expression represents the cost per bottle, where the cost is represented by the variable k and the number of bottles is represented by the number 28.
Analyzing the Options
Now that we have translated the phrase into an algebraic expression, let's analyze the options provided:
A. $\frac{28 \text{ bottles }}{$ k}$
This option is incorrect because it represents the number of bottles divided by the cost per bottle, which is the opposite of what we want to represent.
B. $\frac{$ k}{28 \text{ bottles }}$
This option is correct because it represents the cost per bottle, where the cost is represented by the variable k and the number of bottles is represented by the number 28.
C. $$
This option is incorrect because it does not represent the cost per bottle, and does not include the number of bottles.
Conclusion
In conclusion, translating the phrase "k dollars per 28 bottles" into an algebraic expression requires identifying the key components of the phrase and using mathematical operations to represent the relationship between the variables and constants. The correct algebraic expression is:
\frac{\$ k}{28 \text{ bottles }}
This expression represents the cost per bottle, where the cost is represented by the variable k and the number of bottles is represented by the number 28.
Common Mistakes to Avoid
When translating phrases into algebraic expressions, it's essential to avoid common mistakes such as:
- Confusing the order of operations
- Failing to identify the key components of the phrase
- Using the wrong mathematical operations to represent the relationship between variables and constants
Tips for Translating Phrases into Algebraic Expressions
To translate phrases into algebraic expressions effectively, follow these tips:
- Identify the key components of the phrase
- Use mathematical operations to represent the relationship between variables and constants
- Check your work to ensure that the algebraic expression accurately represents the phrase
Real-World Applications
Algebraic expressions have numerous real-world applications, including:
- Finance: Algebraic expressions are used to calculate interest rates, investment returns, and other financial metrics.
- Science: Algebraic expressions are used to model physical systems, such as the motion of objects and the behavior of electrical circuits.
- Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and buildings.
Conclusion
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is used to represent a relationship between variables and constants, and can be used to solve equations and inequalities.
Q: How do I identify the key components of a phrase to translate it into an algebraic expression?
A: To identify the key components of a phrase, you need to break it down into its individual parts. For example, if the phrase is "k dollars per 28 bottles", you need to identify the cost per bottle (k dollars) and the number of bottles (28 bottles).
Q: What are some common mistakes to avoid when translating phrases into algebraic expressions?
A: Some common mistakes to avoid when translating phrases into algebraic expressions include:
- Confusing the order of operations
- Failing to identify the key components of the phrase
- Using the wrong mathematical operations to represent the relationship between variables and constants
Q: How do I use mathematical operations to represent the relationship between variables and constants in an algebraic expression?
A: To use mathematical operations to represent the relationship between variables and constants in an algebraic expression, you need to identify the type of relationship between the variables and constants. For example, if the phrase is "k dollars per 28 bottles", you need to use division to represent the relationship between the cost per bottle (k dollars) and the number of bottles (28 bottles).
Q: What are some real-world applications of algebraic expressions?
A: Algebraic expressions have numerous real-world applications, including:
- Finance: Algebraic expressions are used to calculate interest rates, investment returns, and other financial metrics.
- Science: Algebraic expressions are used to model physical systems, such as the motion of objects and the behavior of electrical circuits.
- Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and buildings.
Q: How do I check my work to ensure that the algebraic expression accurately represents the phrase?
A: To check your work, you need to:
- Verify that the algebraic expression accurately represents the phrase
- Check that the mathematical operations used are correct
- Check that the variables and constants are correctly identified
Q: What are some tips for translating phrases into algebraic expressions?
A: Some tips for translating phrases into algebraic expressions include:
- Identify the key components of the phrase
- Use mathematical operations to represent the relationship between variables and constants
- Check your work to ensure that the algebraic expression accurately represents the phrase
Q: Can you provide an example of a phrase that can be translated into an algebraic expression?
A: Yes, here is an example of a phrase that can be translated into an algebraic expression:
"5 dollars per 2 pounds of coffee"
This phrase can be translated into the algebraic expression:
\frac{\$ 5}{2 \text{ pounds }}
Q: Can you provide an example of a real-world application of algebraic expressions?
A: Yes, here is an example of a real-world application of algebraic expressions:
A company wants to calculate the cost of producing a certain number of units of a product. The cost per unit is $10, and the company wants to produce 500 units. The algebraic expression to represent this situation is:
\frac{\$ 10}{1 \text{ unit }} \times 500 \text{ units }
This expression can be used to calculate the total cost of producing 500 units of the product.
Conclusion
In conclusion, algebraic expressions are a powerful tool for representing relationships between variables and constants. By following the steps outlined in this article, you can effectively translate phrases into algebraic expressions and apply them to real-world problems.