Write An Expression For The Phrase The Sum Of 9 And K Minus 17
In the realm of mathematics, translating verbal phrases into algebraic expressions is a fundamental skill. This process involves deciphering the meaning of the words and representing them using mathematical symbols and operations. This article will focus on dissecting the phrase "the sum of 9 and k minus 17" and constructing the corresponding algebraic expression. We will explore the step-by-step process of translating the words into mathematical symbols, ensuring a clear understanding of the concepts involved. The ability to accurately translate verbal phrases into algebraic expressions is crucial for solving a wide range of mathematical problems, from simple equations to complex formulas. Therefore, a firm grasp of this skill is essential for success in mathematics and related fields. This article aims to provide a comprehensive explanation of the translation process, enabling readers to confidently tackle similar problems in the future.
Deconstructing the Phrase
To accurately translate the phrase, we must break it down into its constituent parts and understand the mathematical operations they represent. The phrase "the sum of 9 and k" indicates an addition operation between the numbers 9 and the variable k. The word "sum" is a key indicator of addition, signifying that we need to combine these two entities. The variable k represents an unknown quantity, and it is a common practice in algebra to use letters to represent variables. Therefore, "the sum of 9 and k" can be mathematically represented as 9 + k. This is the first crucial step in translating the entire phrase. By identifying the key operations and the elements involved, we can start building the algebraic expression piece by piece. The next part of the phrase, "minus 17," indicates a subtraction operation. The word "minus" clearly signals that we need to subtract 17 from the previous result, which was the sum of 9 and k. Therefore, we need to incorporate this subtraction into our expression. By carefully analyzing each part of the phrase, we can ensure that our final algebraic expression accurately reflects the intended mathematical operation.
Constructing the Algebraic Expression
Having deconstructed the phrase, we can now construct the complete algebraic expression. We've established that "the sum of 9 and k" is represented as 9 + k. The next part of the phrase, "minus 17," tells us to subtract 17 from this sum. Therefore, we append "- 17" to our existing expression. The complete expression then becomes 9 + k - 17. This expression accurately represents the original phrase, capturing both the addition and subtraction operations in the correct order. It is essential to ensure that the order of operations is correctly reflected in the expression. In this case, the addition of 9 and k occurs first, followed by the subtraction of 17. This order is naturally preserved in our expression, 9 + k - 17. The final expression is a concise and accurate representation of the verbal phrase, ready to be used in further mathematical calculations or problem-solving. By carefully following this step-by-step process, we can confidently translate similar phrases into algebraic expressions.
Evaluating the Options
Now let's evaluate the given options to determine which one correctly represents the phrase "the sum of 9 and k minus 17." Option A is 9 + k - 17, which is the expression we derived in the previous section. This option accurately captures the addition of 9 and k, followed by the subtraction of 17. Therefore, Option A is the correct representation of the phrase. Option B, 9k - 17, represents 9 multiplied by k, then subtracting 17. This expression does not include the addition of 9 and k, so it is not a correct representation of the phrase. The absence of the addition operation makes this option clearly incorrect. Option C, 9 - k + 17, represents 9 minus k, plus 17. This expression involves subtraction of k from 9, which is not what the original phrase indicates. The phrase specifies the sum of 9 and k, not the difference. Therefore, Option C is also incorrect. By comparing each option to our derived expression, we can confidently identify Option A as the correct answer. This process of evaluation is crucial for ensuring the accuracy of our translation and expression.
Conclusion
In conclusion, the algebraic expression that correctly represents the phrase "the sum of 9 and k minus 17" is 9 + k - 17. This expression accurately captures the addition of 9 and k, followed by the subtraction of 17. We arrived at this expression by carefully deconstructing the phrase, identifying the mathematical operations, and constructing the expression step by step. The ability to translate verbal phrases into algebraic expressions is a fundamental skill in mathematics, crucial for solving equations, simplifying expressions, and tackling more complex problems. By understanding the meaning of mathematical terms and operations, we can confidently convert verbal descriptions into symbolic representations. This process involves breaking down the phrase into smaller parts, identifying the operations (such as addition, subtraction, multiplication, and division), and representing them using mathematical symbols. The correct expression allows us to manipulate and solve mathematical problems effectively. Understanding the relationship between verbal phrases and algebraic expressions is essential for mathematical proficiency. This article has provided a comprehensive guide to translating the given phrase, highlighting the key steps and considerations involved in the process. By practicing these skills, readers can improve their mathematical comprehension and problem-solving abilities. Therefore, mastering the translation of verbal phrases into algebraic expressions is a valuable asset in the study and application of mathematics.
Translate "The Sum of 9 and k Minus 17" into an Expression
