Jillian Wanted To Determine The Difference Between 7 And A Number, \[$ N \$\]. She Wrote In A Table Several Possible Expressions She Could Use To Represent This. Which Is The Correct Expression
In mathematics, the concept of difference is a fundamental operation that is used to find the value between two numbers. It is an essential part of arithmetic and algebra, and it is used to solve a wide range of problems. In this article, we will explore the concept of difference and how it is represented in mathematics.
What is the Difference Between Two Numbers?
The difference between two numbers is the value that is obtained by subtracting one number from another. For example, if we want to find the difference between 7 and 3, we would subtract 3 from 7, which gives us a result of 4. This means that the difference between 7 and 3 is 4.
Representing the Difference in a Table
Jillian, the student in the problem, wrote several possible expressions in a table to represent the difference between 7 and a number, { n $}$. The table is shown below:
| Expression | Description |
|---|---|
| 7 - n | Subtract n from 7 |
| n - 7 | Subtract 7 from n |
| 7 + (-n) | Add the opposite of n to 7 |
| -7 + n | Add n to the opposite of 7 |
Evaluating the Expressions
Let's evaluate each of the expressions in the table to determine which one represents the difference between 7 and a number, { n $}$.
7 - n
This expression represents the difference between 7 and a number, { n $}$, by subtracting n from 7. For example, if n = 3, then 7 - 3 = 4, which is the difference between 7 and 3.
n - 7
This expression represents the difference between a number, { n $}$, and 7 by subtracting 7 from n. For example, if n = 3, then 3 - 7 = -4, which is not the difference between 7 and 3.
7 + (-n)
This expression represents the difference between 7 and a number, { n $}$, by adding the opposite of n to 7. For example, if n = 3, then -3 + 7 = 4, which is the difference between 7 and 3.
-7 + n
This expression represents the difference between a number, { n $}$, and the opposite of 7 by adding n to -7. For example, if n = 3, then 3 + (-7) = -4, which is not the difference between 7 and 3.
Conclusion
Based on the evaluation of the expressions in the table, we can conclude that the correct expression for representing the difference between 7 and a number, { n $}$, is 7 - n or 7 + (-n). Both of these expressions represent the difference between 7 and a number, { n $}$, by subtracting n from 7 or adding the opposite of n to 7.
Why is the Concept of Difference Important?
The concept of difference is an essential part of mathematics, and it is used to solve a wide range of problems. It is used in arithmetic, algebra, and geometry, and it is a fundamental operation in calculus. The concept of difference is also used in real-world applications, such as finance, economics, and science.
Real-World Applications of the Concept of Difference
The concept of difference is used in a wide range of real-world applications, including:
- Finance: The concept of difference is used to calculate interest rates, investment returns, and loan payments.
- Economics: The concept of difference is used to calculate GDP, inflation rates, and economic growth.
- Science: The concept of difference is used to calculate distances, velocities, and accelerations in physics and engineering.
- Computer Science: The concept of difference is used in algorithms and data structures to compare and manipulate data.
Conclusion
In this article, we will answer some frequently asked questions about the concept of difference in mathematics.
Q: What is the difference between two numbers?
A: The difference between two numbers is the value that is obtained by subtracting one number from another. For example, if we want to find the difference between 7 and 3, we would subtract 3 from 7, which gives us a result of 4.
Q: How do I represent the difference between two numbers in a mathematical expression?
A: To represent the difference between two numbers in a mathematical expression, you can use the subtraction operation. For example, if we want to represent the difference between 7 and a number, { n $}$, we can use the expression 7 - n.
Q: What is the opposite of a number?
A: The opposite of a number is the value that is obtained by changing the sign of the number. For example, the opposite of 3 is -3, and the opposite of -3 is 3.
Q: How do I add the opposite of a number to another number?
A: To add the opposite of a number to another number, you can simply change the sign of the number and add it to the other number. For example, if we want to add the opposite of 3 to 7, we can change the sign of 3 to -3 and add it to 7, which gives us a result of 4.
Q: What is the difference between 7 and a number, { n $}$, represented by the expression 7 + (-n)?
A: The expression 7 + (-n) represents the difference between 7 and a number, { n $}$, by adding the opposite of n to 7. For example, if n = 3, then -3 + 7 = 4, which is the difference between 7 and 3.
Q: Can I use the expression 7 + (-n) to represent the difference between any two numbers?
A: Yes, you can use the expression 7 + (-n) to represent the difference between any two numbers. This expression is a general representation of the difference between two numbers, and it can be used to find the difference between any two numbers.
Q: What is the difference between the expressions 7 - n and 7 + (-n)?
A: The expressions 7 - n and 7 + (-n) are equivalent and represent the same concept, which is the difference between 7 and a number, { n $}$. However, the expression 7 + (-n) is a more general representation of the difference between two numbers, and it can be used to find the difference between any two numbers.
Q: Can I use the expression 7 - n to represent the difference between any two numbers?
A: Yes, you can use the expression 7 - n to represent the difference between any two numbers. This expression is a specific representation of the difference between 7 and a number, { n $}$, and it can be used to find the difference between any two numbers.
Conclusion
In conclusion, the concept of difference is a fundamental operation in mathematics that is used to find the value between two numbers. The difference between two numbers can be represented by the expression 7 - n or 7 + (-n), and it can be used to solve a wide range of problems. The concept of difference is also used in real-world applications, such as finance, economics, and science.