The difference of 8 and nine times a number is a mathematical operation that can be applied in various practical scenarios. This exploration delves into the intricacies of this operation, examining its components, relationships, and real-world applications.
To begin, let’s break down the operation into its constituent parts and illustrate its application with a concrete example.
The Difference of 8 and Nine Times a Number
The mathematical operation “the difference of 8 and nine times a number” can be expressed as:
9x
8
This operation involves subtracting 8 from the product of 9 and a given number x.
Step-by-Step Breakdown
- Multiply the number xby 9.
- Subtract 8 from the result of step 1.
Example
For example, if x= 5:
9(5)
- 8 = 45
- 8 = 37
Relationship between the Number and the Result, The difference of 8 and nine times a number
The result of the operation is influenced by the value of x.
As xincreases, the result of the operation generally increases. This is because multiplying xby 9 increases the value of the product, which in turn increases the difference when 8 is subtracted.
Factors Influencing the Result
- Number 8:The constant 8 represents the amount subtracted from the product. Changing the value of 8 will affect the result of the operation.
- Number 9:The constant 9 represents the multiplier of x. Changing the value of 9 will also affect the result of the operation.
Visual Representation
The following table illustrates the relationship between xand the result of the operation:
| x | 9x
|
|---|---|
| 0 | -8 |
| 1 | 1 |
| 2 | 10 |
| 3 | 19 |
| 4 | 28 |
The graph below shows the relationship between xand the result of the operation:
Real-World Examples
- Calculating the remaining amount after a purchase:If you have $100 and buy an item that costs $25, the difference of 8 and nine times the cost of the item (9(25) – 8 = 217) represents the remaining amount you have.
- Determining the profit after expenses:If you sell a product for $50 and incur expenses of $15, the difference of 8 and nine times the expenses (9(15) – 8 = 137) represents the profit you made.
Expert Answers: The Difference Of 8 And Nine Times A Number
What is the mathematical representation of “the difference of 8 and nine times a number”?
It is expressed as 9x – 8, where x represents the number.
How does the number affect the result of the operation?
The result is directly proportional to the number. As the number increases, the result also increases.
Can you provide an example of a real-world application of this operation?
Suppose you have 10 apples and you want to distribute them equally among 3 friends. You can use this operation to calculate how many apples each friend will receive: (9x – 8) / 3, where x is the number of apples you have.
