Write an expression for the sequence of operations described below. divide 10 by the sum of n and m Do not simplify any part of the expression.
The Correct Answer and Explanation is :
To express the operation “divide 10 by the sum of ( n ) and ( m )” mathematically, we can follow these steps:
- Identify the sum: The sum of ( n ) and ( m ) is written as ( n + m ).
- Division operation: Dividing 10 by the sum we found in the first step can be expressed as ( \frac{10}{n + m} ).
Thus, the final expression for the sequence of operations described is:
[
\frac{10}{n + m}
]
Explanation
In mathematics, expressions often represent operations involving numbers and variables. Here, we are tasked with translating a verbal description into a mathematical expression. The operation we need to perform involves two main components: division and addition.
Step 1: Addition of Variables
The phrase “the sum of ( n ) and ( m )” indicates that we need to add two variables, ( n ) and ( m ). In mathematical notation, this is straightforward and is represented as ( n + m ). Addition is one of the fundamental arithmetic operations, and in this case, it combines the values of ( n ) and ( m ) into a single quantity.
Step 2: Division by the Sum
The next part of the operation involves dividing a constant, which is 10, by the sum we just calculated. Division is another basic arithmetic operation where we distribute one quantity into equal parts based on another quantity. Here, we want to see how many times the sum ( n + m ) fits into 10, or how much of 10 is represented by that sum.
Final Expression
Combining both steps, we create a fraction where the numerator is 10 (the quantity we are dividing) and the denominator is the sum ( n + m ). This yields the final expression:
[
\frac{10}{n + m}
]
This expression effectively communicates the operation described, maintaining the integrity of both the addition and division processes without simplifying any part of it.