Problem 36 - Algebra 1: Concepts and Skills

Question

Write a variable expression for the phrase 9 decreased by a number n.

Step-by-Step Solution

Answer

The variable expression for the phrase '9 decreased by a number n' is \(9-n\).

Step 1: Recognize the value

First identify the fixed value from the expression. Here, the fixed value is 9.

Step 2: Identify the operation

Identify the mathematical operation from the phrase. In this case, 'decreased by' is equivalent to subtraction.

Step 3: Identify the variable

Identify the variable from the phrase. In this case, 'a number n' is our variable.

Step 4: Write the expression

Combine the fixed value, operation, and variable into a mathematical expression. In this case, '9 decreased by a number n' will become \(9-n\).

Key Concepts

Subtraction

Subtraction is one of the essential operations in mathematics. It is used to find the difference between two numbers. When you subtract a number from another, you essentially calculate what remains after a certain quantity is removed. In the world of variable expressions, subtraction plays a crucial role in helping us model real-world problems where quantities are reduced or taken away.

For example, phrases like "decreased by," "less," or "minus" often indicate that subtraction is needed. In the problem, the term "9 decreased by a number n" suggests that we subtract the number `n` from 9. This gives us the expression: - \(9 - n\)

Understanding subtraction as taking away helps to tackle various algebraic challenges effectively.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and mathematical operations. They serve as a way to represent mathematical relationships or problems using symbols. In our exercise, the expression was created to demonstrate how a fixed number can be decreased by an unknown quantity, often referred to as a variable.

Let's break it down:

• **Numbers**: These are fixed and known values; in our case, it's the number 9.
• **Variables**: These are symbols, usually letters, representing unknown numbers; here it is 'n'.
• **Operations**: The actions we perform on these numbers and variables, like addition, subtraction, etc.

In "9 decreased by a number n," the resulting expression \(9-n\) captures exactly these elements. Variable expressions like this can be used to solve equations, find functions, and model a wide range of scenarios in math and beyond.

Mathematical Operations

Mathematical operations are the building blocks of expressions and equations. They show us how to link numbers and variables together to create meaningful relationships. Common operations include addition, subtraction, multiplication, and division.

In our exercise, subtraction is the focus. It shows how we can modify one number by reducing it by another, often a variable. This variable stands for any unknown or changing quantity. Operations take these abstract concepts and allow us to manipulate and solve them in practical situations.

By recognizing terms like "decreased by," one immediately identifies subtraction as the operation required. This makes it easier to form expressions and hence solve real-life mathematical problems. Mastery of these operations allows for efficient handling of more complex algebraic expressions in the future.