Converting Verbal Statements into Algebraic Equations: A Guide to Understanding 'Half of a Number is 200'

Learning to translate verbal statements into algebraic equations is a fundamental skill in mathematics, especially when dealing with word problems. This article will break down the process with a specific problem: ‘half of a number is 200’. We'll explore the step-by-step reasoning and provide a clear algebraic equation.

Step-by-Step Breakdown

To solve the problem, we need to follow a systematic approach:

Identify the variable: Express the given condition: Set up the equation:

Identify the Variable

The first step is to identify the unknown variable. In our problem, we don't know the specific number, so we represent it with a variable. Let's use x to denote this unknown number.

Express the Given Condition

The next step is to express the condition given in the problem using algebra. We know that ‘half of a number is 200’. This can be mathematically expressed as:

Half of x can be written as 1/2 * x.

Set Up the Equation

Combining the above two steps, we can now set up the equation based on the given condition:

According to the problem, half of the number x is equal to 200. Therefore, the algebraic equation is:

[1/2 * x 200]

Solving the Equation

To solve the equation 1/2 * x 200, we can follow these steps:

First, isolate x. We can do this by multiplying both sides by 2:

[2 * (1/2 * x) 2 * 200]

Simplify the equation:

[x 400]

Therefore, the number is 400.

Alternative Forms and Notations

Another way to represent and solve this problem is by using different notations. Let's consider an alternative approach:

Let x be the number such that half of x is 200. Then:

We can write:

“Half of a number” means “a number divided by 2” “Is” means “is equal to”

Therefore, the equation is:

[x/2 200]

Solving for x:

[x 200 * 2]

[x 400]

Understanding the Keywords in the Problem

The keywords in the problem are crucial for forming the correct equation. Let's break them down:

Half: This indicates the fraction 1/2 or 0.5. Number: This is the unknown variable we are solving for. Is: This indicates equality, denoted by the '' symbol.

With these keywords, we can build the equation:

1/2 * n 200

Conclusion

By following the systematic approach of identifying the variable, expressing the condition, and setting up the equation, we can easily convert a verbal statement into an algebraic equation. This problem demonstrates the importance of understanding the meaning of key terms and representing them accurately in mathematical notation.