Problem 16 - Elementary Algebra

Question

Translate the following into a mathematical statement. Seventy-eight is not equal to twelve.

Step-by-Step Solution

Answer

The mathematical statement is \( 78 \neq 12 \).

Step 1: Identify the Numbers

The problem statement provides two numbers: seventy-eight and twelve. First, let's represent these numbers using their numerical values. Seventy-eight is represented as 78 and twelve is represented as 12.

Step 2: Determine the Mathematical Symbol

The statement uses the phrase 'is not equal to.' In mathematics, this is usually represented by the symbol \( eq \), which stands for 'not equal to.'

Step 3: Construct the Mathematical Statement

Now that we have the numbers and the appropriate symbol, we can construct the mathematical statement. We place 78 and 12 with the \( eq \) symbol between them to represent that seventy-eight is not equal to twelve. This gives us the final mathematical statement: \( 78 eq 12 \).

Key Concepts

Translation to Math

Converting written statements into mathematical expressions involves understanding keywords and their corresponding numerical values. This process is known as translating to math. For instance, when a statement reads "seventy-eight," we translate this by simply writing the numeric form: 78. Similarly, the word "twelve" becomes 12 in numeric representation. These translations are essential for forming accurate mathematical statements from verbal or written descriptions.

Translating statements not only requires correct numerical values but also understanding mathematical operations or relationships described in words. Terms like "is," "plus," "minus," "times," and "is not equal to" guide us in selecting proper mathematical symbols. In our example, we focus on the phrase "is not equal to," which sets the context for the kind of operation or relation needed in our mathematical expression.

Inequality Symbols

In mathematics, the comparison between different values necessitates the use of specific symbols, especially when values are compared differently than being equal. These inequality symbols include:

• \( = \): Equals - signifies that two expressions represent the same value.
• \( eq \): Not Equal - shows that two expressions do not represent the same value. It's important to note that this is the correct symbol for expressing a difference, replacing the incorrect "eq" symbol used previously.
• \( < \): Less than - can indicate that one number is smaller than another.
• \( > \): Greater than - indicates that one number is larger than another.
• \( \leq \): Less than or equal to - means a value is either smaller than or precisely equal to another.
• \( \geq \): Greater than or equal to - implies a value is either larger than or equal to another.

Each symbol is crucial in forming correct mathematical statements based on the context provided by the exercise or problem. For instance, using \( eq \) in our case means directly and precisely representing the verbal phrase "not equal to."

Numerical Representation

Numerical representation involves expressing verbal or written numbers in their numeric form. This step is fundamental in translating statements into mathematical formulas. For example, when reading or hearing "seventy-eight," we represent it numerically as 78. This conversion allows for subsequent mathematical operations to be reliably executed.

Moreover, understanding how words map to numbers is crucial for learners, helping them to effortlessly convert any spoken or written quantity into an appropriate numeric format. This lays the groundwork for further mathematical computation and understanding. Hence, the process is essential in both arithmetic and advanced math problem-solving. Proper numerical representation ensures that calculations are carried out accurately and fluently, leading towards the correct solutions to mathematical problems.