Problem 82 - Elementary Algebra

Question

Add or subtract and reduce to lowest terms. $$ 15-14 $$

Step-by-Step Solution

Answer

The result is 1, which is already in its simplest form.

Step 1: Understand the Problem

We are given that we need to subtract two numbers, 15 and 14, and then reduce the result to its lowest terms.

Step 2: Subtract the Numbers

Subtract 14 from 15 to find the difference: \( 15 - 14 = 1 \).

Step 3: Simplify the Result

In this case, the result is already a whole number, 1, which is in its simplest form as there are no further reductions possible.

Key Concepts

Subtraction

Subtraction is one of the basic operations in elementary algebra. It's used to find the difference between two numbers or quantities. You start with a larger number, known as the minuend, and subtract a smaller number, called the subtrahend.
In the exercise, the number 15 is the minuend and 14 is the subtrahend. The subtraction process involves taking away the subtrahend from the minuend.

• Minuend: The number from which another number is subtracted.
• Subtrahend: The number that is to be subtracted.
• Result or Difference: The outcome of the subtraction.

To find the result, we perform: \[15-14=1\]This tells us that the difference between 15 and 14 is 1. Subtraction is essential for solving problems across various math topics, so understanding it is crucial.

Simplification

Simplification in math is the process of reducing a number or equation to its simplest form. When it comes to numbers, simplification often involves reducing fractions or polynomials. In the context of this problem, the result of the subtraction was 1. As this is already a whole number, nothing more needs to be done. However, if your answer was a fraction or a more complex number, simplification would ensure that you present the most clear and reduced form.

• A number is in simplest form when no further operations can simplify it.
• This often involves recognizing common factors and reducing them in fractions.

Understanding simplification is key to algebra because it helps solve equations more efficiently and correctly.

Lowest Terms

Reducing a number or a fraction to its lowest terms is a specific form of simplification. For fractions, it means that both the numerator and the denominator are as small as possible while still maintaining the same value. With whole numbers, like in our exercise, this concept isn't applied as thoroughly since the number is already stored in its simplest form. If the result of a problem like this were a fraction, you'd simplify by dividing both the numerator and denominator by their greatest common divisor (GCD).

• Lowest Terms: When a fraction’s numerator and denominator have no common factors other than 1, it’s in its lowest terms.
• Use GCD for simplifying fractions.

In fractions, such as \( \frac{8}{12} \), you would reduce it to \( \frac{2}{3} \) (use GCD, which is 4), to ensure it's in its lowest terms. This step confirms clarity and understands in mathematical solutions.