Problem 85 - Elementary Algebra

Question

Add or subtract and reduce to lowest terms. $$ 715-310 $$

Step-by-Step Solution

Answer

The result is 405.

Step 1: Identify the Operation

The exercise requires subtraction of two whole numbers: 715 and 310.

Step 2: Perform the Subtraction

Subtract 310 from 715.\[715 - 310 = 405\]

Step 3: Check for Simplification

Since 405 is a whole number and not a fraction, it cannot be simplified further. The answer is already in its lowest terms.

Key Concepts

Subtraction

Subtraction is one of the basic operations in mathematics, valuable in elementary algebra. It involves taking a certain number away from another, finding the difference between them. Subtraction can be expressed as: - **Minuend**: This is the number from which you subtract another number. In our exercise, 715 is the minuend. - **Subtrahend**: This is the number that is subtracted from the minuend, which in this case is 310. - **Difference**: This is the result of subtracting the subtrahend from the minuend. Here, it is 405. In simple terms, if you think of subtraction as a backward movement on a number line, you start from the larger number and count backwards by the size of the smaller number. Subtraction is perfect for determining how much is left or how much was taken away. It's a fundamental operation that forms the basis for more complex calculations.

Whole Numbers

Whole numbers are the set of numbers without fractions or decimals. They start from 0 and include all positive numbers (0, 1, 2, 3, ...). This makes them integral to basic mathematical operations like adding, subtracting, multiplying, and dividing. Whole numbers possess some interesting properties: - **No Negative Numbers**: Whole numbers don't include negative values. They are only positive integers and zero. - **Simplicity**: Because they are complete numbers, working with them is straightforward, eliminating the need for handling decimals or fractions. Understanding whole numbers is critical because they lay the foundation for more advanced topics in mathematics. For the given exercise, both numbers involved in the subtraction, 715 and 310, are whole numbers, making it a simple operation. Whole numbers require straightforward operations due to their non-fractional nature.

Simplification

Simplification involves reducing expressions or results to their simplest form. However, when dealing with whole numbers, this concept is a bit different from simplifying fractions. In the context of the given exercise, simplification means ensuring that the result of subtraction is expressed in the simplest terms possible: - **Whole Numbers**: If your result is a whole number and not part of a fraction, it's already in its simplest form. - **Fractions**: With fractions, it's important to divide both the numerator and the denominator by their greatest common divisor to simplify. In our specific case of subtracting 715 from 310, we obtained 405. Since 405 is already a whole number, there’s nothing further to simplify. Having outcomes in their simplest form helps in maintaining clarity and understanding of the resultant number.