Problem 93 - Elementary Algebra

Question

Add or subtract and reduce to lowest terms. $$ 73-32+215 $$

Step-by-Step Solution

Answer

The result is 256.

Step 1: Perform the Subtraction

Start with the subtraction to simplify the expression. Calculate \( 73 - 32 \). Perform the basic arithmetic: \( 73 - 32 = 41 \).

Step 2: Perform the Addition

Next, add the result of the subtraction (41) to 215. Calculate \( 41 + 215 \). Perform the addition: \( 41 + 215 = 256 \).

Step 3: Simplify the Result (if necessary)

Check if the result can be simplified further. Since 256 is a whole number and cannot be reduced to a lower term, this step confirms that the process is complete.

Key Concepts

Addition

When we talk about addition, we're focusing on the operation where we combine two or more numbers to find their total value. Imagine having a group of objects, like apples or marbles, and bringing more objects into that group. This process of combining is what we know as addition. In our example, after performing a subtraction, we added the result to another number to find a sum. The arithmetic operation is straightforward: pick the numbers you want to add and combine their values. For example, if you have 41 and you want to add 215, you simply find their sum:

• Start with 41
• Add 215

So, 41 plus 215 gives you 256. It's useful in everyday life, from counting money to measuring distances.

Subtraction

Subtraction is all about taking away from a quantity. Imagine you have a certain amount of money, and you spend some on buying a toy; the subtraction helps you find out what's left. In this exercise, we started with the subtraction by removing one quantity from another: 73 minus 32. This part of the problem helped us simplify what we were left with:

• We had 73
• We took away 32

This resulted in 41. Think about subtraction as a way to "backtrack" or "decrease". It's quite helpful when determining distances traveled back or balancing your budget after expenses. Performing the correct subtraction is crucial to finding the correct overall result of a series of operations.

Simplification

Simplification refers to making a mathematical expression as easy to handle as possible. Sometimes, mathematical expressions need to be broken down to their simplest form where fractions or complex expressions are involved. Here, simplification was the last step where we checked if we could break down the final answer further. Since the number 256 is an integer and already in its simplest form, no further simplification was needed.

• Simplification often involves reducing fractions to their lowest terms
• Double-checking for any common factors

This ensures clarity and efficiency, allowing you to work with the cleanest form of the number or expression. Simplification makes it easier to compare and use the results in further calculations or conclusions.