Problem 49 - Fundamentals of Mathematics

Question

Combine the numbers as indicated. $$159+4,085-918-608$$

Step-by-Step Solution

Answer

The result of the combination is 2718.

Step 1: Addition

First, add the two numbers that are required to be summed: 159 and 4,085. Calculate: \[159 + 4085 = 4244\]So, the sum of the first two numbers is 4244.

Step 2: First Subtraction

Next, subtract 918 from the result obtained in Step 1.Calculate:\[4244 - 918 = 3326\]Thus, subtracting 918 from 4244 gives 3326.

Step 3: Second Subtraction

Finally, subtract the last number, 608, from the result of Step 2.Calculate:\[3326 - 608 = 2718\]Therefore, the final result after subtracting 608 from 3326 is 2718.

Key Concepts

Understanding Addition in Arithmetic Operations

Addition is one of the basic operations in arithmetic, representing the process of combining two or more quantities to find their total sum. It is commonly used in everyday situations, like adding shopping bills or calculating total scores in games. The operation is straightforward: you simply add values together to find the total.

• In the given math problem, you first need to add the numbers 159 and 4,085.
• Addition can be done in any order thanks to the Commutative Property of Addition, which states that changing the order of the numbers does not change their sum.

The sum of 159 and 4,085 is calculated as follows: \[159 + 4085 = 4244\]This means combining these two numbers results in a single total value.

Mastering Subtraction in Arithmetic Operations

Subtraction is another fundamental arithmetic operation, where you find the difference between two numbers. It’s like asking, "how much is left if you take away one number from another?" This operation is as essential as addition and is frequently used in calculating discounts or determining change in currency.

• In the given problem, we perform subtraction twice, using the results from previous steps.
• Subtraction is non-commutative, meaning changing the order of numbers can lead to different results.

First, we subtract 918 from 4244—the result of the previous addition:\[4244 - 918 = 3326\]Next, we subtract the final number, 608, from 3326 to get the final result:\[3326 - 608 = 2718\]

The Importance of Step-by-Step Calculation

Understanding how to perform calculations step by step is crucial, especially in complex problems involving multiple operations. Breaking down the problem helps in organizing thoughts and ensures no steps are skipped.

• The process becomes manageable when you tackle one operation at a time.
• Ensures clarity in understanding how each result is derived, reducing mistakes.

In the original exercise, here’s how each step was handled: 1. **Addition**: Combine 159 and 4,085 to get 4244. 2. **First Subtraction**: Deduct 918 from 4244, resulting in 3326. 3. **Second Subtraction**: Lastly, take away 608 from 3326 to achieve the final answer of 2718. Following these steps ensures accuracy and builds confidence in handling arithmetic problems systematically.