Problem 58 - Fundamentals of Mathematics

Question

Add and subtract as in dicated. Add the difference of 843 and 139 to the difference of 4,450 and \(839 .\)

Step-by-Step Solution

Answer

The result is 4,315.

Step 1: Calculate the Difference of 843 and 139

To find the difference between 843 and 139, subtract 139 from 843. \[ 843 - 139 = 704 \]

Step 2: Calculate the Difference of 4,450 and 839

Now, find the difference between 4,450 and 839 by subtracting 839 from 4,450. \[ 4,450 - 839 = 3,611 \]

Step 3: Add the Two Differences

Add the results from the previous steps. Add the difference of 704 (from Step 1) to the difference of 3,611 (from Step 2). \[ 704 + 3,611 = 4,315 \]

Key Concepts

Addition

Addition is one of the basic arithmetic operations where two or more numbers or amounts are combined to make a total sum. It is represented by the plus sign "+". For example, if you have 3 apples and you add 2 more apples, you have a total of 5 apples. This simple concept is the foundation of many mathematical operations and appears in more complex scenarios, such as the one we are discussing here.
When adding, each number being added is called an "addend," and the result is called the "sum." In the context of our exercise, after calculating the differences, we perform addition in the final step by adding two results together: \(704 + 3,611 = 4,315\).

• The first addend is 704.
• The second addend is 3,611.
• The sum is 4,315.

The order in which we add numbers does not affect the sum due to the commutative property of addition, meaning \(a + b = b + a\). Thus, adding 704 to 3,611 yields the same result as adding 3,611 to 704.

Subtraction

Subtraction is another fundamental arithmetic operation, used to find the difference between numbers. It is represented by the minus sign "−". If you have 10 oranges and take away 4, you are left with 6.
In this exercise, we perform subtraction to find the differences needed for the subsequent addition step. In mathematical terms, when subtracting, the first number is called the "minuend," and the second is the "subtrahend". The result is known as the "difference."

• The equation \(843 - 139\) gives a difference of 704.
• Here, 843 is the minuend, and 139 is the subtrahend.
• For \(4,450 - 839\), the difference is 3,611.
• In this case, 4,450 is the minuend, and 839 is the subtrahend.

Understanding these terms helps in recognizing which numbers are being subtracted from each other, an essential step toward accurate problem solving.

Problem Solving Steps

Effective problem solving involves following a systematic approach to ensure accuracy. In arithmetic operations like addition and subtraction, breaking down the task into simple, manageable steps is key.
Let's discuss how we tackled the original exercise, step by step:

• Step 1: Determine the first difference. Subtract 139 from 843. This calculation gives us a difference of 704.
• Step 2: Find the second difference. Here, subtract 839 from 4,450 to arrive at 3,611.
• Step 3: Add the differences obtained from the first two steps. Combining 704 and 3,611 gives us a sum of 4,315.

Approaching complex problems by breaking them down into smaller, sequential tasks helps in thorough understanding and ensures the solution is reached correctly. Additionally, checking each step can prevent mistakes and confirm accuracy of the final result.