Problem 54 - Fundamentals of Mathematics

Question

Add and subtract as in dicated. Subtract 4,355 from the sum of 74 and 7,319 .

Step-by-Step Solution

Answer

The result is 3,038.

Step 1: Identify the Problem Components

The problem consists of first adding two numbers, 74 and 7,319, and then subtracting 4,355 from the result.

Step 2: Perform the Addition

Add the two numbers: \[74 + 7,319 = 7,393\]

Step 3: Perform the Subtraction

Subtract 4,355 from the sum obtained in the previous step:\[7,393 - 4,355 = 3,038\]

Step 4: State the Result

The final result after performing both operations is 3,038.

Key Concepts

Addition

Addition is one of the basic arithmetic operations and is concerned with combining numbers to get a sum. It involves adding one number to another. In the given problem, we add 74 to 7,319. Let's break it down:

• When numbers are added, they are aligned from the least significant digit (usually the rightmost side) to the most significant digit (usually the leftmost side).
• This operation is straightforward: 74 + 7,319 equals 7,393.
• Each place value can be handled separately to prevent errors, particularly when carrying over is necessary.

The total or sum is what you get from this operation. In this case, the sum is 7,393.

Subtraction

Subtraction is another fundamental arithmetic operation. It represents the operation of removing objects from a collection, akin to taking away one number from another. Here, we take 4,355 away from the sum we found before:

• Start by ensuring that both numbers are aligned properly by their place values.
• Subtraction might sometimes involve 'borrowing', which occurs when the top digit is smaller than the bottom digit in any place value column.
• In our example, 7,393 - 4,355, the operation proceeds smoothly across each digit column.

The outcome of subtracting 4,355 from 7,393 is 3,038. This result tells us the difference between the larger number and the smaller one.

Problem Solving

Problem solving in math is about understanding what the problem asks and determining how to approach it systematically. Our exercise involves combining addition and subtraction to find a solution:

• First, dissect the problem to understand its components. In this case, it is the addition of two numbers, followed by a subtraction.
• Next, execute the operations in the correct order. This ensures the solution is accurate.
• Lastly, confirm your result by double-checking each step. Alternately, you can reverse the operations to verify the outcome.

Engaging in problem-solving activities like this example helps develop critical thinking and numerical fluency. It is a valuable skill both inside and outside of the classroom.