Problem 102 - Fundamentals of Mathematics

Question

For the following problems, find the solutions. Subtract the difference between 78 and 43 from the sum of 111 and 89 .

Step-by-Step Solution

Answer

The solution is 165.

Step 1: Find the Sum

First, we need to find the sum of 111 and 89. Add these two numbers:\[111 + 89 = 200\]

Step 2: Find the Difference

Next, we need to find the difference between 78 and 43. Subtract 43 from 78:\[78 - 43 = 35\]

Step 3: Perform the Final Subtraction

Now, subtract the difference you found in Step 2 from the sum you found in Step 1:\[200 - 35 = 165\]

Key Concepts

Addition

Addition is one of the basic arithmetic operations that involves combining two or more numbers to get a total sum. It serves as the foundation for many other mathematical concepts. For instance, when learning to add, it's helpful to understand the order doesn't matter due to the associative property. This means that you can add numbers in any sequence and still get the same result.
In the exercise, we started with addition by calculating the sum of 111 and 89. Here's how you do it effectively:

• Line up the numbers vertically by their rightmost digits (units).
• Add each column starting from the right (units place): 1 + 9 = 10, write 0 carry over 1.
• Then move to the tens place: 1 + 8 + 1 (carry over) = 10; write 0 carry over 1.
• The hundreds place: 1 + 1 + 1 (carry over) = 3.

As a result, this gives us 200. Remember, when performing addition, checking your work by reversing the operation helps ensure accuracy.

Subtraction

Subtraction is the process of taking one number away from another, or finding the difference between two numbers. It's a fundamental skill, often introduced using real-life examples like taking toys from a collection or finding a shorter route.
In our exercise, the goal was to subtract 43 from 78. Here's a simple breakdown of subtraction steps:

• Write the numbers with the larger number on top, aligning them by their units.
• Start subtracting from the rightmost column, borrowing if necessary. Here, 8 - 3 = 5.
• Move to the tens place: 7 - 4 = 3. No borrowing was needed in this example.

This operation yielded a difference of 35. A critical point in subtraction is always verifying your result by adding the difference and the smaller number to see if you return to the original number.

Problem Solving

Problem solving involves using a series of arithmetic operations to reach a solution. It requires reading each problem carefully, planning the steps, solving, and then reviewing your work. This approach helps in building critical thinking.
In the provided exercise, we needed to perform multiple steps:

• Determine the goal: Subtract the difference from a sum.
• Identify operations: Addition first, followed by subtraction.
• Organize information: Calculate the sum of 111 and 89, which is 200. Then find the difference of 78 and 43, which is 35.
• Finally, perform the final subtraction: 200 - 35, resulting in 165.

This structured method can simplify complex problems, helping ensure accuracy and understanding. Always remember to double-check each step to avoid mistakes in calculations.