Problem 19 - Fundamentals of Mathematics

Question

Subtract 712 from the sum of 507 and 387 .

Step-by-Step Solution

Answer

The result is 182.

Step 1: Calculate the Sum

First, find the sum of the numbers 507 and 387. Add these two numbers together: \[ 507 + 387 = 894 \].

Step 2: Subtract from the Sum

Next, subtract 712 from the sum calculated in Step 1. Perform the subtraction: \[ 894 - 712 = 182 \].

Key Concepts

Addition

Addition is an essential arithmetic operation and is often the first one learned by students. It's about combining numbers to find the total or sum. For example, when you add 507 and 387, you combine these two quantities to get a new total. The process follows a straightforward rule:

• Start by adding the digits in the rightmost column and move left, carrying over any extra to the next column if the sum exceeds 9.
• In our example, adding the hundreds column first (5 + 3) gives 8, the tens column (0 + 8) gives 8, and the units column (7 + 7) gives 14, which means you carry over 1 to the tens column. So, you end up with 8 in hundreds, 9 in tens, and 4 in units, totaling 894.

This step of combining values may seem basic, but it lays the foundation for more complex operations.

Subtraction

Subtraction is another core arithmetic operation, and it involves removing a number from another to find the difference. In this exercise, you subtract 712 from 894, the sum we found earlier. Subtraction can be conceptualized as "taking away" or "finding out how much more you have" if you spend or use some of your resources.

• Align the numbers by their place values before you begin the operation.
• Starting from the rightmost digits, subtract each pair of digits. If you need to subtract a larger digit from a smaller one, you "borrow" 10 from the next column to the left.

In our example, you begin with the rightmost digit: 4 minus 2 is 2. In the tens column, 9 minus 1 is 8, and in the hundreds column, 8 minus 7 is 1. This gives the final difference of 182. Remember, accurate alignment and borrowing are key to proper subtraction results.

Problem Solving

Problem-solving in mathematics involves a series of steps to find an answer to an arithmetic problem. It starts with understanding the task and deciding on the correct operations to use. Let's break it down:

• Comprehend the Problem: Understand what is being asked. Here, the goal is to find the difference after summing two numbers and subtracting a third from that sum.
• Plan the Approach: Determine the steps you need, such as performing addition first and subtraction second. Confirm all operations are set to solve the question given.
• Carry Out the Plan: Execute each calculation carefully, ensuring you handle basic arithmetic operations accurately.
• Review and Check: Finally, after finding an answer, it’s important to review each step to check for errors and validate your solution.

This logical approach to problem-solving not only helps in math exercises but is a useful life skill in many decision-making processes.