Problem 57 - Fundamentals of Mathematics

Question

Add and subtract as in dicated. Subtract 20,663 from the difference of 523,150 and \(95,225 .\)

Step-by-Step Solution

Answer

The result is 407,262.

Step 1: Calculate the Difference

First, find the difference between 523,150 and 95,225. To do this, subtract 95,225 from 523,150. Calculate: \[ 523,150 - 95,225 = 427,925 \] Therefore, the difference is 427,925.

Step 2: Subtract 20,663

Now, subtract 20,663 from the result obtained in Step 1. Calculate: \[ 427,925 - 20,663 = 407,262 \] Thus, the final result of the subtraction is 407,262.

Key Concepts

Arithmetic

Arithmetic is one of the fundamental building blocks of mathematics that deals with numbers and operations. In this exercise, we focus on subtraction, which is taking one number away from another. To subtract, we align numbers by their place values - ones, tens, hundreds, etc. This helps in managing the calculation efficiently.
Subtraction has a straightforward method:

• Start from the rightmost digit.
• Subtract each value, borrowing if necessary from higher digits.
• Continue across all digits to the left.

When subtracting large numbers such as 523,150 and 95,225, it's essential to maintain the alignment to ensure accuracy.

Problem Solving

Problem solving in mathematics involves breaking down exercises into smaller, manageable steps. This allows us to tackle complex problems systematically. In our original problem, it was essential to first address the operation inside the phrase "the difference of 523,150 and 95,225" before moving on to subtract 20,663.
Key steps in problem solving include:

• Understanding the problem statement and requirements.
• Identifying knowns and unknowns, and listing operations in order.
• Establishing a step-wise plan to solve the problem, ensuring each step logically follows the last one.

This methodical approach helps in avoiding errors and reaching solutions efficiently.

Mathematics Education

Mathematics education emphasizes not just finding answers, but understanding processes and concepts. When teaching subtraction, it is crucial to instill a strong grasp of the operation’s principles, such as borrowing and place value alignment.
Incorporating examples like the exercise on subtracting large numbers enhances students' practical skills and aids retention. Engaging students in activities that require such calculations boosts their confidence and ability to tackle real-world math problems. Effective education in mathematics promotes critical thinking and encourages learners to explore various problem-solving strategies, thus equipping them with essential tools for future challenges.