Problem 8 - Fundamentals of Mathematics

Question

Find the difference between 88,526 and 26,412 .

Step-by-Step Solution

Answer

The difference is 62,114.

Step 1: Identify the Operation

The exercise asks for the difference between the numbers 88,526 and 26,412. The term 'difference' indicates that we need to perform a subtraction.

Step 2: Write the Subtraction Equation

Set up the subtraction equation based on the numbers given. Write: \[ 88,526 - 26,412 \]

Step 3: Subtract the Units

Start by subtracting the digits in the rightmost column (units). Here, subtract 2 from 6. This equals 4.

Step 4: Subtract the Tens

Move one column to the left and subtract the tens digits. Subtract 1 from 2. This equals 1.

Step 5: Subtract the Hundreds

Subtract the hundreds digits. Subtract 4 from 5. This equals 1.

Step 6: Subtract the Thousands

Move to the thousands column and subtract the thousands digits. Subtract 6 from 8. This equals 2.

Step 7: Subtract the Ten-thousands

Subtract the ten-thousands digits next. Subtract 2 from 8. This equals 6.

Step 8: Write the Final Result

After performing the subtraction in each column from right to left, the resulting number from this subtraction is \[ 62,114 \].

Key Concepts

Understanding the Concept of Difference

Subtraction is a fundamental arithmetic operation that helps us find the 'difference' between two numbers. In mathematical terms, the difference is the result obtained after subtracting one number from another. When you see the word 'difference' in a math problem, it is a cue that subtraction is required.
Understanding the role of difference is crucial because it helps quantify how much larger one number is compared to another. This concept is not only limited to whole numbers but also applicable in various fields including finance, where it can indicate profit or loss, or in measurement, where it can show variation between values. Always remember, when dealing with difference, position matters; subtract the smaller number from the larger number to get a positive result.

Exploring Arithmetic Operations in Subtraction

Arithmetic operations are the basic building blocks of mathematics, including addition, subtraction, multiplication, and division. Subtraction is the process of taking away one quantity from another.
The basic components of subtraction are:

• Minuend: The number from which another number is subtracted. In our example, 88,526 is the minuend.
• Subtrahend: The number that is subtracted from the minuend. Here, 26,412 is the subtrahend.
• Difference: The result of subtracting the subtrahend from the minuend. In this exercise, the difference is 62,114.

Arithmetic operations require careful alignment of numbers, particularly when dealing with subtraction, to ensure each digit is placed correctly in its respective column, like ones, tens, hundreds, etc. Mistakes often arise from misalignment, so it's essential to double-check your placement and borrowing, if necessary, while performing subtraction.

Step by Step Solution for Subtraction

When tackling math exercises, a step-by-step approach simplifies subtraction tasks and avoids errors. Let's revisit the solution by breaking it down into digestible actions:

Step 1: Set Up the Problem

Identify the minuend and the subtrahend. Write them in subtraction form: 88,526 - 26,412

Step 2: Start with the Rightmost Column

Begin by subtracting the units: 6 - 2 = 4

Step 3: Move to the Tens Column

Then proceed to subtract the tens: 2 - 1 = 1

Step 4: Proceed to the Hundreds

Subtract the hundreds: 5 - 4 = 1

Step 5: Shift to Thousands

Continue with the thousands: 8 - 6 = 2

Step 6: Finish with Ten-thousands

Finally subtract ten-thousands: 8 - 2 = 6
By breaking down subtraction into such clearly defined steps, it becomes a manageable process. The outcome is a reliable and clear computation, resulting in the difference: 62,114. This methodical approach ensures accuracy and confidence when solving subtraction problems.