Problem 70 - Fundamentals of Mathematics

Question

Find the difference between 56,108 and 52,911 .

Step-by-Step Solution

Answer

The difference is 3,197.

Step 1: Identify the Numbers

We need to find the difference between the numbers 56,108 and 52,911. So, these are our values for subtraction: 56,108 is the minuend and 52,911 is the subtrahend.

Step 2: Set Up the Subtraction

Arrange the numbers in a vertical format, ensuring that each corresponding digit is aligned properly:\[\begin{array}{c} 56108 \-52911 \\hline\end{array}\]

Step 3: Perform the Subtraction from Right to Left

Subtract each digit starting from the rightmost:- Units: 8 - 1 = 7- Tens: 0 - 1 (we need to borrow from the hundreds)- Hundreds: 10 (borrowed) - 1 = 9- Thousands: 5 - 2 = 3- Ten thousands: 5 - 5 = 0The subtraction becomes:\[\begin{array}{c} 56108 \-52911 \\hline 3197\end{array}\]

Step 4: Verify by Adding

To ensure the result is correct, add 52,911 to the difference we calculated (3,197): \[\begin{array}{c} 3197 \+52911 \\hline 56108\end{array}\]The sum matches the original number 56,108, confirming the subtraction is correct.

Key Concepts

Understanding the Difference

In mathematics, the term "difference" refers to the result of subtracting one number from another. It tells us how much one number varies from the other. To find the difference, you position the two numbers in a subtraction equation. For instance, when calculating the difference between 56,108 and 52,911:

• 56,108 is the larger number, known as the minuend.
• 52,911 is the smaller number, known as the subtrahend.

The difference in this problem is the number that results from subtracting 52,911 from 56,108, which equals 3,197. This number demonstrates the gap or interval between the two original numbers.

Minuend: The Starting Point

The minuend is the number from which another number, the subtrahend, is subtracted. It is the "starting point" in a subtraction problem. In our example, 56,108 acts as the minuend in the subtraction process:

• It sits at the top of our vertical subtraction setup.
• It is important for calculation as it determines what we are subtracting from.

Understanding the role of the minuend is crucial because its size relative to the subtrahend will often determine whether borrowing is necessary in subtraction.

Subtrahend: What We Subtract

The subtrahend is the number subtracted from the minuend. In other words, it's the quantity that we "take away" from the starting point. For this problem, 52,911 serves as the subtrahend:

• It is placed under the minuend in vertical subtraction.
• The primary role of the subtrahend is to define how much is being deducted from the minuend.

Knowing the subtrahend is as important as the minuend because it helps to establish the true difference between the two numbers.

Borrowing in Subtraction

Borrowing is an essential technique in subtraction, used when a digit in the minuend is smaller than the corresponding digit in the subtrahend. It involves taking (or "borrowing") from the next higher place value to make subtraction possible.

• In our example, borrowing occurs in the tens column.
• We can't subtract 1 from 0, so we borrow 10 from the hundreds place, transforming the 0 into a 10.
• This borrowing allows the subtraction to proceed smoothly and accurately.

Mastering borrowing is crucial for correctly solving subtraction problems, especially in scenarios where digits in the minuend are smaller than in the subtrahend.