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Magazine Chapter 1: Problem 92
Find the difference. $$881 ? 606$$
Short Answer
Expert verified
The difference is 275.
Step by step solution
01
Identify the Operation
The task requires finding the difference between two numbers: 881 and 606. The operation for finding the difference is subtraction.
02
Set Up the Subtraction Problem
Write the subtraction expression: subtract 606 from 881. It will look like this: \[ 881 - 606 \]
03
Perform the Subtraction
Subtract the units column first (1 from 6), borrow if necessary:\[1 - 6 \] Since 1 is less than 6, borrow 1 from the next column. The tens column becomes 7 and units column becomes 11, making it:\[ 11 - 6 = 5 \]Move to the tens column (8, after borrowing, becomes 7):\[7 - 0 = 7\] Finally, the hundreds column:\[8 - 6 = 2\]
04
Combine the Results
The results from each column: - Units: 5- Tens: 7- Hundreds: 2Combine them to get the final result:\[ 275 \]
05
Verify the Calculation
Double-check the subtraction:\[ 881 - 606 = 275 \].Ensure that each step follows the borrowing correctly, and confirm that the answer is correct.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Borrowing in Subtraction
Borrowing, also known as regrouping, plays a crucial role when performing subtraction. Especially when the number from which you are subtracting is smaller than the number being subtracted.
Here's how borrowing works:
Borrow 1 from the tens column, changing it from 8 to 7, and add 10 to the units column. Now, instead of 1, you have 11 from which 6 can be subtracted, resulting in 5. This technique ensures that each subtraction step is manageable.
Here's how borrowing works:
- When you encounter a situation where a digit in the minuend (the number from which we subtract) is smaller than the corresponding digit in the subtrahend (the number being subtracted), borrowing is necessary.
- Borrowing involves taking 1 (or 10, in the context of place value) from the next left column. This transforms the digit in question, allowing the subtraction to proceed.
Borrow 1 from the tens column, changing it from 8 to 7, and add 10 to the units column. Now, instead of 1, you have 11 from which 6 can be subtracted, resulting in 5. This technique ensures that each subtraction step is manageable.
The Importance of Place Value
Place value is the value of each digit in a number based on its position. Understanding place value is fundamental when performing subtraction and other arithmetic operations.
Here's why it matters:
Here's why it matters:
- In our number system, each position represents a different power of ten. The rightmost position is the units position, followed by tens, hundreds, and so on.
- Place value dictates how we approach borrowing and regrouping. In subtraction, when borrowing occurs, we actually regroup tens into ones, hundreds into tens, and so forth.
Subtraction as a Fundamental Arithmetic Operation
Subtraction is one of the basic arithmetic operations, alongside addition, multiplication, and division. It's used to find the difference between numbers.
Here's how it works:
Here's how it works:
- Subtraction is essentially the process of taking away a number (the subtrahend) from another number (the minuend) to discover how much is left.
- This operation requires careful alignment of numbers by their place values: units under units, tens under tens, etc. This alignment ensures correct results.
- Additionally, subtraction may involve borrowing or regrouping, an essential process when the digits in a column do not support direct subtraction.
