Problem 18 - Fundamentals of Mathematics

Question

Perform each subtraction. $$ \begin{array}{r} 906 \\ -\quad 18 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

888

Step 1: Subtract the Ones Place

Start by subtracting the digits in the ones place. Here, we have 6 (from 906) and 8 (from 18). Since 6 is less than 8, we need to borrow 1 from the tens place. This turns the 0 in the tens place into a 9 and the ones place into 16. Subtract 8 from 16 to get 8.

Step 2: Subtract the Tens Place

Next, subtract the digits in the new tens place. After borrowing, we have 9 in the tens place (from 906) minus 1 (from 18). 9 minus 1 equals 8.

Step 3: Subtract the Hundreds Place

There is nothing to subtract in the hundreds place except the remaining 9 from 906, as there is no hundreds digit in 18.

Step 4: Final Result

Combine the results from all place values to form the final result: 888.

Key Concepts

Borrowing in Subtraction

When dealing with subtraction, you might encounter a situation where the top digit is smaller than the bottom digit. In such cases, we use a technique called "borrowing." This allows you to subtract more substantial numbers from smaller numbers.
Here's how borrowing works:

• Identify the place value where the top digit is smaller than the bottom digit. For example, in subtracting 8 from 6, 6 is less than 8.
• Borrow from the next left place value. You take "1" from the next higher place value, which typically stands for "10" in the decimal system.
• After borrowing, the digit becomes capable of handling the subtraction. In our example, the 6 becomes 16, allowing you to subtract 8 from 16, leaving you with 8.

Borrowing helps manage subtraction when a direct subtraction of digits isn't possible, making it an invaluable tool in basic arithmetic operations.

Place Value Subtraction

Understanding place value is crucial when performing subtraction. Each digit in a number represents a different place value, such as ones, tens, hundreds, and so on.
When performing subtraction, it's essential to subtract each corresponding place value properly:

• Start with the rightmost digits (ones place) and move left.
• If borrowing is necessary, as described in the previous section, be mindful to adjust each subsequent place value accordingly.

For example, when subtracting 18 from 906:

• Subtracting the ones place: 6 becomes 16 after borrowing, allowing subtraction from 8, resulting in 8.
• Subtracting the tens place: 0 turns to 9 after borrowing, then subtract 1, leaving you with 8.
• The hundreds place only involves the top digit since there is nothing to subtract against it, so it's simply carried down.

Keeping this structure in mind ensures that subtraction is done accurately and systematically.

Arithmetic Operations

Subtraction is one of the four basic arithmetic operations, which also include addition, multiplication, and division. Mastery of these operations is foundational to mathematics.
Subtraction specifically involves finding the difference between numbers and is symbolized by the minus sign (-). Here's how it fits into arithmetic:

• Operates on the principle of taking away or decreasing quantities.
• Inverse of addition—where addition combines numbers, subtraction removes or reduces them.
• Requires skills like borrowing for complex problems, making it a bit more intricate than addition.

The operation is not just about computation but also about understanding relationships between numbers. For example, if given 906 minus 18:

• You start with large parts (hundreds) and ensure every smaller component (tens, ones) follows correctly through techniques like borrowing.

Grasping subtraction and other arithmetic operations enhances problem-solving skills and is essential in everyday calculations.