Problem 30 - Fundamentals of Mathematics

Question

For the following problems, perform the subtractions. You may chedk each difference with a calculator. $$ \begin{array}{r} 12 \\ -\quad 9 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The result is 3.

Step 1: Set up the Problem Vertically

Align the numbers vertically for subtraction. Place the number 12 at the top and the number 9 directly below it, aligning the digits to the right.

Step 2: Start Subtracting from the Rightmost Digit

Subtract the digit in the ones place of the bottom number (9) from the digit in the ones place of the top number (2). Since 2 is less than 9, you need to borrow from the tens place.

Step 3: Borrowing from the Tens Place

Since you need to subtract a larger digit (9) from a smaller one (2), borrow 1 from the tens place of 12. This makes the ones digit 12 (instead of 2) and reduces the tens digit of 12 to 1.

Step 4: Perform the Subtraction of Ones

Subtract 9 from 12, which equals 3. Write 3 below the line in the ones place.

Step 5: Finalize and Write the Result

There is no more subtraction needed in the tens place since we have already borrowed from it. Write down the remaining 1 in the tens place.

Key Concepts

Borrowing in Subtraction

Borrowing in subtraction is a technique used when the digit you need to subtract is larger than the digit you are subtracting from. But don't worry, it's not as complicated as it sounds! Let's simplify it.

Imagine you have the problem of subtracting 9 from 12. If you try to subtract 9 from 2 (the ones place), you can't, because 2 is less than 9. This is where borrowing comes in!

• Borrow "1" from the next higher digit place (in this case, the tens place).
• This turns the 2 in the ones place into 12.
• The tens digit then becomes 1 instead of 2.

Now, with the ones digit changed from 2 to 12, you can easily subtract 9 from it. This small shift, called borrowing, allows you to solve subtraction problems across different columns in a multi-digit number.

Elementary Arithmetic

Elementary arithmetic is the backbone of all math we learn in school. It includes basic operations like addition, subtraction, multiplication, and division.

Let's focus on subtraction, which simply means taking away one number from another. It's a fundamental math operation you use in everyday life, from calculating change to adjusting recipes.

The concept of borrowing in subtraction helps when the number you are subtracting is larger than the top digit in the column. Being comfortable with this process will ease your journey into more complex math. Understanding elements like place value and borrowing is crucial.

Always remember to:

• Align numbers by place value (ones under ones, tens under tens).
• Start subtracting from the rightmost digit.

By mastering these steps, you'll perform elementary arithmetic with confidence, setting a solid foundation for future math skills.

Subtraction Step-by-Step

Step-by-step subtraction involves simple yet structured procedures to solve a problem accurately. Let’s break down the subtraction of 12 minus 9 using a step-by-step guide.

First, you need to align your numbers vertically:

• Write the number 12 on top.
• Write the number 9 below it, aligning the digits to the right.

This setup helps in clear and accurate subtraction.

Next, start with the rightmost digit, which is the ones place:

• Subtract 9 from 2. Since 2 is less than 9, you borrow 1 from the tens place.
• This makes the 2 into 12, allowing the subtraction of 9 from 12, which gives you 3.

Write down the result, 3, under the line in the ones column.

Finally, finish off by dealing with the tens place:

• After borrowing, the tens column shows 1 (instead of 2), and since there’s nothing to subtract from it, write down the remaining 1.

Hence, the final result of 12 minus 9 is 3. This step-by-step approach makes solving subtraction problems clear and straightforward.