Question

Subtract \(800-348\) A. 548 B. \(1,148\) C. 416 D. 452

Short answer

The answer is 452, which corresponds to option D.

Step-by-step solution

Set Up the Problem

Write down the numbers as a subtraction problem: \[800 - 348\] Start with the largest number on top and the number to be subtracted below it.

Align the Digits

Ensure the digits are aligned correctly by place value. So we have:\[\begin{array}{c} 800 \-348 \\hline\end{array}\]Put zero in front of the numbers if needed for clarity, especially in the hundreds place, but in this example, it isn't necessary.

Subtract Each Column

Start subtracting from the right (the units column). We cannot subtract 8 from 0, so we need to borrow from the next column. Borrow 1 from the tens place of 8 which changes it to 7, changing the '0' in the units place to '10'. Now perform the subtraction: \[10 - 8 = 2\]Write 2 below the line in the units column.

Continue to the Tens Column

Now move to the tens column. After borrowing, we have 7 in the tens place. Subtract:\[7 - 4 = 3\]Write 3 below the line in the tens column.

Subtract the Hundreds Column

Finally, subtract the digits in the hundreds column:\[8 - 3 = 5\]Write 5 below the line in the hundreds column.

Putting It All Together

Write out the solution by combining the results of all columns:\[\begin{array}{c} 800 \-348 \\hline 452 \\end{array}\]So, 800 - 348 = 452.

Key concepts

Borrowing in Subtraction

When subtracting, we sometimes encounter situations where the top number in a column is smaller than the bottom number. That's when borrowing is needed. Imagine trying to take away 8 apples, but you see there are 0 apples in the basket. What do you do? You "borrow" from the next basket of apples! In math, borrowing is just like that.

• You borrow from the next biggest column, usually the tens or hundreds.
• This process helps you create a bigger number so that you can subtract more easily.
• Borrowing doesn't change the value of your subtraction problem; it just rearranges numbers to make the math work.

In our example of subtracting 800 - 348, we couldn't subtract 8 from 0. So, we borrowed 1 from the tens place (which had 8, making it 7), turning the 0 into 10. This made subtracting possible! Borrowing may seem a bit tricky at first, but once you understand it, it becomes second nature.

Place Value

Understanding place value is essential in subtraction. Place value tells us how much each digit in a number represents, depending on its position. For instance, in the number 348:

• The 3 is in the hundreds place, meaning 300.
• The 4 is in the tens place, meaning 40.
• The 8 is in the ones place, meaning 8.

This helps you line up numbers correctly during subtraction. Keeping digits in the right columns (hundreds, tens, and ones) ensures that you subtract similar values from each other. For example: - Place hundreds under hundreds, tens under tens, and ones under ones. In our subtraction problem, place value helped us understand why borrowing was necessary. The columns showed that we couldn't subtract 8 from 0 in the ones place without borrowing from the tens, ensuring each place value was clear and managed correctly. Remember, place value is the map that guides you through subtraction.

Step-by-Step Subtraction

Now that we know how borrowing and place value work, let's dive into solving subtraction problems step-by-step. - **Step 1:** Start by writing down the problem vertically, ensuring the *larger number* is on top. This sets up your problem neatly. - **Step 2:** Look at each column, starting from the right (the ones). If the top number is smaller in any column, borrow from the next column to the left. - **Step 3:** Subtract each column, remembering to adjust for any borrowing you've done.

• For 800 - 348, subtract the ones: Adjust 0 to 10 and do 10 - 8 to get 2.
• Move to the tens: Subtract 7 - 4 to get 3.
• Finally, subtract the hundreds: 8 - 3 to get 5.

- **Step 4:** Write the result below, combining what you found in each column: the answer *452*. Following these steps makes subtraction easier and ensures accuracy. The structure brings clarity, allowing you to tackle even complex subtraction without hesitation.