Problem 52 - Fundamentals of Mathematics

Question

Add and subtract as in dicated. Subtract 387 from 6,342 .

Step-by-Step Solution

Answer

6,342 minus 387 equals 5,955.

Step 1: Understand the Problem

The problem requires us to subtract 387 from 6,342. This means we need to find the difference when 387 is taken away from 6,342.

Step 2: Setup the Subtraction

Write the numbers in a column format with 6,342 on top and 387 right below it, aligning the digits according to their place value (units, tens, hundreds, thousands):\[\begin{array}{c} 6,342 \- \,387 \\hline \\end{array}\]

Step 3: Subtract the Units Place

Start subtracting from the rightmost digit. Subtract the units: 2 (from 6,342) minus 7 (from 387). Since 2 is smaller than 7, borrow 1 from the tens place, making it 12. Then, 12 minus 7 equals 5.

Step 4: Subtract the Tens Place

After borrowing, the tens place becomes 3 (after reducing it by 1). Now, subtract the tens place: 3 minus 8. Again, 3 is smaller than 8, so borrow 1 from the hundreds place, making it 13. Then, 13 minus 8 equals 5.

Step 5: Subtract the Hundreds Place

After borrowing, the hundreds place becomes 2. Subtract the hundreds: 2 minus 3. Since 2 is smaller than 3, borrow 1 from the thousands place, making it 12. Then, 12 minus 3 equals 9.

Step 6: Subtract the Thousands Place

Now, subtract the thousands place: 5 (after borrowing) minus 0 (since there is no thousands digit in 387). 5 minus 0 equals 5.

Step 7: Record the Final Answer

Combine all the results from each place value to get the final answer. The difference is 5,955. So, 6,342 minus 387 equals 5,955.

Key Concepts

Place Value

Understanding place value is fundamental when dealing with subtraction problems, especially with larger numbers. Every digit in a number has a specific place value that tells us how much that digit is worth in relation to the whole number. For instance, in the number 6,342, each digit is positioned as follows:

• The digit '2' is in the units place, meaning it represents 2 ones.
• '4' is in the tens place, standing for 40.
• '3' is in the hundreds place, equating to 300.
• '6' is in the thousands place, representing 6,000.

Recognizing these positions helps us accurately line up numbers during subtraction. This ensures that numbers are subtracted from the correct place, which is crucial for obtaining the correct result.

Borrowing in Subtraction

Borrowing is a critical technique used when the digit we need to subtract is larger than the digit above it. Let's illustrate this concept:
Suppose you need to subtract 7 from 2 in the units place of 6,342. Since 2 is smaller than 7, it's impossible to subtract directly. Here's how borrowing helps:

• Borrow 1 from the adjacent left column, the tens place in this situation.
• This borrowing reduces the tens digit by one but increases the current column by ten.
• In our example, borrowing one from '4' in the tens place turns '2' into '12'. The '4' becomes '3.'
• Now, we can subtract 7 from 12, which gives us 5.

Importantly, borrowing is a sequential action, only affecting the digits immediately involved. Always remember to follow the correct borrowing process to ensure accuracy.

Column Subtraction

Column subtraction is a systematic approach to solving subtraction problems. It involves writing numbers in a vertical column, ensuring that each digit aligns correctly according to its place value. Here’s why this method is beneficial:

• It simplifies the subtraction process by dealing with one digit-pair at a time, starting from the rightmost digit.
• Helps in managing multiple borrows by clearly showing the change in digits.
• Allows for error checking down each column as you proceed.

For example, while subtracting 387 from 6,342, you write the numbers as: \[\begin{array}{c}6,342 \\- \,387 \\hline\end{array}\] Start with the units, progress to the tens, hundreds, and finally thousands, adjusting for any borrowing en route. This structured method is particularly helpful in ensuring accuracy while dealing with large numbers.