Problem 73 - Fundamentals of Mathematics

Question

How much bigger is 3,006 than \(1,918 ?\)

Step-by-Step Solution

Answer

3,006 is 1,088 larger than 1,918.

Step 1: Understand the problem

The question asks how much larger or bigger 3,006 is compared to 1,918. This is a subtraction problem where we need to find the difference between the two numbers.

Step 2: Set Up the Subtraction

We will set up the problem as a subtraction problem: \[ 3,006 - 1,918 \] This will help us find the difference between 3,006 and 1,918.

Step 3: Perform the Subtraction

Perform the subtraction by aligning the numbers by the right and subtract each column starting from the units column: \[ \begin{array}{c} 3,006 \ - 1,918 \ \hline \end{array} \] Starting from the right, we need to borrow as needed because 6 is less than 8. However, let's break it down: 1. Units: 6 - 8 (take 1 from the tens) = 16 - 8 = 8 (after borrowing). 2. Tens: 0 - 1 (because we borrowed) = 9.3. Hundreds: 0 - 9 (borrow from the thousands) = 10 - 9 = 1.4. Thousands: 3 - 2 (after borrowing) = 1. The final result is 1,088.

Step 4: Verify the Answer

Double check the subtraction by adding the result (1,088) to the smaller number (1,918): \[ 1,088 + 1,918 \] This should equal the larger number, 3,006. Calculating it confirms that 3,006 is indeed the sum, verifying our answer is correct.

Key Concepts

Borrowing in Subtraction

When subtracting numbers, sometimes the digit in one column is smaller than the digit below it. This is when borrowing comes into play, which is a crucial skill to master in subtraction.
When you look at the numbers starting from the right, if the top digit is smaller than the bottom digit, you need to "borrow" from the next column to the left.
This is how you carry out borrowing:

• Units column: with 6 - 8, you borrow 1 from the tens. So, 6 becomes 16, and 16 - 8 gives you 8.
• Tens column: After borrowing, you have 0 left in tens. So 0 - 1 can be changed to 10 - 1, (borrowing from hundreds) giving you 9.
• Hundreds column: You notice a 0. You need another borrow from the thousands, changing the hundreds to 10. Thus, 10 - 9 is 1.
• Thousands column: After borrowing, subtract 2 from 3, which results in 1.

This borrowing process ensures each digit gets subtracted correctly, turning daunting problems into simpler tasks.

Checking Subtraction with Addition

A great way to verify your subtraction is to use addition. It's like a math detective checking their work! After getting the subtraction result, add it back up with the smaller number. If you end with the larger number, your initial subtraction was spot-on!
In this example, the subtraction resulted in 1,088. To verify:

• Add 1,088 to 1,918.
• Calculate: 1,088 + 1,918 = 3,006.

If your addition result gives you the larger original number (3,006), your subtraction is confirmed. This method serves as a reliability check, reinforcing your confidence in final answers.

Subtraction Problem Setup

Setting up a subtraction problem correctly can save both time and effort. It's important to align your numbers properly by their digits, ensuring each value sits in the right column: units, tens, hundreds, and thousands.

• Think of it as writing numbers one beneath the other, in columns, for a clean start.
• For our example: neatly layout 3,006 on top and 1,918 beneath it.
• Remember to line up numbers so units are under units, tens under tens, etc.

This proper setup prevents mistakes, helping you visualize easier borrowing and faster calculations. A tidy arrangement paves the way for smoother subtraction operations.