Problem 62 - Fundamentals of Mathematics

Question

How much bigger is 14,061 than \(7,509 ?\)

Step-by-Step Solution

Answer

14,061 is 6,552 bigger than 7,509.

Step 1: Understand the Problem

We are asked to find out how much bigger the number 14,061 is than 7,509. In simpler terms, we need to find the difference between these two numbers by performing a subtraction.

Step 2: Setup the Subtraction

To find the difference between two numbers, we subtract the smaller number from the larger number. Here, 14,061 is the larger number and 7,509 is the smaller number, so we set up the subtraction as follows: 14,061 - 7,509.

Step 3: Perform the Subtraction

Subtract each digit starting from the rightmost digit (ones place) going to the left. If necessary, borrow from the next column to the left: - In the ones column: 1 - 9 cannot be done, so borrow 1 from the tens column (making it 11 - 9): Result is 2. - Next, in the tens column: 5 (after borrowing 1) - 0 = 5. - In the hundreds column: 0 - 5 cannot be done, so borrow 1 from the thousands column (making it 10 - 5): Result is 5. - In the thousands column: 0 (after borrowing 1 from the 14,061, making it 0 now; borrow 1 from next column if needed) - 7 + (borrowed 1 from ten thousands makes the column 10): Result becomes 6. - In the ten thousands column: 1 (remember borrowed from 14,061 to make a 0; so now it's 0) - 0 = 0. Now, numerical subtraction results in: 14,061 - 7,509 = 6,552.

Step 4: Conclusion

After performing the subtraction, we determine that 14,061 is 6,552 larger than 7,509.

Key Concepts

Borrowing in Subtraction

When performing subtraction, especially with multi-digit numbers, you might need to use a method called "borrowing." Borrowing occurs when a digit in the top number is smaller than the digit you are subtracting it from. In such cases, you "borrow" from the next higher place value to make the subtraction possible.

• For example, in the subtraction 14,061 - 7,509, you start from the rightmost digit: 1 - 9 isn't possible because 1 is smaller than 9.
• Therefore, you need to borrow from the tens column, turning the 0 into a 9, and the 1 into 11.
• After borrowing, you perform the subtraction: 11 - 9 = 2.

This method ensures each place value is subtracted correctly, maintaining accuracy in calculations. Borrowing is a fundamental technique in arithmetic to facilitate proper subtraction.

Arithmetic Operations

Arithmetic operations are the basic calculations used in mathematics, such as addition, subtraction, multiplication, and division. Subtraction is a fundamental arithmetic operation that finds the difference between two numbers. In our example, we are tasked with determining how much larger 14,061 is compared to 7,509.

• The operation performed is subtraction because we want to find the difference.
• Set up the subtraction by aligning the numbers according to their place values.
• Perform the subtraction column by column, from right to left.

Understanding these operations, like subtraction, is essential as they form the basis for more complex mathematics and everyday problem-solving tasks.

Problem-Solving Steps

Effective problem-solving involves systematic steps to reach a solution. Let's explore these steps using our subtraction example as a guide.
First, clearly understand the problem. We need to calculate how much larger 14,061 is than 7,509, which is determined by subtraction.

• Next, set up the subtraction correctly by writing the larger number above the smaller one, aligning place values precisely.
• Perform the subtraction from right to left, checking if borrowing is necessary.
• Once you subtract each digit accordingly and apply borrowing when needed, arrive at the final difference.
• In our exercise, the subtraction 14,061 - 7,509 equals 6,552, indicating how much larger the first number is.

Following these steps helps in systematically solving arithmetic problems, ensuring accuracy and clarity in your calculations.