Problem 206 - Prealgebra

Question

In the following exercises, simplify. $$ 2,020-1,984 $$

Step-by-Step Solution

Answer

2,020 - 1,984 = 36.

Step 1: Write down the numbers

Identify the numbers that need to be subtracted. Here, the numbers are 2,020 and 1,984.

Step 2: Subtract the numbers

Perform the subtraction: 2,020 - 1,984. Subtract digit by digit, starting from the rightmost digit (unit place) and moving to the left.

Step 3: Perform digit-by-digit subtraction

Start from the unit place: 0 - 4 can't be done, borrow from the tens place. 2 becomes 1, and 0 becomes 10, then 10 - 4 = 6. Move to the tens place now: 1 - 8 can't be done, borrow from the hundreds place. 0 becomes 9, and 1 becomes 11, then 11 - 8 = 3. Move to the hundreds place now: 9 - 9 = 0. Finally, move to the thousands place: 2 - 1 = 1.

Step 4: Write the final answer

After performing the digit-by-digit subtraction: 2,020 - 1,984 = 36.

Key Concepts

Digit-by-Digit Subtraction

When performing subtraction, we work from right to left, digit by digit. This means we start with the units place, then move to the tens place, and so on. By breaking down the subtraction problem into smaller steps, we can handle even complex problems with ease. For instance, if we have \(2,020 - 1,984\), we start by subtracting the rightmost digits (0 - 4). If the top digit is smaller than the bottom digit, we may need to borrow, but more on that in the next section.

Borrowing in Subtraction

Borrowing is essential in subtraction when the top digit is smaller than the bottom digit. For example, in our problem \(2,020 - 1,984\), we start at the unit place: \(0 - 4\). Since 0 is smaller than 4, we can't subtract directly. We borrow from the tens place next door. The 2 in the tens place becomes 1, and the 0 in the units place becomes 10. Now, we perform \(10 - 4 = 6\).
This process continues for each digit. If we move to the tens place and realize that \(1 - 8\) can't be done, we borrow from the hundreds place. Here, the 2 in the thousands place helps out by decreasing to 1, and our tens place calculation becomes \(11 - 8 = 3\).

Place Value

Understanding place value is crucial when performing subtraction. Each digit in a number has a specific value depending on its position. For instance, in the number 2,020:

• The digit 2 in the thousands place represents 2,000.
• The digit 0 in the hundreds place represents 0.
• The digit 2 in the tens place represents 20.
• The digit 0 in the units place represents 0.

Recognizing these values helps us know where and how to borrow correctly. For example, when borrowing across places, the value of each digit changes appropriately. If we borrow for the tens place, it impacts our calculation through the place values, helping us solve our subtraction problems efficiently and accurately.