Problem 181 - Prealgebra

Question

In the following exercises, subtract and then check by adding. $$ 43,650-8,982 $$

Step-by-Step Solution

Answer

43,650 - 8,982 = 34,668; Check: 34,668 + 8,982 = 43,650.

Step 1: Set Up the Subtraction

Write the numbers in a column with the larger number on top: \[ \begin{array}{r} 43650 \ - 8982 \end{array} \]

Step 2: Perform the Subtraction

Subtract the numbers starting from the rightmost digit (units) and move to the left. \[ \begin{array}{r} 43650 \ - 8982 \ \hline 34668 \end{array} \]

Step 3: Set Up the Addition for Checking

Write the difference (result from subtraction) and the smaller number in a column to add them back together: \[ \begin{array}{r} 34668 \ + 8982 \end{array} \]

Step 4: Perform the Addition

Add the numbers starting from the rightmost digit (units) and move to the left. \[ \begin{array}{r} 34668 \ + 8982 \ \hline 43650 \end{array} \]

Step 5: Verify the Result

Compare the result of the addition with the original larger number. Since both are 43,650, the subtraction was done correctly.

Key Concepts

Subtraction

Subtraction is one of the fundamental operations in arithmetic. It represents the process of taking one number away from another. Following are the key steps:

• Set up the subtraction problem with the larger number on top, and the smaller number below it.
• Start subtracting from the rightmost digit and move leftward, borrowing from the next column if necessary.
• Write the result directly below the line in the same order from right to left.

In our example, we subtract 8,982 from 43,650 with these steps and get the result 34,668.

Addition

Addition is another primary arithmetic operation. It entails combining two numbers to find their total. The following steps explain addition:

• Arrange the numbers you want to add so that their digits line up correctly by place value (units, tens, hundreds, etc.).
• Begin adding from the rightmost digit (units) and proceed leftward, carrying over to the next column if the sum of the column is greater than 9.
• Place the resulting sum directly below the line.

By adding 34,668 and 8,982, we verify the subtraction operation done previously.

Checking Subtraction with Addition

Checking subtraction with addition helps ensure your subtraction result is correct. Essentially, you reverse the subtraction process by adding the difference to the subtrahend. If the sum equals the minuend (the original larger number), then the subtraction is accurate.

• Take the result of the subtraction (difference) and the smaller number (subtrahend).
• Add them using the addition method described.
• Compare the sum to the original larger number (minuend).

Here, 34,668 was the difference. Adding it to 8,982 should give us the original 43,650. Since it does, our original subtraction is verified.

Arithmetic Operations

Arithmetic operations are the building blocks of mathematics and include addition, subtraction, multiplication, and division. Subtraction and addition are often used together for verification.

• Subtraction helps determine the difference between numbers.
• Addition helps combine numbers to see if our operations or transformations (like subtraction) are correct.

Being proficient in both allows you to check your work and understand the relationship between numerical changes and transformations. Remember, always perform and cross-check your operations to ensure accuracy!