Problem 169 - Prealgebra

Question

In the following exercises, subtract and then check by adding. $$ 5,946-4,625 $$

Step-by-Step Solution

Answer

The result is 1,321. Verification: 1,321 + 4,625 = 5,946.

Step 1: Subtract the Units Place

Start from the rightmost digit (units place). Subtract the units place digit of 4,625 from the units place digit of 5,946. Here, it's 6 - 5 = 1. Write 1 in the units place of the result.

Step 2: Subtract the Tens Place

Move one place to the left, to the tens place. Subtract the tens place digit of 4,625 from the tens place digit of 5,946. Here, it's 4 - 2 = 2. Write 2 in the tens place of the result.

Step 3: Subtract the Hundreds Place

Next, subtract the hundreds place digit of 4,625 from the hundreds place digit of 5,946. Here, it's 9 - 6 = 3. Write 3 in the hundreds place of the result.

Step 4: Subtract the Thousands Place

Finally, subtract the thousands place digit of 4,625 from the thousands place digit of 5,946. Here, it's 5 - 4 = 1. Write 1 in the thousands place of the result. The complete result is 1,321.

Step 5: Check by Adding

To check the subtraction, add the result 1,321 to 4,625 and verify if the sum is equal to 5,946. Starting from the right: 1 + 5 = 6, 2 + 2 = 4, 3 + 6 = 9, 1 + 4 = 5. Therefore, the addition gives 5,946, verifying that our subtraction was correct.

Key Concepts

subtraction verification

Subtraction verification involves checking the accuracy of your subtraction by performing the reverse operation—addition. This ensures that no mistakes were made.

For example, after subtracting 4,625 from 5,946 and getting 1,321, we can add 1,321 back to 4,625. If our result is correct, the total should be 5,946.

Verifying subtraction like this is simple:

• Add the subtraction result to the smaller number (minuend).
• Make sure this addition matches the original larger number (subtrahend).

If the addition matches, your subtraction is correct.

place value subtraction

Place value subtraction means solving subtraction problems from the rightmost digit (units place) to the leftmost digit (largest place value). This helps in maintaining accuracy.

When subtracting 5,946 - 4,625, we subtract as follows:

• Units place: 6 - 5 = 1
• Tens place: 4 - 2 = 2
• Hundreds place: 9 - 6 = 3
• Thousands place: 5 - 4 = 1

This strategy ensures each digit falls in the correct place, leading to an accurate result.

basic arithmetic operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These form the foundation of math.

Subtraction specifically involves taking one number away from another. For accurate subtraction:

• Always start from the right.
• Subtract each digit pair step-by-step.
• Check your result, if needed.

Practicing subtraction along with verification solidifies understanding and prevents errors.