Problem 180 - Prealgebra

Question

In the following exercises, subtract and then check by adding. $$ 4,245-899 $$

Step-by-Step Solution

Answer

4,245 - 899 = 3,346. Verification by addition: 3,346 + 899 = 4,245.

Step 1: Subtract

First, subtract 899 from 4,245. Line up the numbers by the right-hand side:\[4245 \ - \ 0899 \ = \ 3346\]

Step 2: Check by Adding

Now, add the result (3,346) to 899. The sum should equal the original number (4,245):\[3346 \ + \ 0899 \ = \ 4245\]

Key Concepts

Subtraction

Subtraction is one of the basic arithmetic operations. It involves taking one number away from another. To subtract numbers correctly, line up the digits according to their place values (ones, tens, hundreds, etc.). In our example, we subtract 899 from 4,245. Start with the rightmost digit (units), moving to the left:

• If the top digit is smaller than the bottom digit, borrow 1 from the next column to the left.
• Continue this process for each column.

In our exercise, after aligning the digits, we subtract 899 from 4245 to get 3,346: ewline ewline \[4245 ewline- 0899 ewline= 3346\]

Addition

Addition is the process of bringing two numbers together to get their total. To check the correctness of a subtraction, add the subtracted value to the result. If it equals the original number, the subtraction was successful. Let's revisit our example. We add 3,346 and 899:

• Align the numbers by their right-hand side.
• Add each column of numbers, from right to left. Carry over any value more than 9 to the next left column.

Adding 3,346 to 899 should give us our original number 4,245: ewline \[3346 ewline+ 0899 ewline= 4245\]

Checking Answers

Checking your answers is vital in confirming that calculations are correct. After performing a subtraction, we can use addition to ensure our result is accurate.

• If our sum after adding equals the original number from which we subtracted, the work is correct.
• If it doesn't match, recheck each step to find where the mistake might have happened.

In our example, since adding 3,346 and 899 equals 4,245, we are confident that our subtraction was done correctly. Checking by adding helps in verifying the accuracy of our calculations.