Problem 160 - Prealgebra

Question

In the following exercises, subtract and then check by adding. $$9-3$$

Step-by-Step Solution

Answer

The result is 6. Verification: 6 + 3 = 9.

Step 1: Understanding the Problem

Identify that this problem requires subtraction first and then verification by addition.

Step 1 - Subtract

Subtract 3 from 9. \[ 9 - 3 = 6 \]

Step 2 - Check by Adding

Add the result (6) to the number subtracted (3) to check if the original number (9) is obtained. \[ 6 + 3 = 9 \]

Key Concepts

Subtraction

Subtraction is the process of taking one number away from another. In our problem, we are asked to subtract 3 from 9. This means we take away 3 units from 9 units. The subtraction process is straightforward and will look like this: \[ 9 - 3 = 6 \] Think of it like having 9 apples and giving 3 of them away. You will be left with 6 apples. This value (6) is what remains after the subtraction.

Addition

Addition is the opposite operation of subtraction. It's the process of combining numbers to get a total. In our exercise, we use addition to verify our subtraction result. After subtracting, we need to add the result back to the number we originally subtracted to confirm if we would return to the original number. Taking our problem, the result of the subtraction was 6. We take this number and add it to the number we subtracted (3) as shown below: \[ 6 + 3 = 9 \] Here, by adding 6 and 3, we obtain 9, which is our original number. This confirms our subtraction was done correctly.

Verification Process

The verification process involves checking the correctness of our subtraction result using addition. This is an important step because it helps ensure there were no mistakes in the subtraction. In our exercise, we start with 9, subtract 3 to get 6, and then add 6 and 3 to check if we get back 9. Verification works as a safety check in mathematics, confirming that our operations are accurate. A quick tip: always perform the verification step anytime you subtract numbers. This helps solidify understanding and ensure accuracy.