Problem 510 - Prealgebra

Question

Subtract and then check by adding. $$12-7$$

Step-by-Step Solution

Answer

The result of 12 - 7 is 5. Checking by adding: 5 + 7 = 12.

Step 1 - Subtract the Numbers

Calculate the result of subtracting 7 from 12. \[ 12 - 7 = 5 \]

Step 2 - Check the Result by Adding

Add the result from Step 1 (5) to the smaller number of the original subtraction (7) to ensure it equals the larger number (12). \[ 5 + 7 = 12 \]

Key Concepts

Subtracting Numbers

Subtraction is one of the fundamental operations in basic arithmetic. It's used to find the difference between two numbers. In the provided exercise, we needed to subtract 7 from 12. Here’s how we did it:

• We started with 12, which is our larger number.
• We subtracted 7 from 12. First, we can visualize this by removing 7 units from a group of 12 units.
• After removing 7 units from 12, we're left with 5 units.

This operation can be represented as: \( 12 - 7 = 5 \). Subtracting numbers is essentially about taking away a part from a whole and finding out what remains. Practicing this with different numbers helps you get better at subtracting quickly and correctly.

Addition to Check Subtraction

Checking your subtraction with addition is a helpful technique. It assures that your subtraction was correct. In the provided exercise, after subtracting 7 from 12 to get 5, we checked our work:

• Add the difference (5) to the smaller number (7) from the original subtraction.
• Check if the sum equals the larger number (12).

So, in our example, we added 5 + 7 and got 12, confirming our subtraction was indeed correct. This double-check makes sure that no mistakes were made:
\[ 5 + 7 = 12 \] This method can be always used to verify your subtraction results quickly. If the sum does not match the original larger number, you should recheck your subtraction for errors.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. In this exercise, we focused on subtraction and how to verify it with addition:

• Subtraction helps us find the difference between numbers.
• Addition allows us to combine numbers or check our subtraction.

These operations are essential foundational skills in math, used everywhere from simple problem solving to more complex mathematical calculations. Knowing how to perform and verify these operations accurately is crucial for building confidence and proficiency in math. Regular practice and applying these operations to real-life scenarios can improve your understanding and speed.