Problem 1 - Prealgebra

Question

Subtract. $$7-5$$

Step-by-Step Solution

Answer

The result of the subtraction is 2.

Step 1: Understand the Problem

We need to subtract the number 5 from the number 7.

Step 2: Perform Subtraction

Start with the number 7 and count backwards by 5 steps. This can be visualized as hops down from 7 on a number line: 7, 6, 5, 4, 3, 2. Hence, when 5 is subtracted from 7, we reach the number 2.

Step 3: Verify the Result

Check that the subtraction was done correctly by adding the result back to the subtracted number. Add 2 (our result) and 5, and check if the sum equals the original number: 2 + 5 = 7. This confirms our subtraction is correct.

Key Concepts

Understanding the Number Line

The number line is a visual tool that helps us perform and understand subtraction. Imagine a horizontal line with numbers placed at equal intervals. Zero is at the center, and to the right, numbers increase. To the left, they decrease.
To subtract using a number line, start at the initial number (in this exercise, 7). You then "hop" to the left by the amount you want to subtract. Each hop represents moving one number down the line.

• Begin at 7 and move 5 hops to the left.
• Each hop lands you on the next lower number.
• The sequence is: 7, 6, 5, 4, 3, and finally 2.

When you reach the last number, you have completed the subtraction, with 2 being your result. This visual approach can make abstract ideas more concrete.

Grasping Basic Arithmetic

Basic arithmetic involves simple calculations that most mathematical learning is built on, such as addition, subtraction, multiplication, and division. Here, we focus on subtraction.
The operation of subtraction involves finding the difference between two numbers. It can be understood as taking away a certain amount from a starting number. So, when we subtract 5 from 7:

• Start with the larger number (7).
• Count backwards, reducing by 1 incrementally until you've counted down by 5.

This method gives us confidence in the result, as it is consistent with how subtraction is foundationally designed and aids in future complex arithmetic skills.

Checking Subtraction Results

After performing a subtraction, it’s always good practice to check your work. The simplest way is by doing the reverse operation—addition.
To verify your subtraction:

• Add the result of your subtraction to the number you subtracted (2 + 5).
• If the total equals the original number (in this case, 7), your subtraction is correct.

This method ensures accuracy, and as you practice, you'll get quicker at both performing and checking arithmetic results. Verification not only helps maintain accuracy but also builds confidence in mathematical abilities.