Problem 61 - Beginning and Intermediate Algebra

Question

Find each difference. $$ 7-(-3) $$

Step-by-Step Solution

Answer

10

Step 1 - Recognize the Signs

First, observe that the expression involves a subtraction of a negative number: 7 - (-3).

Step 2 - Convert the Double Negative

When you subtract a negative number, it is equivalent to adding a positive number. So, 7 - (-3) becomes 7 + 3.

Step 3 - Perform the Addition

Now, simply add the numbers: 7 + 3 = 10.

Key Concepts

double negative

When you see two negative signs together, like in 7 - (-3), this is referred to as a 'double negative.'
It might sound complicated, but it’s pretty straightforward.
In math, subtracting a negative number is the same as adding its positive counterpart.
Think of it this way: if you owe someone a debt, and your debt gets canceled, you're effectively gaining money.
So, 7 - (-3) basically changes into 7 + 3.
This rule helps avoid confusion and makes your calculations easier.

addition

Adding numbers is one of the most basic arithmetic operations.
Once you've converted 7 - (-3) into 7 + 3, you simply add the two numbers together.
This is very straightforward: start from 7 and move 3 steps forward.
For example, you can count up: 7, 8, 9, 10.
So, 7 + 3 equals 10.
Adding positive numbers increases the total, making it larger.
Practicing simple addition regularly can help you get faster and more accurate.

basic arithmetic operations

Arithmetic operations include addition, subtraction, multiplication, and division.
These are the building blocks of math.
For basic operations:

• Addition involves combining quantities: 5 + 4 = 9.


• Subtraction involves taking one quantity away from another: 8 - 2 = 6.


• Multiplication involves repeated addition: 4 x 3 means adding 4 three times, giving 12.


• Division involves splitting a number into equal parts: 12 ÷ 3 means splitting 12 into 3 equal parts, resulting in 4.

Knowing the rules and relationships between these operations is essential.
These skills are used in both simple and complex math problems.