Mastering Negative Numbers Basic Operations

Think of negative numbers as taking steps backward. Just like temperature can drop below zero, negative numbers fall to the left of zero on the number line.

 

Understanding Negative Numbers

Imagine a number line with zero in the middle. Numbers to the right of zero are positive (like $+ 1, +2$  ), and numbers to the left of zero are negative (like $-1, -2$ ).

Example: If you’re at zero and take 3 steps left, you’re at $-3$.

 

Adding and Subtracting Negative Numbers

Adding and subtracting with negatives is a bit like moving along the number line. Here’s how it works:

• Adding a Negative: Move to the left.
• Subtracting a Negative: Move to the right (yes, it’s like adding!).

 

Example 1: Adding a Negative Number

Let's try $5 + (-3)$ 

1. Start at $5$
2. Move 3 steps to the left because we're adding a negative. 
3. Answer:  $5 + (-3) = 2$

Example 2: Subtracting a Negative Number

Now, let’s look at $5 - (-3)$ .

1. Start at 5
2. Subtracting a negative is like adding, so move 3 steps to the right.
3. Answer: $5 - (-3) = 8$

 

Quick Tip: Subtracting a negative is the same as adding a positive!

 

Multiplying Negative Numbers

Multiplying negatives is like flipping a switch.

• Positive × Positive = Positive
• Negative × Negative = Positive
• Positive × Negative (or Negative × Positive) = Negative

 

Example: Multiplying Negative Numbers

Multiply $-4 \times 3$

1. A negative times a positive gives a negative.
2. $4 \times 3 = 12$
3. Answer: $-4 \times 3 = -12$

 

 

 

Dividing Negative Numbers

Dividing negatives follows the same pattern as multiplication.

• Positive ÷ Positive = Positive
• Negative ÷ Negative = Positive
• Positive ÷ Negative (or Negative ÷ Positive) = Negative

 

Example: Dividing Negative Numbers

Divide $-12 \div 3$

1. A negative divided by a positive gives a negative.
2. $12 \div 3 = 4$
3. Answer: $-12 \div 3 = -4$