### Key Concepts

- Add two negative integers
- Add integers with different signs
- Identify additive inverse and opposite integers

## 1.3.1 Add Two Negative Integers

**Definition:**

#### Integers:

A set of positive and negative numbers are called integers.

#### Positive integer:

Positive numbers are the whole numbers that are to the left of zero on a number line.

#### Negative integer:

Negative numbers are the whole numbers that are to the right of zero on a number line.

#### Absolute value:

The absolute value of a number is defined as the distance from zero along a number line. The absolute values are always positive.

**How to add two integers?**

### Algebra tile method

Let yellow tiles represent positive numbers, and red tiles represent negative numbers.

**Example 1:**

Add: 5 + (−2)

The addition problem 5 + (−2) can be represented as

Group the two negative tiles with two positive tiles.

Since 2 + (−2) = 0, these tiles disappear. We are left with 3 positive tiles.

So, 5 + (−2) = 3.

### Number line method

When you **add a positive **number, you move to the **right **on the number line.

When you **add a negative **number, you move to the **left **on the number line.

**Example 2:**

Add 6+(−8) using a number line.

Start at 6, and move 8 units to the left.

6 + (−8) = −2.

**The rules:**

It can all be put into **two rules**:

**Adding two negative numbers:**

### Number line method:

**Example 3:**

Use number line to add: (–3) + (–2).

+ (−) are **unlike** signs. So, the result will be a **negative sign**.

−3+(−2) = −3 **–** 2

Start at −3 on the number line, move back 2, and you end up at −5.

(−3) + (−2) = −3 **−** 2 = −5

### Absolute method:

Add the integers (–3) + (–2).

We moved 2 units and then 3 units in the same direction on the number line and added the absolute values to find the sum.

Because we have moved to the left twice, the sum is negative.

**1.3.2 Add Integers with Different Signs**

**Example 4:**

Add: 6+(−8) using a number line.

Start at 6 and move 8 units to the left.

6 + (−8) = −2

**1.3.3 Identify Additive Inverse and Opposite Integers**

#### What is an additive inverse?

An **additive inverse** of a number is defined as the value, which on adding with the original number, results in zero value.

For instance, if **a** is the original number, then its additive inverse will be minus of **a,** i.e., −a, such that;

a+(−a) = a – a = 0

**Example 5:**

Mike got a + 2 on the first hole and 2 on the second hole while playing golf. What is his combined score for the first two holes?

Mike’s combined score for the first two holes is 0.

## Exercise:

- What is the rule for adding integers?
- If I added this set of integers, what would be my steps?: 18+( 3)+4
- The temperature in Canada yesterday was -30 degrees. By this morning, it rose 10 degrees. What is the new temperature in Canada?
- Joey bought an Xbox 360 for 200 dollars. He took it home and plugged it in to play it, and it did not work. He took it back to the store, and the manager refunded him 200 dollars. What is the correct expression and answer for this problem?
- James borrowed 15 dollars from his sister. He babysat for 2 hours and gave her the 8 dollars he earned. How much does he still owe her?
- What is the definition of opposites?
- What is an additive inverse?
- What is the definition of absolute value?
- A shark was swimming at 300 feet below sea level. It swam up to the surface 300 feet. How many feet above sea level is the shark now?
- Use the number line to solve ( 36) + (+12).

### What we have learned:

- Subtract positive rational numbers for which the difference is positive or zero
- Add rational numbers in any form
- Understand that subtracting an integer is the same as adding its opposite, p – q = p + ( q)
- Understand the distance between two integers on the number line as the absolute value of their difference
- Model adding and subtracting integers using integer chips and horizontal and vertical number lines

### Concept Map:

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