### Key Concepts

- Subtract positive integers
- Subtract integers with different signs
- Subtract negative integers

**1.4.1 Subtract positive integers**

Subtracting positive numbers is just a simple subtraction.

We can take away balloons (we are **subtracting positive** values)

The basket gets pulled downwards (negative)

**Example: **

Subtract 3 from 6

I.e., 6 − 3 = 3

It says, “positive 6 minus positive 3 equals positive 3.”

We could write it as (+6) − (+3) = (+3).

### Subtraction of Integers

The subtraction of integers has three possibilities. They are:

- Subtraction between two positive numbers

- Subtraction between two negative numbers
- Subtraction between a positive number and a negative number

**Example: **

Subtracting the numbers, 5 − (+ 6)

Subtraction is simply just addition.

We must take the opposite sign of the number following it.

We can rewrite the problem as

Locate the first number, which is 5, and then move it 6 units to the left.

This gives us the answer of 5 − (+6) = 5 + (– 6) = – 1**.**

**1.4.2 Subtract integers with different signs**

Adding and subtracting negative numbers:

We can add weights (we are **adding negative** values)

The basket gets pulled downwards (negative)

**Example: **

Subtract 3 from 6

I.e., 6 + (– 3) = 3

It says, “positive 6 plus negative 3 equals positive 3”

We could write it as (+6) + (– 3) = (+3).

**Example 1:**

Ian’s football team lost 2-yards on a running play. Then they received a 5-yards penalty. What is the team’s total change in yards?

The subtraction expression to represent the change in yards

– 2 – 5

Re-writing into equivalent addition expression

= (– 2) + (– 5)

Now, add the expression

|−2|−2

= 2 and

|−5|−5= 5

2 + 5 = 7

(– 2) + (– 5) = – 2 – 5 = – 7

The team’s total change in yards is represented by – 7, so they lost 7 yards.

**1.4.3 Subtract negative integers**

Subtracting a number is the same as adding its opposite.

- Subtracting a positive
**left**on the number line. - Subtracting a negative
**right**on the number line.

**Example 4: **

Subtract − 4 − (−7).

Start at − 4, and move 7 units to the right.

−4 − (−7) = 3.

**Example 5: **

Evaluate 9 – 10 +(– 5) + 6.

**Solution:** First open the brackets.

9 – 10 – 5 + 6

Add the positive and negative integers separately.

= 9 + 6 – 10 – 5

= 15 – 15 = 0.

**Example 6: **

Find – 7 – (– 8).

**Solution:**

Write – 7 – (– 8) as an equivalent addition expression. Then add,

– 7 + 8

|– 7| = 7 and | 8 | = 8

– 7 = 7, 8 = 8

8 – 7 = 1

– 7 – (– 8) = 1

## Exercise:

Use the number line to find the difference of the following:

- 0 – (–7)
- 1 – 10
- – 6 – 2
- 5 – 4
- – 8 – (–3)
- Explain how to simplify the expression – 98 – 31 using the additive inverse.
- How is subtracting integers related to adding integers?
- What is the value of the expression – 9 – (–15)
- It was 12
^{ }C when Preston got home from school. The weather report shows a storm front moving in that direction will drop the temperature by 17 C. What is the expected temperature? - Max sprints forward 10 feet and then stops and sprints back 15 feet. Use subtraction to explain where Max is relative to where he started.

### 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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