6th Grade - Adding and Subtracting Integers

Introduction

• Integers are a set of whole numbers (0, 1, 2, 3, ....) and their opposites. For example, 1, -1,  2, -2, 3, -3, and so on.
• 0 is an integer. It is also called the origin. 0 does not carry any sign. When any integer is added to 0, the answer is the same number. e.g. $-9 + 0 = -9$
• The integer with a positive sign is greater than 0 and is to the right of 0 on the number line.
• The integer with a negative sign is less than 0 and is to the left of 0 on the number line.

• In a vertical number line, numbers above 0 are positive, and numbers below zero are negative.

 

Opposites and Additive Inverse

• Two integers are opposite if they have different signs and exactly the same distance from 0, such as $-5 and 5; 3 and -3.$
• The opposite of an opposite is a positive, for e.g. $-\left(-3\right) = 3$.
• The additive inverse is when a number and its opposite are added resulting in "0". E.g. $\left(-2\right) + \left(+2\right) = 0$.

Adding Integers

• Rule 1: When adding two integers with the same signs, add the numbers and keep the same sign.
• Rule 2: When adding two integers with different signs, subtract the numbers and keep the sign of the greater number.

Subtracting Integers

• Rule: When subtracting two integers:

First, change the subtraction sign to the addition.

Next, change the sign of the number that is being subtracted.

Last, follow the rules of the addition of integers.

• Follow the order of operations when working with more than two integers.

Solved Examples

Example 1: What is the opposite of -9?

Solution: The opposite of -9 is 9, as it has exactly the same distance from 0.

 

Example 2: What is the value of -(-24)?

Solution: The opposite of opposite is positive.

-(-24) = 24

 

Example 3: Add: $\left(+2\right) + \left(+7\right)$

Solution:  Use the rule for adding integers with the same sign.

$\left(+2\right) + \left(+7\right) = 9$

 

Example 4: Add: $\left(-7\right) + \left(+5\right)$

Solution: Use the rule for the addition of integers with different signs.

 $\left(-7\right) + \left(+5\right) = -2$

 

Example 5: Subtract: $\left(-3\right) - \left(-5\right)$

Solution: Use the rule for the subtraction of the integers.

$\left(-3\right) - \left(-5\right)$

$= \left(-3\right) + \left(+5\right)$

$= 2$

 

Example 6: Subtract: $\left(-7\right) - \left(+8\right)$

Solution: Use the rule for the subtraction of the integers.

$\left(-7\right) - \left(+8\right)$

$= \left(-7\right) + \left(-8\right)$

$= -15$

 

Example 7: Compare: $-3 \boxed{ ? }-10$

Solution: $-3 \boxed{>} -10$, as -3 is at the right of -10 on a number line.

Cheat Sheet

• A number without any sign is considered positive (except 0, as 0 is neither positive nor negative). 
• The sign indicates the direction.
  • The number with a positive sign is positioned to the right of 0.
  • The number with a negative sign is positioned to the left of 0.
  • When comparing two numbers, the number on the right compared to the other number on the number line, irrespective of its sign, is greater.
• The opposite of an opposite is a positive, for e.g. $-\left(-3\right) = 3$
• When finding the difference in the temperature, consider using a number line.

Blunder Area

• If a number is written without any sign, it should be assumed to have a positive sign. 
• Follow the Order of Operations when working with more than two integers.