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. --3 = 3.
  • The additive inverse is when a number and its opposite are added resulting in "0". E.g. -2 + +2 = 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: +2 + +7 

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

+2 + +7 = 9

 

Example 4: Add: -7 + +5 

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

 -7 + +5 = -2

 

Example 5: Subtract: -3 - -5

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

-3 - -5

= -3 + +5

= 2

 

Example 6: Subtract: -7 - +8

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

-7 - +8

= -7 +  -8

= -15

 

Example 7: Compare: -3  ? -10

Solution: -3 > -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. --3 = 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.