Podcast
Questions and Answers
What is the result of $8 + (-3)$?
What is the result of $8 + (-3)$?
- 1
- 11
- 3
- 5 (correct)
Subtracting a positive integer from a negative integer always results in a negative integer.
Subtracting a positive integer from a negative integer always results in a negative integer.
True (A)
What is the sum of the integers -7 and 4?
What is the sum of the integers -7 and 4?
-3
When you add two negative integers, the result is a ______ integer.
When you add two negative integers, the result is a ______ integer.
Match the following operations with their outcomes:
Match the following operations with their outcomes:
Flashcards
Adding Integers
Adding Integers
Adding integers is combining numbers with the same sign or different signs. When combining numbers with the same sign, we add the numbers and keep the same sign. When combining numbers with different signs, we subtract the smaller number from the larger number and keep the sign of the larger number.
Subtracting Integers
Subtracting Integers
Subtracting integers is the same as adding the opposite. To subtract an integer, we change the subtraction sign to an addition sign and change the sign of the integer we are subtracting. For example, 5 - 3 is the same as 5 + (-3).
Number Line for Integers
Number Line for Integers
A number line can be a helpful tool for visualizing adding and subtracting integers. Positive numbers move to the right, and negative numbers move to the left.
Finding the Sum or Difference
Finding the Sum or Difference
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Practice Problems
Practice Problems
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Study Notes
Adding Integers
- Positive integers can be thought of as movements to the right on a number line.
- Negative integers can be thought of as movements to the left on a number line.
- To add integers with the same sign, add their absolute values and keep the same sign.
- Example: 3 + 5 = 8
- Example: -3 + (-5) = -8
- To add integers with different signs, find the difference between their absolute values and use the sign of the integer with the greater absolute value.
- Example: 3 + (-5) = -2
- Example: -3 + 5 = 2
Subtracting Integers
- Subtracting an integer is the same as adding its opposite.
- Example: 5 - 3 = 5 + (-3) = 2
- Example: -5 - 3 = -5 + (-3) = -8
- Example: 5 - (-3) = 5 + 3 = 8
- Example: -5 - (-3) = -5 + 3 = -2
- To subtract integers, keep the first number the same, change the operation to addition, and change the sign of the second number.
Practice Problems - Addition
- 5 + 7 = ?
- -2 + (-4) = ?
- 8 + (-3) = ?
- -6 + 9 = ?
- 12 + (-15) = ?
Practice Problems - Subtraction
- 9 - 4 = ?
- -7 - 2 = ?
- 10 - (-6) = ?
- -15 - (-8) = ?
- 3 - 17 =?
Mixed Practice
- (-2) + 8 - (-10) = ?
- 11 - (-7) + (-5) = ?
- 5 + (-7) + 14 – (+2) = ?
- 17 - (-8) - 2 + 1 = ?
Explanations to Mixed Problems
-
For the first practice problem: Change subtraction to addition by adding the opposite. (-2) + 8 + (+10). Add the positive numbers and then the negative numbers. These combine to 8+10 = 18 and -2 . Add these together 18 + (-2) = 16.
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Further explanations are omitted for brevity and clarity
Summary Table
| Operation | Rule | Example 1 | Example 2 |
|---|---|---|---|
| Addition (same sign) | Add absolute values, keep the sign. | 5 + 7 = 12 | -2 + (-4) = -6 |
| Addition (different signs) | Find difference of absolute values, use the sign of the larger. | 5 + (-7) = -2 | -2 + 8 = 6 |
| Subtraction | Change the subtraction to addition, change the sign of the second number. | 5 - 3 = 5 + (-3) = 2 | -5 - (-3) = -5 + 3 = -2 |
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