Podcast
Questions and Answers
What is the result of $8 + (-3)$?
What is the result of $8 + (-3)$?
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
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.
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Match the following operations with their outcomes:
Match the following operations with their outcomes:
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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
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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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Description
This quiz covers the concepts of adding and subtracting integers, including rules for handling positive and negative numbers. You'll practice both addition and subtraction with various integers to reinforce your understanding. Test your skills with practical problems and examples provided.
